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Introduction to Data Science (DS 215)
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Module 9
Linear Regression and the Bias-Variance Tradeoff
1
Linear Regression with NumPy and Gradient Descent
Implement Linear Regression from scratch using NumPy, including the gradient descent optimization algorithm.
2
Bias-Variance Decomposition of Generalization Error
Mathematically decompose the generalization error into its Bias, Variance, and Irreducible Noise components.
Closed-Form Solution for Ridge Regression
Derive the closed-form solution for Ridge Regression (L2 Regularization).
4
L1 vs. L2 Regularization: Impact on Coefficients
Explain how L1 (Lasso) and L2 (Ridge) regularization affect model coefficients differently.
5
Building and Evaluating Regularized Linear Models
Project: Build and evaluate a regularized linear model to predict a continuous variable, analyzing the effect of the regularization parameter.
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Hypothesis Testing and Statistical Significance
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Classification, Clustering, and Mixture Models