Machine learning and artificial intelligence

  Machine Learning: Chapter 6 - Statistical Decision Theory: Classification Introduction Statistical decision theory forms the backbone of many machine learning techniques, especially in the domain of classification. Classification is a fundamental problem in machine learning, where the goal is to assign a label to a given input based on its features. In this article, we will delve into the mathematical foundation of classification using statistical decision theory, explore key concepts, and provide Python code to illustrate these ideas. 1. The Basics of Classification Classification is the task of predicting a discrete label y y y (such as a class) given an input vector x \mathbf{x} x . The input vector x \mathbf{x} x represents the features of the data, and y y y is the class label. In the context of statistical decision theory, we aim to find a decision rule that minimizes the probability of misclassification. 2. Probability Distributions in Classification In statistical deci...

  Machine Learning (Chapter 5): Statistical Decision Theory - Regression Introduction Statistical Decision Theory is a framework used to make decisions under uncertainty. In the context of machine learning, it helps in choosing the best model or hypothesis given the data and associated risks or costs. Regression, a fundamental concept in machine learning, deals with predicting a continuous output based on input features. In this article, we explore regression within the framework of Statistical Decision Theory, focusing on the mathematical foundations and practical implementation in Python. 1. Basics of Statistical Decision Theory Statistical Decision Theory involves selecting a decision function δ ( X ) \delta(X) δ ( X ) that minimizes a loss function L ( Y , δ ( X ) ) L(Y, \delta(X)) L ( Y , δ ( X )) , where Y Y Y is the true output, and X X X is the input feature vector. The objective is to minimize the expected loss, also known as risk, given by: R ( δ ) = E [ L ( Y , δ ( X ...

  Machine Learning (Chapter 4): Reinforcement Learning Introduction Reinforcement Learning (RL) is a subfield of Machine Learning where an agent learns to make decisions by performing certain actions and observing the rewards or penalties resulting from those actions. Unlike supervised learning, where the model learns from a labeled dataset, RL focuses on learning from interaction with an environment. This interaction is modeled as a Markov Decision Process (MDP), where the agent's goal is to maximize cumulative rewards over time. Key Concepts in Reinforcement Learning Agent : The learner or decision-maker. Environment : The world through which the agent moves and interacts. State (S) : A representation of the current situation of the agent in the environment. Action (A) : The choices the agent can make in each state. Reward (R) : The feedback from the environment after the agent takes an action. Policy (π) : A strategy used by the agent to determine its actions based on the curren...