Mathematics For Machine Learning And Llms

How is math used in AI

What you'll learn

Machine Learning mathematics

linear algebra, statistics, probability and calculus for machine learning

How algorithms works

How algorithms are parametrizided

Requirements

Basic notions of machine learning

Description

Machine Learning is one of the hottest technologies of our time! If you are new to ML and want to become a Data Scientist, you need to understand the mathematics behind ML algorithms. There is no way around it. It is an intrinsic part of the role of a Data Scientist and any recruiter or experienced professional will attest to that. The enthusiast who is interested in learning more about the magic behind Machine Learning algorithms currently faces a daunting set of prerequisites: Programming, Large Scale Data Analysis, mathematical structures associated with models and knowledge of the application itself. A common complaint of mathematics students around the world is that the topics covered seem to have little relevance to practical problems. But that is not the case with Machine Learning.This course is not designed to make you a Mathematician, but it does provide a practical approach to working with data and focuses on the key mathematical concepts that you will encounter in machine learning studies. It is designed to fill in the gaps for students who have missed these key concepts as part of their formal education, or who need to catch up after a long break from studying mathematics.Upon completing the course, students will be equipped to understand and apply mathematical concepts to analyze and develop machine learning models, including Large Language Models.

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 The Learning Diagram

Lecture 3 Python

Section 2: Types of Learning

Lecture 4 Supervised Learnimg

Lecture 5 Unsupervised Learning

Lecture 6 Reinforcement Learning

Lecture 7 When to Use and Not to Use ML

Lecture 8 How to chose ML Algorithms

Section 3: Data Preparation

Lecture 9 Preeliminar Analysis

Lecture 10 The Target Variable

Lecture 11 Missing Data

Lecture 12 Log Transformation - Homocedasticity

Lecture 13 Outliers and Anomaly Detection

Lecture 14 Data Transformation

Lecture 15 Data Transformation (cont.)

Section 4: Statistics in the Context off ML

Lecture 16 Significant Differences

Lecture 17 Descriptive and Inferential Statistics

Section 5: Descriptive Statistics

Lecture 18 Variables and Metrics

Lecture 19 Correlation and Covariance

Section 6: Probabilities for ML

Lecture 20 Uncertainity

Lecture 21 Frquentist versus Bayesian Probabilities

Lecture 22 Random Variables and Sampling

Lecture 23 Sampling Spaces

Lecture 24 Basic Definitions of Probabilities

Lecture 25 Axions, Theorems, Independence

Lecture 26 Conditional Probability

Lecture 27 Bayes Theorem and Naive Bayes Algorithm

Lecture 28 Expectation, Chance and Likelihood

Lecture 29 Maximum Likelihood Estimation (MLE)

