This page is a compilation of blog sections we have around this keyword. Each header is linked to the original blog. Each link in Italic is a link to another keyword. Since our content corner has now more than 4,500,000 articles, readers were asking for a feature that allows them to read/discover blogs that revolve around certain keywords.
The keyword holdout method has 16 sections. Narrow your search by selecting any of the keywords below:
- training set (13)
- bootstrap method (12)
- testing set (11)
- training testing sets (8)
- models performance (7)
- absolute percentage error (7)
- fold cross (6)
- validation set (6)
- root squared error (6)
- absolute error (6)
- data set (6)
- sensitivity analysis (6)
- squared error (5)
1.Techniques for Model Validation[Original Blog]
Cross-validation is a popular technique used for validating models. It involves dividing the data into two sets: a training set and a validation set. The training set is used to train the model, while the validation set is used to test the model's performance. Cross-validation helps to prevent overfitting, which occurs when the model is too complex and fits the training data too well, but does not generalize well to new data. An example of cross-validation is k-fold cross-validation, where the data is divided into k subsets, and the model is trained and tested k times, with each subset used once for testing and the remaining k-1 subsets used for training.
The holdout method involves dividing the data into a training set and a testing set. The model is trained on the training set and then tested on the testing set. The holdout method is simple and easy to implement, but it can be biased if the data is not representative of the population. An example of the holdout method is using 70% of the data for training and 30% of the data for testing.
The bootstrap method involves creating multiple samples of the data by randomly selecting observations with replacement. The model is trained on each sample, and the performance is evaluated on the original data. The bootstrap method helps to estimate the variability of the model, but it can be computationally intensive. An example of the bootstrap method is creating 1000 samples of the data, each with 70% of the observations, and training the model on each sample.
4. Leave-One-Out Cross-Validation
Leave-one-out cross-validation (LOOCV) is a special case of k-fold cross-validation, where k is equal to the number of observations in the data. LOOCV involves training the model on all but one observation and testing the model on the left-out observation. LOOCV is computationally intensive, but it provides an unbiased estimate of the model's performance. An example of LOOCV is training the model on all but one of the 1000 observations and testing the model on the left-out observation.
5. Monte Carlo Cross-Validation
Monte Carlo cross-validation (MCCV) involves randomly dividing the data into training and testing sets multiple times and averaging the performance over the iterations. MCCV helps to reduce the variability of the estimate and provides a more stable estimate of the model's performance. An example of MCCV is randomly dividing the data into 10 training and testing sets and averaging the performance over 100 iterations.
Overall, validating credit risk models is crucial to ensure their reliability and accuracy. These techniques can be used to assess the performance of the models and make necessary adjustments to improve their performance.
Techniques for Model Validation - Assessing the Reliability of Credit Risk Models 2
2.Techniques for Model Validation[Original Blog]
1. Cross-Validation
Cross-validation is a popular technique used for validating models. It involves dividing the data into two sets: a training set and a validation set. The training set is used to train the model, while the validation set is used to test the model's performance. Cross-validation helps to prevent overfitting, which occurs when the model is too complex and fits the training data too well, but does not generalize well to new data. An example of cross-validation is k-fold cross-validation, where the data is divided into k subsets, and the model is trained and tested k times, with each subset used once for testing and the remaining k-1 subsets used for training.
The holdout method involves dividing the data into a training set and a testing set. The model is trained on the training set and then tested on the testing set. The holdout method is simple and easy to implement, but it can be biased if the data is not representative of the population. An example of the holdout method is using 70% of the data for training and 30% of the data for testing.
The bootstrap method involves creating multiple samples of the data by randomly selecting observations with replacement. The model is trained on each sample, and the performance is evaluated on the original data. The bootstrap method helps to estimate the variability of the model, but it can be computationally intensive. An example of the bootstrap method is creating 1000 samples of the data, each with 70% of the observations, and training the model on each sample.
4. Leave-One-Out Cross-Validation
Leave-one-out cross-validation (LOOCV) is a special case of k-fold cross-validation, where k is equal to the number of observations in the data. LOOCV involves training the model on all but one observation and testing the model on the left-out observation. LOOCV is computationally intensive, but it provides an unbiased estimate of the model's performance. An example of LOOCV is training the model on all but one of the 1000 observations and testing the model on the left-out observation.
5. Monte Carlo Cross-Validation
Monte Carlo cross-validation (MCCV) involves randomly dividing the data into training and testing sets multiple times and averaging the performance over the iterations. MCCV helps to reduce the variability of the estimate and provides a more stable estimate of the model's performance. An example of MCCV is randomly dividing the data into 10 training and testing sets and averaging the performance over 100 iterations.
Overall, validating credit risk models is crucial to ensure their reliability and accuracy. These techniques can be used to assess the performance of the models and make necessary adjustments to improve their performance.
Techniques for Model Validation - Assessing the Reliability of Credit Risk Models update
3.Model Selection and Validation for Credit Risk Time Series[Original Blog]
One of the most important steps in credit risk time series analysis and forecasting is to select an appropriate model that can capture the dynamics and patterns of the data. However, there is no single best model that can fit all types of credit risk time series, as different models may have different strengths and weaknesses depending on the characteristics of the data, such as the level of noise, trend, seasonality, nonlinearity, heteroscedasticity, and autocorrelation. Therefore, it is essential to compare and evaluate different models based on some criteria and select the one that performs the best for the given data and forecasting horizon. In this section, we will discuss the following aspects of model selection and validation for credit risk time series:
1. Criteria for model selection and validation: There are various criteria that can be used to measure the goodness-of-fit and predictive accuracy of a model, such as the mean squared error (MSE), the mean absolute error (MAE), the root mean squared error (RMSE), the mean absolute percentage error (MAPE), the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and the adjusted R-squared. These criteria can be calculated using the in-sample data (the data used to estimate the model parameters) or the out-of-sample data (the data not used for estimation but for validation). Generally, the lower the values of these criteria, the better the model fits the data and forecasts the future values. However, these criteria may have some limitations and trade-offs, such as the bias-variance trade-off, the overfitting problem, and the sensitivity to outliers. Therefore, it is advisable to use multiple criteria and compare them across different models rather than relying on a single criterion.
2. Methods for model selection and validation: There are various methods that can be used to select and validate a model for credit risk time series, such as the holdout method, the cross-validation method, the bootstrap method, and the rolling window method. These methods differ in how they split the data into training and testing sets, how they estimate the model parameters, and how they evaluate the model performance. For example, the holdout method splits the data into a single training and testing set, while the cross-validation method splits the data into multiple folds and uses each fold as a testing set once. The bootstrap method resamples the data with replacement and creates multiple pseudo-samples, while the rolling window method uses a fixed-size window that moves along the data and updates the model parameters and forecasts. Each method has its own advantages and disadvantages, such as the computational efficiency, the stability, and the robustness. Therefore, it is important to choose a method that suits the data and the model characteristics and objectives.
3. Examples of model selection and validation for credit risk time series: To illustrate the concepts and methods discussed above, we will provide some examples of model selection and validation for credit risk time series using real-world data and popular models, such as the autoregressive (AR) model, the moving average (MA) model, the autoregressive moving average (ARMA) model, the autoregressive integrated moving average (ARIMA) model, the generalized autoregressive conditional heteroscedasticity (GARCH) model, and the neural network (NN) model. We will use the Python programming language and some libraries, such as pandas, numpy, statsmodels, and sklearn, to perform the data analysis and modeling. We will also use some plots and tables to visualize and summarize the results. The code and the data are available in the following link: https://github.com//credit-risk-time-series-example.
4.A Powerful Tool for Overfitting Prevention[Original Blog]
Overfitting is a common problem in machine learning, where a model is trained too well on a particular set of data, resulting in poor generalization to new data. Overfitting occurs when a model is too complex and captures noise in the data instead of the underlying pattern. Cross-validation is a powerful tool for overfitting prevention that evaluates the performance of a model on an independent dataset and helps to select the best model with the optimal level of complexity.
1. What is Cross-Validation?
Cross-validation is a statistical method for estimating the performance of a machine learning model on an independent dataset. It involves dividing the dataset into two or more subsets, where one subset is used for training the model, and the other subset is used for testing the model. The process is repeated multiple times, with different subsets used for training and testing, and the results are averaged to provide an estimate of the model's performance.
