Monthly Archives: May 2024
Causal ML Book: Summary of Key Concepts from Chapter 5
Causal inference is a cornerstone of research and analysis in many fields, from economics to medicine to social sciences. Chapter 5 of the Causal ML Book delves into advanced methodologies that ensure comparability between treatment and control groups, which is crucial for valid causal inference. This post will summarize the key concepts discussed in Chapter…
Understanding Neyman Orthogonality in High-Dimensional Linear Regression
Introduction In the realm of data science and statistics, accurately determining the relationships between variables is essential, particularly when dealing with high-dimensional data. High-dimensional settings, where the number of predictors (p) is large relative to the number of observations (n), pose significant challenges for traditional statistical methods. This blog post delves into the concept of…
Penalized Regression Methods: Lasso, Ridge, Elastic Net, and Lava Explained
In the realm of high-dimensional data analysis, traditional linear regression techniques often fall short due to the presence of numerous predictors, which can lead to overfitting and poor predictive performance. To address these challenges, penalized regression methods introduce penalties to the regression model, effectively shrinking the coefficients and providing a balance between model complexity and…
Balancing Complexity and Accuracy: Variable Selection in Lasso
In Lasso regression, a new predictor (regressor) is included in the model only if the improvement in predictive accuracy (marginal benefit) outweighs the increase in model complexity (marginal cost) due to adding the predictor. This helps prevent overfitting by ensuring that only predictors that contribute significantly to the model’s performance are included. Mathematical Explanation Let’s…
Why Lasso Does Not Guarantee Correct Variable Selection? A Thorough Explanation
While Lasso regression helps in variable selection by shrinking some coefficients to zero, it does not guarantee that it will select the exact set of true predictors. This limitation is especially pronounced in situations where predictors are highly correlated or when the true model does not exhibit strong sparsity. Mathematical Explanation Let’s consider the linear…
Approximate Sparsity Explained: Why should we use Lasso with high dimensional data?
Approximate sparsity refers to the situation in a high-dimensional regression model where only a small number of predictors (regressors) have significant (large) coefficients, while the majority of predictors have coefficients that are either zero or very close to zero. This concept is crucial in high-dimensional settings, where the number of predictors pp is large, often…
Singular Value Decomposition (SVD): Definitions and Applications In Python?
Introduction Singular Value Decomposition (SVD) is a fundamental technique in linear algebra with numerous applications in data science, machine learning, and various scientific fields. This comprehensive guide delves into the mathematical foundations of SVD, its importance, and its practical applications, providing intuitive examples to help you understand this powerful tool. 1. What is SVD? Mathematical…
Understanding OLS in High-Dimensional Settings: Insights and Practical Implications
In the world of data science and machine learning, linear regression stands as a foundational tool for predictive modeling. Despite its simplicity, its proper implementation, especially in high-dimensional settings, demands a nuanced understanding. This blog post dives into the intricacies of linear regression, focusing on how dimensionality impacts wage gap estimates and the challenges associated…