This page provides a list of topics and resources to build a good undergraduate level foundation in various topics related to Machine Learning, Linear Algebra, Artificial Intelligence, Information Retrieval, Social Networks, Deep Learning and Statistics

Foundation/Basics

Deep Learning - NPTEL IIT M
MIT 6.S191: Introduction to Deep Learning
Machine Learning: Tom Mitchell
Various Optimization Algorithms For Training Neural Network | Towards Data Science
Activation Functions in Neural Networks | by SAGAR SHARMA | Towards Data Science
Common Loss functions in machine learning | by Ravindra Parmar | Towards Data Science
Artificial Intelligence - All in One - YouTube
DeepLearningAI - YouTube

Conceptual Introduction

• Perceptron - What is a perceptron, how does it learn linear functions, What type of logical gates can it learn? What about XOR?
• Linear functions vs. non-linear functions
• How to deal with non-linearity? Activation functions - Sigmoid, RELU, TanH (Where to use these activations - binary classification, multi-class classification, softmax type situations, regression)
• Regression vs. classification

Math behind “Learning”

• Minimization of loss
• Dynamic Learning Rate
• Backpropagation math
• Difference between overfitting and under-fitting - What happens when u can fully learn the training data but cannot fit to test data
• Momentum - how to gradually converge to the target function that you are trying to learn
• Exponential smoothing - how is momentum a smoothing function?
• Nesterov’s accelerated gradient - Look ahead momentum
• AdaGrad, RMSProp, Adam Optimizers
• Different Types of Errors
• Mean Squared Error
• L1 Loss, L2 Loss
• Regularization - What is it? Lasso and Ridge
• Dropout - why is it necessary
• Batch Normalization vs. Layer Normalization
• Binary Cross Entropy
• What is Entropy?
• KL Divergence - How are two distributions similar, different? What is the distance between two distributions
• Precision, Accuracy, Recall, F1 Score, ROC Curve

Handling Images, Graphics (Computer Vision)

A Gentle Introduction to Generative Adversarial Networks (GANs) - MachineLearningMastery.com
Unsupervised Feature Learning and Deep Learning Tutorial (stanford.edu)
Convolutional Neural Networks, Explained | by Mayank Mishra | Towards Data Science

• Autoencoders - Reducing dimensions, Minimizing Standard Deviation + KL Divergence - Variational Autoencoders
• Denoising Autoencoders
• Convolutional Neural Networks - 2D Filters, 3D Filters
• Activation Map, Max Pooling, Average Pooling
• 3D Filters, 2D Filters
• Vanishing Gradient
• Generative Adversarial Networks
• Fine tuning and Transfer Learning
• YOLO models
• DALL-E
• When do GANS achieve convergence - Nash Equilibrium. Why is it adversarial training?

Artificial Intelligence

MIT 6.034 Artificial Intelligence, Fall 2010
Python implementation of algorithms from Russell And Norvig's "Artificial Intelligence - A Modern Approach":Acknowledgements (berkeley.edu)
Artificial Intelligence: A Modern Approach Russell and Norvig 3rd Edition

• Solving problems by searching for the solution in a space of solutions
• Intelligent agents - Rationality
• Uninformed search - DFS, BFS, Depth limited search, iterative deepening search
• Search strategies - Greedy heuristic search, A-Star search
• Local Search - Hill Climbing search, Stochastic Hill Climbing, Simulated annealing, beam search, gradient descent, Genetic Algorithm (Important)
• Adversarial search, games, Alpha Beta Pruning, Minimax games - Tic Tac Toe
• Constraint Satisfaction problems - Map Coloring with constraints
• Propositional Logic vs. First Order Logic

Python Tools for ML

Blog (machinelearningmastery.com)
Towards Data Science

• Pytorch - Different types of Neural Networks
• Tensorflow/Keras
• SkLearn - other ML Models
• Huggingface - pretrained language models
• Spacy, NLTK - NLP tools

Linear Algebra and Stats

Introduction to Linear Algebra, 4th Edition (aiu.edu)
A First Course in Probability: Sheldon Ross
Probability, Random Variables, Random Signal Principles: Peyton Z Peebles

• Bayesian stuff
• Joint Probability
• Correlation and Covariance
• Conditional Probability and Independence
• Multivariate Random Variable
• Expectation, Binomial RV, Gaussian RV, Poisson RV
• Identity, Inverse, Diagonal, Orthogonal, Orthonormal matrices
• Eigen Values and Eigen Vectors
• EigenDecomposition
• Singular Value Decomposition
• Sampling data
• Maximum Likelihood Estimates
• Maximum A-Posteriori Estimate
• Bias-Variance Tradeoffs
• Hypothesis Testing and Statistical Significance

Handling Text

Introduction to Information Retrieval (stanford.edu)
PageRank algorithm, fully explained | by Amrani Amine | Towards Data Science
CS 230 - Recurrent Neural Networks Cheatsheet (stanford.edu)

• Representing text - Term Frequency, Inverse Document Frequency
• Bigrams, Tri-grams
• Vector Space Model
• Inverted Index - What is it, how is it useful for querying large text corpora
• Minimum edit distance - how to deal with spelling mistakes while querying text (Not ML)
• Page Rank Algorithm for Google page ranking (Not ML, tangentially related to text ML)
• Dimensionality reduction - Principal Component Analysis (PCA)
• Latent Semantic Indexing
• Contextualized word representation (Meaning changes with context - bear:animal, bear:tolerate) - Word2Vec, BERT, GPT-2, GPT-3, ChatGPT, BARD, Bing AI
• Glove embeddings - static embeddings for words
• Non-Negative Matrix Factorization - optimization problem with Frobenius norm
• Recurrent Neural Networks - Image Captioning, Language translation
• LSTM, GRU