2. Types of Cross-Validation
There are several types of cross-validation, including:
- k-fold cross-validation: The dataset is divided into k subsets, where each subset is used for testing the model, and the remaining subsets are used for training the model. The process is repeated k times, with each subset used once for testing.
- Leave-one-out cross-validation: Each observation in the dataset is used once for testing the model, and the remaining observations are used for training the model. The process is repeated for each observation in the dataset.
- Stratified cross-validation: The dataset is divided into subsets based on a specific criterion, such as the class distribution, and each subset is used for testing the model. Stratified cross-validation is useful when the dataset is imbalanced.
3. Benefits of Cross-Validation
Cross-validation provides several benefits for overfitting prevention, including:
- It helps to estimate the model's performance on an independent dataset, which is a better measure of the model's generalization ability than the training dataset.
- It helps to select the best model with the optimal level of complexity, as it evaluates the performance of the model with different levels of complexity.
- It helps to detect overfitting, as it evaluates the performance of the model on independent datasets and identifies if the model is capturing noise in the data.
4. Cross-Validation vs. Holdout Method
The holdout method is another approach for estimating the performance of a machine learning model on an independent dataset. It involves dividing the dataset into two subsets, where one subset is used for training the model, and the other subset is used for testing the model. The holdout method is simple and easy to implement, but it has several limitations compared to cross-validation. The holdout method can result in high variance in the estimate of the model's performance, as the estimate depends on the particular subset used for testing. In contrast, cross-validation provides a more stable estimate of the model's performance, as it averages the results from multiple subsets.
5. Conclusion
In summary, cross-validation is a powerful tool for overfitting prevention in machine learning. It helps to estimate the performance of a model on an independent dataset, select the best model with the optimal level of complexity, and detect overfitting. Cross-validation is a better approach than the holdout method, as it provides a more stable estimate of the model's performance. By using cross-validation, machine learning practitioners can improve the generalization ability of their models and reduce the risk of overfitting.
A Powerful Tool for Overfitting Prevention - Overfitting: Avoiding Model Risk through Overfitting Prevention Techniques
5.What is cross-validation and why is it important for click through modeling?[Original Blog]
Cross-validation is a technique that allows us to evaluate the performance of a machine learning model on unseen data. It is especially useful for click through modeling, which is the task of predicting whether a user will click on an online advertisement or not. Click through modeling is a challenging problem because the data is often imbalanced, noisy, and dynamic. Overfitting is a common issue that occurs when the model learns too much from the training data and fails to generalize to new data. Overfitting can lead to poor accuracy, low revenue, and wasted resources. To avoid overfitting, we need to use cross-validation to test our model on different subsets of the data and select the best one.
There are different types of cross-validation methods that can be applied to click through modeling. Some of the most common ones are:
1. Holdout method: This method splits the data into two parts: a training set and a test set. The model is trained on the training set and evaluated on the test set. The advantage of this method is that it is simple and fast. The disadvantage is that it may not use all the available data and may be sensitive to the choice of the split ratio.
2. K-fold method: This method divides the data into k equal parts, called folds. The model is trained on k-1 folds and tested on the remaining fold. This process is repeated k times, each time using a different fold as the test set. The average performance across the k folds is used as the final evaluation. The advantage of this method is that it uses all the data and reduces the variance of the estimate. The disadvantage is that it is more computationally expensive and may introduce bias if the folds are not representative of the population.
3. Leave-one-out method: This method is a special case of the k-fold method, where k is equal to the number of observations in the data. The model is trained on all the data except one observation and tested on that observation. This process is repeated for each observation in the data. The advantage of this method is that it has the least bias and the highest variance. The disadvantage is that it is very time-consuming and may not be feasible for large datasets.
4. Stratified method: This method is a variation of the k-fold method, where the folds are created such that they preserve the proportion of the classes in the data. For example, if the data has 80% positive examples and 20% negative examples, each fold will have the same ratio. The advantage of this method is that it ensures that the model is trained and tested on balanced data and reduces the risk of overfitting. The disadvantage is that it may not reflect the true distribution of the data in the real world.
An example of how cross-validation can be used for click through modeling is as follows:
- Suppose we have a dataset of 10,000 online ads and their click-through rates (CTR), which is the ratio of clicks to impressions. The CTR is our target variable that we want to predict.
- We want to compare two models: a logistic regression model and a decision tree model. We use the stratified 5-fold method to split the data into 5 folds, each with 2,000 ads and the same proportion of CTR values.
- For each fold, we train both models on the other 4 folds and test them on the current fold. We compute the accuracy, precision, recall, and F1-score for each model on each fold.
- We average the performance metrics across the 5 folds and select the model with the highest F1-score as the best one.
What is cross validation and why is it important for click through modeling - Cross validation: How to use cross validation for click through modeling and avoid overfitting
6.Sectioning Your Data Sets for Cross Validation[Original Blog]
One of the most important steps in cross validation is to section your data sets into different subsets that can be used for training, testing, and validating your investment model. This process allows you to evaluate how well your model performs on unseen data and avoid overfitting or underfitting. There are different ways to section your data sets depending on the size, type, and characteristics of your data. In this section, we will discuss some of the common methods and their advantages and disadvantages. We will also provide some examples of how to apply them in practice.
Some of the common methods for sectioning your data sets are:
1. Holdout method: This method involves splitting your data set into two parts: a training set and a test set. The training set is used to fit your model, and the test set is used to evaluate its performance. The typical ratio of the split is 80% for training and 20% for testing, but this can vary depending on the size of your data set. The advantage of this method is that it is simple and easy to implement. The disadvantage is that it can be inefficient and unreliable, as it only uses a fraction of your data for testing and may not reflect the true performance of your model on new data.
2. K-fold cross validation: This method involves splitting your data set into k equal-sized subsets, or folds. Then, you use one fold as the test set and the remaining k-1 folds as the training set. You repeat this process k times, each time using a different fold as the test set. You then average the results from the k tests to get a final performance measure. The advantage of this method is that it uses all of your data for both training and testing, and reduces the variance of the performance estimate. The disadvantage is that it can be computationally expensive and time-consuming, especially for large data sets or complex models.
3. Leave-one-out cross validation: This method is a special case of k-fold cross validation, where k is equal to the number of observations in your data set. This means that you use one observation as the test set and the rest as the training set. You repeat this process for each observation in your data set. You then average the results from all the tests to get a final performance measure. The advantage of this method is that it gives the most unbiased and stable estimate of the performance, as it uses all of your data except one for training and testing. The disadvantage is that it can be very computationally intensive and impractical for large data sets or complex models.
4. Stratified cross validation: This method is a variation of k-fold cross validation, where you ensure that each fold has the same proportion of observations from each class or category of your target variable. For example, if your target variable is binary, you make sure that each fold has the same percentage of positive and negative cases. This helps to preserve the distribution of your data and reduce the bias of the performance estimate. The advantage of this method is that it improves the representativeness and generalizability of your model, especially for imbalanced or skewed data sets. The disadvantage is that it can be difficult to implement and may not be applicable for some types of data or models.
To illustrate how to section your data sets for cross validation, let us consider an example of a data set that contains information about 1000 stocks and their returns over a period of one year. Our goal is to build a model that can predict the future returns of the stocks based on their historical and fundamental features. We can use the following methods to section our data sets:
- Holdout method: We can randomly split our data set into a training set of 800 stocks and a test set of 200 stocks. We can then fit our model on the training set and evaluate its performance on the test set using metrics such as mean squared error (MSE) or R-squared (R^2).
- K-fold cross validation: We can randomly split our data set into 10 folds of 100 stocks each. We can then use one fold as the test set and the remaining nine folds as the training set. We can repeat this process 10 times, each time using a different fold as the test set. We can then average the performance metrics from the 10 tests to get a final estimate of the performance of our model.
- Leave-one-out cross validation: We can use each stock as the test set and the remaining 999 stocks as the training set. We can repeat this process for each stock in our data set. We can then average the performance metrics from the 1000 tests to get a final estimate of the performance of our model.