Lecture 30 Simulations

Lecture 31 Monte Carlo Simulation, Markov Chainn

Lecture 32 Probability Distributions

Lecture 33 Families of Distributions

Lecture 34 Normal Distribution

Lecture 35 Tests for Normality

Lecture 36 Exponential Distribution

Lecture 37 Weibull Distribution and Survival Analysis

Lecture 38 Binomial Distribution

Lecture 39 Poisson Distribution

Section 7: Statiscs Tests

Lecture 40 Hypothesis Testing

Lecture 41 The p- value

Lecture 42 Critical Value, Significance, Confidence, CLT, LLN

Lecture 43 Z and T Tests

Lecture 44 Degrees of Freedom and F statistics

Lecture 45 ANOVA

Lecture 46 Chi Squared Test

Lecture 47 Statistical Power

Lecture 48 Robustness and Statistical Sufficiency

Section 8: Time Series

Lecture 49 Times Series Decommposition

Lecture 50 Autoregressive Models

Lecture 51 Arima

Section 9: Linear ad Non Linear Models

Lecture 52 Linear and Non Linear Models

Section 10: Linear Algebra for ML

Lecture 53 Introduction to Linear Algebra

Lecture 54 Types of Matrices

Lecture 55 Matrices Operations

Lecture 56 Linear Transformations

Lecture 57 Matrix Decomposition and Tensors

Section 11: Calculus for ML

Lecture 58 Functions

Lecture 59 Limits

Lecture 60 The Derivative

Lecture 61 Calculating the Derivative

Lecture 62 Maximum and Minimum

Lecture 63 Analitical vs Numerical Solutions

Lecture 64 Numerical and Analytic Solution

Lecture 65 Gradient Descent

Section 12: Distances, Similarities, knn and k means

Lecture 66 Distance Measurements

Lecture 67 Similarities

Lecture 68 Knn and K means

Lecture 69 Distances in Python

Section 13: Training, Testing ,Validation

Lecture 70 Training, Testin, Validation

Lecture 71 Training, Testing, Validation (cont)

Section 14: The Cost Function

Lecture 72 The Cost Function

Lecture 73 Cost Function for Regression and Classification

Lecture 74 Minimazing the Cost Function with Gradient Descent

Lecture 75 Batch annd Stochastic Gradient Descent

Section 15: Bias and Variance

Lecture 76 Bias and Variance Introduction

Lecture 77 Complexity

Lecture 78 Regularization

Lecture 79 Regularization (Cont)

Section 16: Parametric andd Non Parametric Algorithms

Lecture 80 Parametric and Non Parametric Algorithms

Section 17: Learning Curves

Lecture 81 Learning Curves

Lecture 82 Learning Curves in Python

Section 18: Dimensionality Reduction

Lecture 83 PCA and SCD

Lecture 84 Eigenvectors and Eigenvalues

Lecture 85 Dimensionality Reduction in Python

Section 19: Entropy and Information Gain

Lecture 86 Entropy and Information Gain

Lecture 87 Entropy and Information Gain (cont)

Section 20: Linear Regression

Lecture 88 Linear Regression

Lecture 89 Linear Regression (cont)

Lecture 90 Polinomial Regression

Section 21: Classification

Lecture 91 Logistic Function

Lecture 92 Generalized Linear Models (GLM)

Lecture 93 Decision Boundaries

Lecture 94 Confusion Matrix

Lecture 95 ROC and AUC

Lecture 96 Visualization of Class Distribution

Lecture 97 Precision and Recall

Section 22: Decision Trees

Lecture 98 Introduction to Decision Trees

Lecture 99 Gini Index

Lecture 100 Hyperparameters

Lecture 101 Decision Trees in Python

Section 23: Suport Vector Machines

Lecture 102 Introduction to SVMs

Lecture 103 Introduction to SVMs (cont)

Lecture 104 Mathematics of SVMs

Lecture 105 SVM in Python

Section 24: Ensemble Algorithms

Lecture 106 Wisdom of the Crowds

Lecture 107 Bagging and Random Forest

Lecture 108 Adaboost, Gradient Boosting, XGBoosting

Section 25: Natural Language Processing

Lecture 109 Introduction to NLP

Lecture 110 Tokenization and Embeddings

Lecture 111 Weights and Representation

Lecture 112 Sequences and Sentiment Analysis

Section 26: Neural Networks

Lecture 113 Mathematical Model of Artificial Neuron

Lecture 114 Activation Functions

Lecture 115 Activation Functions (cont)

Lecture 116 Weights and Bias Parameters

Lecture 117 Feedforward and Backpropagation Concepts

Lecture 118 Feedforward Process

Lecture 119 Backpropagation Process

Lecture 120 Recurent Neural Networks (RNN)

Lecture 121 Convolution Neural Networks (CNN)

Lecture 122 Convolution Neural Networks (CNN) (cont)

Lecture 123 Seq2Seq and Aplications of NN

Section 27: Large Language Models

Lecture 124 Generative vs Descriptive AI

Lecture 125 LLMs Properties

Section 28: Transformers

Lecture 126 Introduction to Transformers

Lecture 127 Training and Inference

Lecture 128 Basic Arquitecture of Transformers

Lecture 129 Encoder Workflow

Lecture 130 Sel Attention

Lecture 131 Multi-Head Attention

Lecture 132 Normalization and Residual Connections

Lecture 133 Decoder

Lecture 134 Types of Transformers Arquitecture

Data Scientists and AI professionals