Handling Graphs and Networks

• Walks, Paths, Euler circuit, Hamiltonian Circuit, Degrees
• Connected graph, Directed Acyclic Graph, Bipartite Graph, Tree
• Reciprocity, transitivity
• Clustering Coefficient
• Graph Neural Networks
• Random Networks - Erdos Renyi
• Six Degrees of Separation
• Power Law degree distribution
• Homophily
• Watts and Strogatz network
• Barabasi Albert Network
• Scale Free Networks
• Zipf Law
• Communities in graphs, cliques, clustering - hierarchical, Girvan Neumann, Louvain, Clique Percolation

Game Theory

Game Theory textbook (ucdavis.edu)
Game Theory in Artificial Intelligence | by Pier Paolo Ippolito | Towards Data Science

• Utility function, payoff function, Reinforcement Learning, Q-Learning
• Strict Dominance, weak dominance
• Prisoner’s Dilemma, Pareto Superior, Pareto Optimal
• Strictly dominated strategy vs. Weakly dominated Strategy
• Nash Equilibrium, Pareto Optimal, Social Optimal
• Hawk-Dove Games
• Mixed Strategies

Machine Learning beyond Neural Networks (Scikit-Learn)

Support Vector Machine — Introduction to Machine Learning Algorithms | by Rohith Gandhi | Towards Data Science
Naive Bayes Classifier. What is a classifier? | by Rohith Gandhi | Towards Data Science
Hidden Markov Model. Elaborated with examples | Towards Data Science

Support Vector Machines

• What is a margin in classification
• What are support vectors?
• Primal Function, max margin
• Min-max of Lagrangian
• Adding a slack variable to allow non-separable datasets
• Projecting to higher dimensions
• Kernel Function
• Multi-class SVM - one vs. one, one-vs-rest

Naive Bayes Classifier

• Probabilistic classification
• Likelihood
• MLE
• Laplace Smoothing and Laplace Correction

Decision Trees and Random Forests

• Entropy and Information Gain
• Gini Gain
• Pruning to prevent Overfitting, Post Pruning
• Reduced Error Pruning
• K-Fold Cross Validation
• ID3 Algorithm

K-Nearest Neighbors

• What is a nearest neighbor
• Euclidean Distance, Manhattan Distance, Mahalanobis Distance
• 1NN vs K-NN

Logistic Regression
Ensemble Learning

• Ensemble Learning
• Boosting and Bagging
• AdaBoost Algorithm
• Random Forests

Clustering

• K-Means Clustering
• Unsupervised learning
• How to cluster based on centroids
• Hierarchical Clustering
• Probabilistic Clustering
• Gaussian Mixture Models

Hidden Markov Models

• Hidden Markov Models
• Markov Chains
• Discrete Markov processes
• Viterbi Algorithm
• Baum Welch Algorithm
• Markov Chain Monte CarloP

Market Basket Analysis

• Expectation Maximization
• Estimating when data is hidden
• Purity
• Normalized Mutual Information Gain

Genetic Algorithms
Particle Swarm Optimization

Advanced Topics

Advanced Math/algorithms for “Learning”

randomized-algorithms-motwani-and-raghavan.pdf (wordpress.com)
Convex Optimization: Boyd Vandenberghe

• What is a convex function
• Jensen's Inequality
• Convex Optimization
• Smooth Optimization
• Min-Cut Algorithm, Las Vegas and Monte Carlo Algorithms
• Markov and Chebyshev Inequalities
• Concentration Bounds - Chernoff, Hoeffdings
• Max Sat Problems, Expanding Graphs
• Lovasz Local Lemma
• Fingerprinting and Frievalds
• Submodularity
• Monotone Functions
• Hessians, Cauchy Schwartz Inequality
• Constrained Optimization vs. Unconstrained Optimization
• Pseudo Inverse of a matrix
• Explainability - LIME and SHAP Functions

More ML Topics

Pattern Recognition and Machine Learning (microsoft.com)

• Hypothesis Space, Instance Space
• Version Space
• Inductive Bias, Expressivity, Decision Boundaries
• Mistake Bound Learning
• Polynomial Kernels, Gaussian Kernels
• Empirical Risk Minimization
• Sub Gradient Descent
• PAC Learning - Probably Approximately Correct
• K-CNF
• Agnostic Learning
• VC Dimensions - Shattering

Current Research Topics

Attention and Transformer Models. “Attention Is All You Need” was a… | by Helene Kortschak | Towards Data Science
What are Stable Diffusion Models and Why are they a Step Forward for Image Generation? | by J. Rafid Siddiqui, PhD | Towards Data Science
Understanding Vector Quantized Variational Autoencoders (VQ-VAE) | by Shashank Yadav | Medium
Neural Operator (zongyi-li.github.io)
NeRF: Neural Radiance Fields (matthewtancik.com)
Michael Black | Perceiving Systems - Max Planck Institute for Intelligent Systems (mpg.de)
Distill - Machine Learning Journal 2016-2021

• Transformers - Attention based models, Cross attention
• Sparse Transformers - Learning vs. Memorization
• Stable Diffusion
• Neural Operators
• VQ-VAE
• Cross Modal Learning
• Neural Radiance Fields (NERF)
• Mel-Spectrograms Synthesis through Diffusion
• Learning Embeddings