- Stratified cross validation: We can group our stocks into different classes or categories based on their returns. For example, we can classify them as high, medium, or low performers based on their annualized returns. We can then split our data set into 10 folds, ensuring that each fold has the same proportion of stocks from each class. We can then use one fold as the test set and the remaining nine folds as the training set. We can repeat this process 10 times, each time using a different fold as the test set. We can then average the performance metrics from the 10 tests to get a final estimate of the performance of our model.
Sectioning Your Data Sets for Cross Validation - Cross Validation: How to Validate the Robustness of Your Investment Model Using Different Data Sets
7.Building Predictive Models for Customer Lifetime Value[Original Blog]
Customer lifetime value (CLV) is a metric that estimates the present value of the future cash flows generated by a customer over their entire relationship with a business. It is a key indicator of customer loyalty, retention, and profitability. building predictive models for CLV can help businesses optimize their marketing strategies, allocate their resources, and increase their revenues. In this section, we will discuss how to build predictive models for CLV using different approaches and techniques. We will also provide some examples of how businesses can use CLV models to make better decisions and improve their performance.
Some of the steps involved in building predictive models for CLV are:
1. Define the objective and scope of the model. Depending on the business context and the available data, the model can have different objectives and scopes. For example, the model can aim to predict the CLV of individual customers, segments, or cohorts. The model can also focus on a specific time horizon, such as one year, three years, or lifetime. The model can also account for different factors that affect CLV, such as customer behavior, product features, or external events.
2. Choose the appropriate modeling technique. There are various techniques that can be used to model CLV, such as historical, probabilistic, machine learning, or hybrid methods. Each technique has its own advantages and limitations, and the choice depends on the data quality, quantity, and characteristics. For example, historical methods use past data to calculate the average CLV of customers, but they do not account for changes in customer behavior or market conditions. Probabilistic methods use statistical models to estimate the probability of customer retention, churn, and purchase frequency, but they require certain assumptions and parameters. Machine learning methods use algorithms to learn from data and make predictions, but they can be complex and computationally intensive. Hybrid methods combine different techniques to leverage their strengths and overcome their weaknesses.
3. Collect and prepare the data. The data used for CLV modeling should be relevant, reliable, and representative of the customer population and the business environment. The data should also be cleaned, transformed, and standardized to ensure consistency and accuracy. Some of the common data sources for CLV modeling are transactional data, behavioral data, demographic data, and attitudinal data. Transactional data include information about the purchases made by customers, such as date, amount, product, and channel. Behavioral data include information about the actions and interactions of customers with the business, such as website visits, app usage, email clicks, and social media engagement. Demographic data include information about the characteristics and attributes of customers, such as age, gender, location, and income. Attitudinal data include information about the preferences and opinions of customers, such as satisfaction, loyalty, and feedback.
4. Build and validate the model. The model should be built using the chosen technique and the prepared data. The model should also be validated using appropriate metrics and methods to evaluate its performance and accuracy. Some of the common metrics for CLV modeling are mean absolute error (MAE), root mean squared error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R-squared). Some of the common methods for CLV model validation are holdout, cross-validation, and bootstrapping. Holdout method splits the data into training and testing sets, and uses the training set to build the model and the testing set to evaluate it. Cross-validation method divides the data into k folds, and uses k-1 folds to build the model and the remaining fold to evaluate it, and repeats this process k times. Bootstrapping method resamples the data with replacement, and uses each sample to build and evaluate the model, and averages the results.
5. Interpret and apply the model. The model should be interpreted and applied in a way that is meaningful and actionable for the business. The model should provide insights into the drivers and patterns of CLV, such as customer segments, product categories, or marketing channels. The model should also provide recommendations and suggestions for improving CLV, such as targeting, retention, cross-selling, or up-selling strategies. The model should also be monitored and updated regularly to reflect the changes in data, customer behavior, and business environment.
Building Predictive Models for Customer Lifetime Value - Predictive Analytics and Lifetime Value Modeling: How to Forecast Future Revenue and Profitability from Your Customers
8.How to Choose the Right Tools, Techniques, and Metrics?[Original Blog]
Data analytics is the process of collecting, organizing, analyzing, and interpreting data to gain insights, make decisions, and solve problems. Data analytics can help businesses improve their performance, optimize their operations, enhance their customer experience, and increase their revenue. However, data analytics is not a one-size-fits-all solution. Depending on the business goals, data sources, data quality, and data complexity, different tools, techniques, and metrics may be more suitable than others. In this section, we will discuss some of the best practices of data analytics, and how to choose the right tools, techniques, and metrics for your business needs.
Some of the best practices of data analytics are:
1. Define your business objectives and key performance indicators (KPIs). Before you start any data analysis, you need to have a clear idea of what you want to achieve, and how you will measure your success. KPIs are quantifiable metrics that reflect your business goals, such as revenue, profit, customer satisfaction, retention, etc. KPIs help you track your progress, evaluate your performance, and identify areas of improvement. For example, if your objective is to increase your annual revenue, you may want to measure your KPIs such as sales volume, average order value, conversion rate, etc.
2. Choose the right data sources and data quality. Data is the foundation of any data analysis, so you need to ensure that you have access to relevant, reliable, and accurate data sources. Depending on your business domain, you may have different types of data sources, such as internal data (e.g., transactional data, customer data, operational data, etc.), external data (e.g., market data, competitor data, social media data, etc.), or third-party data (e.g., industry reports, surveys, benchmarks, etc.). You also need to ensure that your data quality is high, meaning that your data is complete, consistent, valid, and error-free. Data quality issues can affect your data analysis results and lead to wrong conclusions or decisions. For example, if your data source is missing some important variables, or has incorrect or outdated values, you may not be able to get a comprehensive or accurate picture of your business situation.
3. Choose the right data analysis tools and techniques. Data analysis tools and techniques are the methods and processes that you use to manipulate, transform, explore, and visualize your data. Depending on your data characteristics, such as data size, data format, data structure, data distribution, etc., you may need different tools and techniques to handle your data. For example, if your data is large and complex, you may need tools such as big data platforms (e.g., Hadoop, Spark, etc.), cloud computing services (e.g., AWS, Azure, etc.), or distributed databases (e.g., Cassandra, MongoDB, etc.) to store, process, and analyze your data. If your data is structured and tabular, you may need tools such as spreadsheets (e.g., Excel, Google Sheets, etc.), relational databases (e.g., MySQL, PostgreSQL, etc.), or business intelligence tools (e.g., Power BI, Tableau, etc.) to query, aggregate, and visualize your data. If your data is unstructured and textual, you may need tools such as text analytics tools (e.g., NLTK, spaCy, etc.), natural language processing tools (e.g., GPT-4, BERT, etc.), or sentiment analysis tools (e.g., TextBlob, VADER, etc.) to extract, classify, and analyze your data. Similarly, depending on your data analysis objectives, such as data exploration, data modeling, data prediction, data optimization, etc., you may need different techniques to perform your data analysis. For example, if your objective is to explore your data and find patterns, trends, or outliers, you may need techniques such as descriptive statistics (e.g., mean, median, mode, standard deviation, etc.), data visualization (e.g., charts, graphs, maps, etc.), or exploratory data analysis (e.g., correlation, distribution, hypothesis testing, etc.). If your objective is to model your data and find relationships, causes, or effects, you may need techniques such as regression analysis (e.g., linear regression, logistic regression, etc.), classification analysis (e.g., decision trees, k-nearest neighbors, etc.), or clustering analysis (e.g., k-means, hierarchical clustering, etc.). If your objective is to predict your data and forecast future outcomes, you may need techniques such as time series analysis (e.g., ARIMA, exponential smoothing, etc.), machine learning (e.g., neural networks, support vector machines, etc.), or deep learning (e.g., convolutional neural networks, recurrent neural networks, etc.). If your objective is to optimize your data and find the best solutions, you may need techniques such as linear programming (e.g., simplex method, interior point method, etc.), nonlinear programming (e.g., gradient descent, Newton's method, etc.), or genetic algorithms (e.g., crossover, mutation, selection, etc.).
