Machine learning and artificial intelligence

  Chapter 8: Linear Regression Linear Regression is a fundamental machine learning technique used for predicting a continuous target variable based on one or more features. It models the relationship between the dependent variable and one or more independent variables using a linear equation. In this chapter, we will explore the mathematical formulation of Linear Regression, its implementation in Python, and provide a practical example. Mathematical Formulation In its simplest form, Linear Regression involves a single feature. The relationship between the feature x x x and the target variable y y y can be expressed using the following linear equation: y = β 0 + β 1 x + ϵ y = \beta_0 + \beta_1 x + \epsilon y = β 0 ​ + β 1 ​ x + ϵ Where: y y y is the dependent variable (target). x x x is the independent variable (feature). β 0 \beta_0 β 0 ​ is the y-intercept of the line. β 1 \beta_1 β 1 ​ is the slope of the line. ϵ \epsilon ϵ represents the error term (residuals), which acco...

  Machine Learning Chapter 7: Bias-Variance Tradeoff In machine learning, understanding the bias-variance tradeoff is crucial for building effective models. This chapter delves into the concepts of bias and variance, explores their implications, and provides practical examples with mathematical formulas and Python code. 1. Understanding Bias and Variance Bias refers to the error introduced by approximating a real-world problem, which may be complex, by a simplified model. High bias can cause an algorithm to miss the important patterns, leading to underfitting. Variance refers to the error introduced by the model’s sensitivity to small fluctuations in the training set. High variance can lead to overfitting, where the model performs well on the training data but poorly on unseen data. Bias-Variance Tradeoff : There is a tradeoff between bias and variance. A model with low bias has high variance, and vice versa. The goal is to find a balance where both bias and variance are minimize...