4. Choose the right data analysis metrics and evaluation methods. Data analysis metrics and evaluation methods are the criteria and procedures that you use to assess the quality, validity, and usefulness of your data analysis results. Depending on your data analysis objectives, you may need different metrics and methods to evaluate your data analysis. For example, if your objective is to model your data and find relationships, causes, or effects, you may need metrics such as coefficient of determination (R-squared), mean squared error (MSE), accuracy (ACC), precision (PRE), recall (REC), F1-score (F1), etc. To measure how well your model fits your data, how much error your model makes, how correctly your model classifies your data, how precisely your model identifies relevant data, how completely your model retrieves relevant data, and how balanced your model is between precision and recall. You may also need methods such as cross-validation (CV), bootstrap (BS), confusion matrix (CM), receiver operating characteristic curve (ROC), etc. To test the robustness, stability, and generalizability of your model, and to compare the performance of different models. If your objective is to predict your data and forecast future outcomes, you may need metrics such as mean absolute error (MAE), mean absolute percentage error (MAPE), root mean squared error (RMSE), forecast accuracy (FA), etc. To measure how close your predictions are to the actual values, how much error your predictions make in percentage terms, how much error your predictions make in squared terms, and how correctly your predictions match the actual values. You may also need methods such as holdout method (HM), rolling window method (RWM), backtesting (BT), forecast evaluation (FE), etc. To split your data into training and testing sets, to update your model with new data, to simulate your predictions with historical data, and to compare the performance of different predictions. If your objective is to optimize your data and find the best solutions, you may need metrics such as objective function (OF), constraints (C), feasible region (FR), optimal solution (OS), etc. To define your optimization problem, to specify the limitations and requirements of your problem, to identify the set of possible solutions, and to find the best solution among them. You may also need methods such as sensitivity analysis (SA), shadow price (SP), reduced cost (RC), optimality test (OT), etc. To measure how your optimal solution changes with the changes in your problem parameters, to measure how much your objective function value changes with the changes in your constraints, to measure how much your objective function value changes with the changes in your decision variables, and to check whether your optimal solution is indeed optimal or not.
Most entrepreneurs are very gut driven - they have to be because the odds and data are often stacked against them. If your gut says something is the right thing to do, then do it.
9.Techniques for Model Validation[Original Blog]
Cross-validation is a popular technique used for validating models. It involves dividing the data into two sets: a training set and a validation set. The training set is used to train the model, while the validation set is used to test the model's performance. Cross-validation helps to prevent overfitting, which occurs when the model is too complex and fits the training data too well, but does not generalize well to new data. An example of cross-validation is k-fold cross-validation, where the data is divided into k subsets, and the model is trained and tested k times, with each subset used once for testing and the remaining k-1 subsets used for training.
The holdout method involves dividing the data into a training set and a testing set. The model is trained on the training set and then tested on the testing set. The holdout method is simple and easy to implement, but it can be biased if the data is not representative of the population. An example of the holdout method is using 70% of the data for training and 30% of the data for testing.
The bootstrap method involves creating multiple samples of the data by randomly selecting observations with replacement. The model is trained on each sample, and the performance is evaluated on the original data. The bootstrap method helps to estimate the variability of the model, but it can be computationally intensive. An example of the bootstrap method is creating 1000 samples of the data, each with 70% of the observations, and training the model on each sample.
4. Leave-One-Out Cross-Validation
Leave-one-out cross-validation (LOOCV) is a special case of k-fold cross-validation, where k is equal to the number of observations in the data. LOOCV involves training the model on all but one observation and testing the model on the left-out observation. LOOCV is computationally intensive, but it provides an unbiased estimate of the model's performance. An example of LOOCV is training the model on all but one of the 1000 observations and testing the model on the left-out observation.
5. Monte Carlo Cross-Validation
Monte Carlo cross-validation (MCCV) involves randomly dividing the data into training and testing sets multiple times and averaging the performance over the iterations. MCCV helps to reduce the variability of the estimate and provides a more stable estimate of the model's performance. An example of MCCV is randomly dividing the data into 10 training and testing sets and averaging the performance over 100 iterations.
Overall, validating credit risk models is crucial to ensure their reliability and accuracy. These techniques can be used to assess the performance of the models and make necessary adjustments to improve their performance.
Techniques for Model Validation - Assessing the Reliability of Credit Risk Models 2
10.Evaluating and Validating Trend Analysis Models[Original Blog]
Evaluating and validating trend analysis models is an essential step in any trend analysis project. Trend analysis models are mathematical or statistical methods that attempt to capture the patterns and relationships in the data and use them to make predictions or explain the underlying causes. However, not all models are equally effective or reliable. Some models may fit the data well, but fail to generalize to new or unseen situations. Some models may be too complex or too simple, leading to overfitting or underfitting problems. Some models may have hidden assumptions or biases that affect their performance or interpretation. Therefore, it is important to assess the quality and validity of the models before using them for decision making or reporting purposes.
There are different ways to evaluate and validate trend analysis models, depending on the type, purpose, and scope of the model. Here are some common methods and criteria that can be used to assess the models:
1. Visual inspection: This is the simplest and most intuitive way to evaluate a model. It involves plotting the data and the model's predictions or estimates on a graph and visually comparing them. This can help to identify any obvious discrepancies, outliers, or anomalies in the data or the model. For example, if the model predicts a linear trend, but the data shows a nonlinear or cyclical pattern, then the model is clearly inadequate. Visual inspection can also help to check the model's assumptions, such as normality, homoscedasticity, or stationarity of the data. However, visual inspection is not sufficient to validate a model, as it can be subjective, misleading, or inaccurate. For instance, a model may appear to fit the data well, but it may have a high variance or a low bias, which means it is overfitting the data and not capturing the true underlying trend. Therefore, visual inspection should be complemented by other methods of evaluation and validation.
2. Statistical tests: These are more rigorous and objective ways to evaluate a model. They involve applying various statistical tests or measures to the data and the model's predictions or estimates, and comparing them to some benchmarks or thresholds. These tests or measures can help to quantify the model's accuracy, precision, robustness, or significance. For example, some common tests or measures are:
- Mean squared error (MSE): This measures the average squared difference between the actual and predicted values. It indicates how well the model fits the data. A lower MSE means a better fit. However, MSE can be sensitive to outliers or extreme values, and it does not account for the scale or variability of the data.
- root mean squared error (RMSE): This is the square root of the MSE. It has the same unit as the data and the predictions, which makes it easier to interpret. It also indicates how well the model fits the data. A lower RMSE means a better fit. However, RMSE can also be sensitive to outliers or extreme values, and it does not account for the scale or variability of the data.
- Mean absolute error (MAE): This measures the average absolute difference between the actual and predicted values. It indicates how well the model fits the data. A lower MAE means a better fit. MAE is less sensitive to outliers or extreme values than MSE or RMSE, but it still does not account for the scale or variability of the data.
- Mean absolute percentage error (MAPE): This measures the average absolute percentage difference between the actual and predicted values. It indicates how well the model fits the data relative to the magnitude of the data. A lower MAPE means a better fit. MAPE is more robust to outliers or extreme values than MSE, RMSE, or MAE, and it accounts for the scale or variability of the data. However, MAPE can be undefined or infinite if the actual value is zero or very close to zero, and it can be biased if the data has a skewed distribution or a large range.
- Coefficient of determination (R-squared): This measures the proportion of the variance in the data that is explained by the model. It indicates how well the model captures the trend or relationship in the data. A higher R-squared means a better fit. However, R-squared can be misleading or inflated if the model is too complex or has too many parameters, which leads to overfitting. Therefore, R-squared should be adjusted for the degrees of freedom or the number of parameters in the model, which is called the adjusted R-squared.
- F-test: This tests the overall significance of the model. It compares the variance explained by the model to the variance not explained by the model, and calculates the ratio of the two. It indicates whether the model is better than a baseline model that has no predictors or parameters. A higher F-ratio means a more significant model. However, F-test can also be misleading or inflated if the model is too complex or has too many parameters, which leads to overfitting. Therefore, F-test should be adjusted for the degrees of freedom or the number of parameters in the model, which is called the adjusted F-test.
- t-test: This tests the significance of each predictor or parameter in the model. It compares the estimated value of the predictor or parameter to its standard error, and calculates the ratio of the two. It indicates whether the predictor or parameter has a significant effect on the outcome or response variable. A higher t-ratio means a more significant predictor or parameter. However, t-test can also be misleading or inflated if the model is too complex or has too many parameters, which leads to multicollinearity or correlation among the predictors or parameters. Therefore, t-test should be complemented by other tests or measures that assess the multicollinearity or correlation among the predictors or parameters, such as the variance inflation factor (VIF) or the correlation matrix.
- p-value: This measures the probability of obtaining the observed or more extreme results under the null hypothesis, which is the assumption that there is no effect or relationship in the data. It indicates the strength of the evidence against the null hypothesis. A lower p-value means a stronger evidence against the null hypothesis. However, p-value can be misleading or misinterpreted if the sample size is too small or too large, or if the significance level or the threshold for rejecting the null hypothesis is not specified or agreed upon. Therefore, p-value should be reported with the confidence interval or the range of values that are compatible with the data and the model, which indicates the uncertainty or the margin of error of the estimate or the prediction.
3. Cross-validation: This is a more robust and reliable way to validate a model. It involves splitting the data into two or more subsets, such as training and testing sets, or k-folds. The model is then fitted on one or more subsets, and evaluated on the remaining subset or subsets. This can help to assess the model's generalizability or performance on new or unseen data. For example, some common methods of cross-validation are:
- Holdout method: This splits the data into two subsets, such as 80% for training and 20% for testing. The model is fitted on the training set, and evaluated on the testing set. This can help to avoid overfitting or underfitting problems, and to estimate the model's prediction error or accuracy. However, holdout method can be sensitive to the choice or the randomness of the split, and it can waste some data that are not used for fitting or evaluating the model.
- k-fold cross-validation: This splits the data into k subsets or folds, such as 5 or 10. The model is then fitted on k-1 folds, and evaluated on the remaining fold. This is repeated k times, so that each fold is used once for evaluation. The results are then averaged or aggregated to obtain the overall estimate or measure of the model's performance. This can help to reduce the sensitivity or the variability of the split, and to use all the data for fitting and evaluating the model. However, k-fold cross-validation can be computationally expensive or time-consuming, especially if the data is large or the model is complex.
- Leave-one-out cross-validation: This is a special case of k-fold cross-validation, where k is equal to the number of observations in the data. The model is then fitted on all the observations except one, and evaluated on the remaining one. This is repeated for each observation in the data. The results are then averaged or aggregated to obtain the overall estimate or measure of the model's performance. This can help to minimize the bias or the variance of the estimate or measure, and to use all the data for fitting and evaluating the model. However, leave-one-out cross-validation can be very computationally expensive or time-consuming, especially if the data is large or the model is complex.
4. Sensitivity analysis: This is a more comprehensive and systematic way to validate a model. It involves varying the inputs, parameters, assumptions, or scenarios of the model, and observing the effects or impacts on the outputs, predictions, or estimates of the model. This can help to assess the model's robustness, stability, or uncertainty under different conditions or situations. For example, some common methods of sensitivity analysis are:
- One-way sensitivity analysis: This varies one input, parameter, assumption, or scenario of the model at a time, and observes the effect or impact on the output, prediction, or estimate of the model. This can help to identify the most influential or critical factors or variables that affect the model's performance or outcome. However, one-way sensitivity analysis can be simplistic or unrealistic, as it does not account for the interactions or the correlations among the factors or variables.
- Multi-way sensitivity analysis: This varies two or more inputs, parameters, assumptions, or scenarios of the model at the same time, and observes the effect or impact on the output, prediction, or estimate of the model.
Evaluating and Validating Trend Analysis Models - Trend Analysis: How to Identify and Forecast the Patterns in Your Financial Data
11.Cross-Validation Techniques[Original Blog]
### Perspectives on Cross-Validation
1. The Holdout Method: A Simple Start
- The holdout method, also known as the train-test split, is the most straightforward form of cross-validation. Here's how it works:
- We divide our dataset into two subsets: a training set (used for model training) and a test set (used for evaluation).
- The model is trained on the training set, and its performance is assessed on the test set.
- While simple, this approach has limitations:
- It can be sensitive to the specific random split of data.
- The test set may not be representative of unseen data.
- We lose valuable training data by setting it aside for testing.
2. K-Fold Cross-Validation: Robustness and Efficiency
- K-fold cross-validation addresses the limitations of the holdout method. Here's how it works:
- We divide the data into K equally sized folds (typically 5 or 10).
- The model is trained K times, each time using K-1 folds for training and the remaining fold for testing.
- The final performance metric is the average of the K test performances.
- Benefits of K-fold CV:
- Robustness: Reduces the impact of random data splits.
- Efficiency: Utilizes the entire dataset for both training and testing.
- Example:
- Suppose we have 1000 samples. We split them into 5 folds (each with 200 samples). The model trains on 4 folds and tests on the remaining fold. This process repeats 5 times, and the average performance is reported.
3. Stratified K-Fold: Handling Imbalanced Classes
- When dealing with imbalanced datasets (e.g., rare diseases), stratified K-fold ensures that each fold maintains the same class distribution as the original dataset.
- Example:
- If only 5% of samples belong to a rare class, stratified K-fold ensures that each fold contains roughly the same proportion of rare class samples.
4. Leave-One-Out Cross-Validation (LOOCV): Extreme Case
- LOOCV takes K-fold to the extreme by leaving out just one sample as the test set.
- Benefits:
- Provides an unbiased estimate of model performance.
- Useful when data is scarce (e.g., medical studies with limited samples).
- Drawbacks:
- Computationally expensive (especially for large datasets).
5. Nested Cross-Validation: Model Selection
- When tuning hyperparameters or comparing different models, nested cross-validation is essential.
- Outer loop (model selection):
- K-fold CV to assess model performance.
- Inner loop (hyperparameter tuning):
- Another K-fold CV to find the best hyperparameters.
- Example:
- We compare different algorithms (e.g., linear regression, random forests) using nested CV.
### Conclusion
Cross-validation techniques allow us to strike a balance between model performance estimation and efficient use of data. By understanding these methods and their trade-offs, we can make better decisions when building and evaluating predictive models. Remember, there's no one-size-fits-all approach; choose the right technique based on your specific problem and available data.
Cross Validation Techniques - Rating Validation: The Methods and Metrics of Rating Validation
12.How to Choose the Best Regression Model for Your Data and Objective?[Original Blog]
One of the most important steps in cost regression analysis is model selection. Model selection refers to the process of choosing the best regression model for your data and objective. There are many factors that can influence the choice of a regression model, such as the type and distribution of the variables, the number and quality of the predictors, the assumptions and limitations of the models, the complexity and interpretability of the models, and the performance and accuracy of the models. In this section, we will discuss some of the common methods and criteria for model selection, and provide some examples of how to apply them in practice.
Some of the methods and criteria for model selection are:
1. exploratory data analysis (EDA): EDA is a preliminary step that involves visualizing and summarizing the data to get a better understanding of its characteristics and relationships. EDA can help to identify potential outliers, missing values, multicollinearity, nonlinearity, heteroscedasticity, and other issues that may affect the choice and validity of a regression model. For example, if the response variable is skewed, a transformation or a nonparametric model may be more appropriate than a linear model. If the predictors are highly correlated, a dimensionality reduction technique or a regularization method may be needed to avoid overfitting.
2. Model specification: Model specification involves defining the functional form and the variables of the regression model. The functional form determines how the response variable is related to the predictors, such as linear, quadratic, logarithmic, exponential, etc. The variables include the main effects, the interactions, and the higher-order terms of the predictors. Model specification can be based on theoretical knowledge, empirical evidence, or trial and error. For example, if the cost of a project is expected to increase exponentially with the duration, a logarithmic transformation or an exponential model may be suitable. If the cost depends on the interaction between the type and the size of the project, an interaction term may be included in the model.
3. Model comparison: Model comparison involves evaluating and comparing the performance and accuracy of different regression models using various criteria and metrics. Some of the common criteria and metrics are:
- R-squared: R-squared measures the proportion of the variance in the response variable that is explained by the predictors in the model. It ranges from 0 to 1, with higher values indicating better fit. However, R-squared does not account for the number of predictors or the complexity of the model, and it may increase artificially as more variables are added to the model. Therefore, R-squared alone is not sufficient for model selection, and it should be used in conjunction with other criteria.
- Adjusted R-squared: Adjusted R-squared is a modified version of R-squared that penalizes the model for adding more predictors that do not improve the fit. It adjusts the R-squared value by the degrees of freedom of the model, which is the number of predictors minus one. Adjusted R-squared is always lower than or equal to R-squared, and it may decrease as more variables are added to the model. Adjusted R-squared is more suitable for model selection than R-squared, as it balances the fit and the complexity of the model.
- Akaike information criterion (AIC): AIC is a criterion that measures the trade-off between the fit and the complexity of the model. It is calculated as AIC = 2k - 2ln(L), where k is the number of predictors and L is the likelihood of the model. AIC rewards the model for fitting the data well, but penalizes it for having more predictors. The lower the AIC value, the better the model. AIC can be used to compare models with different functional forms and variables, as long as they are fitted to the same data set.
- Bayesian information criterion (BIC): BIC is another criterion that measures the trade-off between the fit and the complexity of the model. It is similar to AIC, but it penalizes the model more severely for having more predictors. It is calculated as BIC = kln(n) - 2ln(L), where k is the number of predictors, n is the number of observations, and L is the likelihood of the model. The lower the BIC value, the better the model. BIC can also be used to compare models with different functional forms and variables, as long as they are fitted to the same data set.
For example, suppose we have three regression models for the cost of a project: a linear model, a quadratic model, and a cubic model. The R-squared, adjusted R-squared, AIC, and BIC values of the models are shown in the table below:
| Model | R-squared | Adjusted R-squared | AIC | BIC |
| Linear | 0.75 | 0.74 | 1200 | 1210 |
| Quadratic | 0.78 | 0.77 | 1180 | 1195 |
| Cubic | 0.79 | 0.77 | 1185 | 1205 |
Based on the table, we can see that the quadratic model has the highest adjusted R-squared value, the lowest AIC value, and the second lowest BIC value. Therefore, the quadratic model may be the best choice among the three models, as it has a good fit and a reasonable complexity. The cubic model may be overfitting the data, as it has a higher R-squared value but a lower adjusted R-squared value, and a higher AIC and BIC value than the quadratic model. The linear model may be underfitting the data, as it has a lower R-squared and adjusted R-squared value, and a higher AIC and BIC value than the quadratic model.
4. Model validation: Model validation involves checking the validity and reliability of the regression model using various methods and tests. Some of the common methods and tests are:
- Residual analysis: Residual analysis involves examining the residuals, which are the differences between the observed and the predicted values of the response variable. Residual analysis can help to assess the assumptions and the fit of the model, and to identify potential problems and outliers. Some of the common residual plots are:
- Residuals vs fitted values plot: This plot shows the residuals on the y-axis and the fitted values on the x-axis. It can help to check the linearity and the homoscedasticity of the model. Ideally, the plot should show a random scatter of points around zero, with no obvious pattern or trend. If the plot shows a curved or a funnel-shaped pattern, it may indicate nonlinearity or heteroscedasticity, respectively.
- Normal probability plot: This plot shows the standardized residuals on the y-axis and the theoretical quantiles of the normal distribution on the x-axis. It can help to check the normality of the residuals. Ideally, the plot should show a straight line, indicating that the residuals are normally distributed. If the plot shows a deviation from the line, especially at the tails, it may indicate non-normality of the residuals.
- Residuals vs predictors plot: This plot shows the residuals on the y-axis and one of the predictors on the x-axis. It can help to check the relationship and the effect of the predictor on the response variable. Ideally, the plot should show a random scatter of points around zero, with no obvious pattern or trend. If the plot shows a curved or a non-constant variance pattern, it may indicate nonlinearity or heteroscedasticity, respectively.
- cross-validation: Cross-validation involves splitting the data into two or more subsets, such as training and testing sets, and using one subset to fit the model and another subset to evaluate the model. Cross-validation can help to assess the generalization and the accuracy of the model, and to avoid overfitting or underfitting the data. Some of the common cross-validation methods are:
- Holdout method: This method involves randomly splitting the data into a training set and a testing set, usually in a ratio of 70:30 or 80:20. The model is fitted to the training set and evaluated on the testing set using a metric such as mean squared error (MSE) or root mean squared error (RMSE). The lower the MSE or RMSE, the better the model. However, this method may be sensitive to the choice of the split, and it may not use all the available data for fitting or testing the model.
- K-fold method: This method involves randomly splitting the data into k equal-sized folds, where k is usually 5 or 10. The model is fitted to k-1 folds and evaluated on the remaining fold, and this process is repeated k times, each time using a different fold as the testing set. The average MSE or RMSE across the k folds is used as the measure of the model performance. The lower the average MSE or RMSE, the better the model. This method is more robust and efficient than the holdout method, as it uses all the data for fitting and testing the model, and it reduces the variability of the estimate.
- Bootstrap: Bootstrap involves resampling the data with replacement, and creating multiple samples of the same size as the original data. The model is fitted to each sample and evaluated on the original data or another sample, and the results are averaged or aggregated to obtain the estimate of the model performance. bootstrap can help to estimate the uncertainty and the variability of the model parameters and predictions, and to provide confidence intervals or standard errors for the estimates. Bootstrap is especially useful when the data is small or the model is complex, and the analytical methods are not available or reliable.
How to Choose the Best Regression Model for Your Data and Objective - Cost Regression Analysis: How to Perform a Cost Regression Analysis for Your Projects
13.Evaluating and Validating Cost Forecasts[Original Blog]
Evaluating and validating cost forecasts is an essential step in any cost forecasting process. It helps to ensure that the forecasts are reliable, accurate, and useful for decision-making. Evaluation and validation can be done from different perspectives, such as the data quality, the model performance, the forecast accuracy, and the forecast value. In this section, we will discuss some of the methods and techniques that can be used to evaluate and validate cost forecasts, as well as some of the challenges and limitations that may arise.
Some of the methods and techniques for evaluating and validating cost forecasts are:
1. data quality assessment: This involves checking the quality and reliability of the data used for cost forecasting, such as the historical cost data, the cost drivers, and the assumptions. Data quality assessment can help to identify and correct any errors, outliers, missing values, or inconsistencies in the data. It can also help to determine the level of uncertainty and variability in the data, and how they may affect the forecast results. Data quality assessment can be done using various statistical tools, such as descriptive statistics, histograms, box plots, scatter plots, correlation analysis, and regression analysis.
2. Model performance evaluation: This involves measuring how well the cost model fits the historical data, and how well it captures the underlying patterns and trends in the cost data. Model performance evaluation can help to compare and select the best cost model among different alternatives, and to identify and improve any weaknesses or limitations in the model. Model performance evaluation can be done using various metrics, such as the coefficient of determination ($R^2$), the root mean square error (RMSE), the mean absolute percentage error (MAPE), and the Akaike information criterion (AIC).
3. Forecast accuracy assessment: This involves comparing the forecasted costs with the actual costs, and measuring how close they are. Forecast accuracy assessment can help to evaluate the validity and reliability of the cost forecasts, and to identify and correct any sources of forecast error or bias. Forecast accuracy assessment can be done using various methods, such as the holdout method, the cross-validation method, the rolling window method, and the bootstrap method.
4. Forecast value analysis: This involves assessing the usefulness and relevance of the cost forecasts for decision-making, and measuring how they contribute to the achievement of the objectives and goals. Forecast value analysis can help to justify the cost and effort of cost forecasting, and to communicate and present the forecast results to the stakeholders. Forecast value analysis can be done using various techniques, such as the expected value of perfect information (EVPI), the expected value of sample information (EVSI), the value of forecast accuracy (VFA), and the value of forecast precision (VFP).
Some of the challenges and limitations that may arise when evaluating and validating cost forecasts are:
- Data availability and accessibility: The quality and quantity of the data available for cost forecasting may vary depending on the source, the industry, the project, and the time period. Some data may be difficult to obtain, access, or use due to legal, ethical, or technical issues. This may limit the scope and accuracy of the cost forecasts, and affect the evaluation and validation process.
- Model complexity and uncertainty: The cost model used for cost forecasting may involve many variables, parameters, assumptions, and equations, which may increase the complexity and uncertainty of the model. Some of the model components may be difficult to estimate, calibrate, or validate, or may have significant errors or biases. This may affect the performance and reliability of the cost model, and the evaluation and validation process.
- Forecast horizon and frequency: The forecast horizon and frequency refer to the time span and the time interval of the cost forecasts, respectively. The longer the forecast horizon and the higher the forecast frequency, the more difficult and uncertain the cost forecasting becomes. This may affect the accuracy and value of the cost forecasts, and the evaluation and validation process.
- Stakeholder expectations and preferences: The stakeholders of the cost forecasts may have different expectations and preferences regarding the cost forecasting process, the cost model, the forecast results, and the evaluation and validation methods. These may depend on their roles, interests, objectives, and perspectives. This may create conflicts, disagreements, or misunderstandings among the stakeholders, and affect the evaluation and validation process.
Evaluating and Validating Cost Forecasts - Cost Forecasting: How to Forecast Future Costs Using Cost Model Simulation and Time Series Analysis
14.Understanding Cross-Validation[Original Blog]
Cross-validation is a popular technique in machine learning that helps to evaluate the performance of a model. The purpose of this technique is to estimate the accuracy of a model by testing it on an independent data set. Cross-validation is an important process in the development of machine learning models as it helps to identify overfitting and underfitting and enables the selection of the best model that generalizes well on unseen data. There are different types of cross-validation techniques such as the k-fold cross-validation, leave-one-out cross-validation, and the holdout method.
1. K-fold Cross-Validation: This technique divides the data set into k partitions of equal size. The model is trained on k-1 partitions and tested on the remaining partition. This process is repeated k times, with each partition being used once as the test set. The results are then averaged to obtain a single estimation of the model's performance. This technique is useful when the data set is large and the model has a high variance.
2. Leave-One-Out Cross-Validation: This technique is similar to k-fold cross-validation, except that k is equal to the number of data points in the data set. This means that each data point is used as a test set once, and the model is trained on the remaining data points. This technique is useful when the data set is small.
3. Holdout Method: This technique divides the data set into two parts: a training set and a testing set. The model is trained on the training set and tested on the testing set. The holdout method is useful when the data set is large and there is a need to quickly test the model's performance.
Cross-validation is an important technique in the development of machine learning models. It helps to estimate the performance of a model on unseen data and prevents overfitting and underfitting. By using cross-validation, it is possible to select the best model that generalizes well on unseen data. For example, a k-fold cross-validation technique may be used to evaluate the performance of a neural network model on a large data set. The technique can help to identify the optimal number of hidden layers and neurons in the model.
Understanding Cross Validation - Sum of Squares Cross Validation: Enhancing Model Performance
15.Techniques for Modeling Complex Relationships[Original Blog]
One of the challenges of cost modeling is to capture the complex relationships between various factors that affect the cost of a product or service. These factors may include the quantity, quality, location, time, and type of inputs and outputs, as well as the interactions and dependencies among them. A cost modeling function is a mathematical expression that represents these relationships and allows us to estimate the cost of a given scenario. In this section, we will discuss some of the techniques for developing and using a cost modeling function to model complex relationships. We will cover the following topics:
1. How to choose an appropriate form and level of detail for the cost modeling function
2. How to identify and measure the relevant variables and parameters for the cost modeling function
3. How to validate and test the accuracy and robustness of the cost modeling function
4. How to apply the cost modeling function to different scenarios and perform sensitivity analysis
## 1. How to choose an appropriate form and level of detail for the cost modeling function
The form and level of detail of the cost modeling function depend on the purpose and scope of the cost analysis, as well as the availability and reliability of the data. Some of the common forms of cost modeling functions are:
- Linear functions: These are the simplest and most widely used form of cost modeling functions. They assume that the cost is a linear function of one or more independent variables, such as the quantity or quality of inputs or outputs. For example, the cost of producing a widget may be expressed as $C = a + bQ$, where $C$ is the total cost, $a$ is the fixed cost, $b$ is the variable cost per unit, and $Q$ is the quantity of widgets produced. Linear functions are easy to estimate and interpret, but they may not capture the nonlinearities and interactions that exist in reality.
- Nonlinear functions: These are more complex and flexible forms of cost modeling functions that can account for the nonlinearities and interactions among the variables. They may involve exponential, logarithmic, power, or polynomial functions, or combinations of them. For example, the cost of producing a widget may be expressed as $C = a + bQ + cQ^2$, where $c$ is the coefficient of the quadratic term that captures the increasing or decreasing marginal cost of production. Nonlinear functions can fit the data better and reflect the reality more accurately, but they may also require more data and computational power, and may be harder to estimate and interpret.
- Discrete functions: These are cost modeling functions that have discrete or categorical variables, such as the location, time, or type of inputs or outputs. They may involve conditional statements, such as if-then-else or switch-case, or dummy variables, such as binary or ordinal variables. For example, the cost of producing a widget may depend on the location of the factory, such as $C = a + bQ + cL$, where $L$ is a dummy variable that takes the value of 1 if the factory is in city A, and 0 if the factory is in city B. Discrete functions can capture the heterogeneity and diversity of the scenarios, but they may also increase the complexity and dimensionality of the cost modeling function.
The level of detail of the cost modeling function refers to the number and granularity of the variables and parameters that are included in the function. A higher level of detail may provide more accuracy and precision, but it may also increase the data requirements and the risk of overfitting or underfitting the data. A lower level of detail may provide more simplicity and generality, but it may also increase the uncertainty and error of the estimates. Therefore, the optimal level of detail depends on the trade-off between the benefits and costs of adding more variables and parameters to the cost modeling function.
## 2. How to identify and measure the relevant variables and parameters for the cost modeling function
The variables and parameters of the cost modeling function are the inputs and outputs of the function that represent the factors that affect the cost of the product or service. The variables are the independent or explanatory variables that can be controlled or manipulated by the decision maker, such as the quantity or quality of inputs or outputs. The parameters are the coefficients or constants that reflect the relationship between the variables and the cost, such as the fixed or variable cost per unit. The identification and measurement of the variables and parameters are crucial steps for developing and using a cost modeling function.
The identification of the variables and parameters involves selecting the relevant and significant factors that influence the cost of the product or service, and defining them clearly and consistently. The selection of the variables and parameters should be based on the purpose and scope of the cost analysis, as well as the availability and reliability of the data. The definition of the variables and parameters should be based on the conceptual and operational definitions of the factors, and should be consistent with the form and level of detail of the cost modeling function. For example, if the cost modeling function is a linear function of the quantity and quality of inputs and outputs, then the variables and parameters should be defined as the quantity and quality of inputs and outputs, and the fixed and variable cost per unit of input or output.
The measurement of the variables and parameters involves collecting and processing the data that represent the values of the factors, and estimating and validating the coefficients or constants of the cost modeling function. The collection and processing of the data should be based on the sources and methods of data collection, and should ensure the validity and reliability of the data. The estimation and validation of the coefficients or constants should be based on the statistical and analytical techniques, such as regression analysis or optimization methods, and should ensure the accuracy and robustness of the estimates. For example, if the cost modeling function is a linear function of the quantity and quality of inputs and outputs, then the coefficients or constants can be estimated by using the ordinary least squares (OLS) method, and validated by using the goodness-of-fit measures, such as the R-squared or the root mean squared error (RMSE).
## 3. How to validate and test the accuracy and robustness of the cost modeling function
The validation and testing of the cost modeling function are important steps for ensuring the quality and reliability of the cost modeling function. They involve checking and verifying the assumptions, limitations, and performance of the cost modeling function, and identifying and correcting the potential errors and biases of the cost modeling function. The validation and testing of the cost modeling function can be done by using various methods and criteria, such as:
- Internal validation: This refers to the validation and testing of the cost modeling function using the same data that were used to estimate the cost modeling function. It involves checking the fit and significance of the cost modeling function, and detecting and correcting the issues of multicollinearity, heteroscedasticity, autocorrelation, or non-normality of the residuals. For example, if the cost modeling function is a linear function of the quantity and quality of inputs and outputs, then the internal validation can be done by using the OLS method and the diagnostic tests, such as the F-test, the t-test, the variance inflation factor (VIF), the Breusch-Pagan test, the Durbin-Watson test, or the jarque-Bera test.
- External validation: This refers to the validation and testing of the cost modeling function using different data that were not used to estimate the cost modeling function. It involves checking the generalizability and applicability of the cost modeling function, and detecting and correcting the issues of overfitting or underfitting the data. For example, if the cost modeling function is a linear function of the quantity and quality of inputs and outputs, then the external validation can be done by using the cross-validation or the holdout method, and the predictive measures, such as the mean absolute error (MAE), the mean absolute percentage error (MAPE), or the mean squared prediction error (MSPE).
- Sensitivity analysis: This refers to the validation and testing of the cost modeling function by changing the values of the variables and parameters of the cost modeling function, and observing the changes in the cost estimates. It involves checking the stability and sensitivity of the cost modeling function, and detecting and correcting the issues of outliers, leverage points, or influential observations. For example, if the cost modeling function is a linear function of the quantity and quality of inputs and outputs, then the sensitivity analysis can be done by using the graphical or numerical methods, such as the scatter plots, the box plots, the Cook's distance, or the DFBETAS.
## 4. How to apply the cost modeling function to different scenarios and perform sensitivity analysis
The application of the cost modeling function to different scenarios and the performance of sensitivity analysis are useful steps for using the cost modeling function to support decision making and planning. They involve using the cost modeling function to estimate the cost of different scenarios, and comparing and evaluating the results of the cost estimates. The application of the cost modeling function to different scenarios and the performance of sensitivity analysis can be done by using various methods and criteria, such as:
- Scenario analysis: This refers to the application of the cost modeling function to different scenarios that represent the possible or plausible situations or outcomes of the product or service. It involves defining and specifying the scenarios, and using the cost modeling function to estimate the cost of each scenario. For example, if the cost modeling function is a linear function of the quantity and quality of inputs and outputs, then the scenario analysis can be done by using the what-if analysis or the monte Carlo simulation, and specifying the values of the quantity and quality of inputs and outputs for each scenario.
- Break-even analysis: This refers to the application of the cost modeling function to the break-even scenario that represents the situation or outcome where the total revenue equals the total cost of the product or service.
16.How to test and evaluate the performance and accuracy of your cost forecasting model?[Original Blog]
One of the most important steps in developing a cost forecasting model is to validate its performance and accuracy. model validation is the process of checking whether the model can produce reliable and realistic results that match the actual data and the business objectives. Model validation can help you identify and correct any errors, biases, or limitations in your model, as well as assess its robustness and sensitivity to different scenarios and assumptions. In this section, we will discuss how to test and evaluate the performance and accuracy of your cost forecasting model from different perspectives, such as statistical, operational, and business. We will also provide some tips and best practices for model validation, as well as some examples of common validation techniques and metrics.
To test and evaluate the performance and accuracy of your cost forecasting model, you can follow these steps:
1. Define the validation criteria and metrics. Before you start validating your model, you need to define what are the criteria and metrics that you will use to measure its performance and accuracy. These criteria and metrics should be aligned with the purpose and scope of your model, as well as the data and methods that you used to build it. Some examples of common validation criteria and metrics are:
- Mean absolute error (MAE): This is the average of the absolute differences between the actual and forecasted costs. It measures how close the forecasts are to the actual costs, regardless of the direction of the errors. A lower MAE indicates a more accurate model.
- Mean absolute percentage error (MAPE): This is the average of the absolute percentage differences between the actual and forecasted costs. It measures how close the forecasts are to the actual costs, relative to the magnitude of the actual costs. A lower MAPE indicates a more accurate model.
- root mean square error (RMSE): This is the square root of the average of the squared differences between the actual and forecasted costs. It measures how close the forecasts are to the actual costs, with more weight given to larger errors. A lower RMSE indicates a more accurate model.
- R-squared (R2): This is the proportion of the variance in the actual costs that is explained by the model. It measures how well the model fits the data, or how much the model can reduce the uncertainty in the forecasts. A higher R2 indicates a better fit and a more reliable model.
- Confidence intervals (CI): These are the ranges of values that contain the true value of the forecasted costs with a certain probability, based on the model's assumptions and errors. They measure how precise the forecasts are, or how much uncertainty there is in the forecasts. A narrower CI indicates a more precise model.
2. Perform the validation tests. After you define the validation criteria and metrics, you need to perform the validation tests on your model. There are different types of validation tests that you can use, depending on the data and methods that you used to build your model. Some examples of common validation tests are:
- Backtesting: This is the process of comparing the model's forecasts with the actual costs that occurred in the past, using the same data and methods that were used to build the model. Backtesting can help you evaluate how well the model can replicate the historical patterns and trends in the data, as well as how stable and consistent the model's performance is over time. Backtesting can also help you identify any overfitting or underfitting issues in your model, which means that the model is either too complex or too simple to capture the true relationship between the variables. To perform backtesting, you can use different techniques, such as:
- Holdout method: This is the simplest technique, where you split the data into two sets: a training set and a test set. You use the training set to build the model, and the test set to evaluate the model's performance and accuracy. The test set should be representative of the data and the time period that you want to forecast. You can use different methods to split the data, such as random sampling, chronological sampling, or cross-validation.
- Rolling window method: This is a more advanced technique, where you use a moving window of data to build and evaluate the model. You start with a window of data that covers a certain period of time, and use it to build the model and generate forecasts for the next period. Then, you move the window forward by one period, and repeat the process. This way, you can evaluate the model's performance and accuracy over multiple periods, and see how it adapts to the changing data and conditions. You can use different methods to define the window size and the forecast horizon, such as fixed or variable length, or adaptive or non-adaptive.
- Scenario analysis: This is the process of testing the model's performance and accuracy under different scenarios and assumptions, such as changes in the input variables, the model parameters, or the external factors. scenario analysis can help you evaluate how robust and sensitive the model is to different situations and uncertainties, as well as how the model can support the decision making and planning processes. scenario analysis can also help you identify any potential risks or opportunities that may affect the forecasts. To perform scenario analysis, you can use different techniques, such as:
- Sensitivity analysis: This is the technique of changing one input variable or model parameter at a time, and observing the impact on the forecasted costs. sensitivity analysis can help you measure how much the forecasts depend on each variable or parameter, and how they vary with different values. You can use different methods to change the values, such as percentage change, absolute change, or range of values.
- What-if analysis: This is the technique of changing multiple input variables or model parameters at the same time, and observing the impact on the forecasted costs. What-if analysis can help you measure how the forecasts respond to different combinations of values, and how they compare with different scenarios or alternatives. You can use different methods to define the scenarios, such as best case, worst case, or base case, or use a scenario matrix or a scenario tree.
3. Evaluate the validation results. After you perform the validation tests, you need to evaluate the validation results and compare them with the validation criteria and metrics that you defined. You need to analyze the results from different perspectives, such as statistical, operational, and business, and see how well the model meets your expectations and requirements. You also need to interpret the results and draw conclusions and recommendations for improving or using the model. Some examples of questions that you can ask to evaluate the validation results are:
- Statistical perspective: How accurate and reliable are the model's forecasts? How well does the model fit the data? How much uncertainty and error are there in the forecasts? How consistent and stable is the model's performance over time? How robust and sensitive is the model to different scenarios and assumptions? How does the model compare with other models or methods?
- Operational perspective: How easy and efficient is it to use and maintain the model? How flexible and scalable is the model to different data sources and formats? How fast and responsive is the model to generate and update the forecasts? How transparent and explainable is the model's logic and output? How compatible and integrable is the model with other systems and tools?
- Business perspective: How relevant and useful are the model's forecasts for the business objectives and decisions? How aligned and consistent are the model's forecasts with the business strategy and plans? How actionable and feasible are the model's forecasts for the business operations and activities? How valuable and beneficial are the model's forecasts for the business performance and outcomes?
model validation is a crucial step in developing a cost forecasting model, as it can help you ensure the quality and credibility of your model and its forecasts. By following the steps and techniques that we discussed in this section, you can test and evaluate the performance and accuracy of your cost forecasting model from different perspectives, and improve or use your model accordingly. We hope that this section has provided you with some insights and guidance on how to validate your cost forecasting model. Thank you for reading!
How to test and evaluate the performance and accuracy of your cost forecasting model - Cost Forecasting Models: How to Develop and Validate Your Cost Forecasting Models