ML & AI Foundations: From Intuition to Implementation

Explore probability and statistics foundations, including population and sample, mean, variance, central limit theorem, and Bayes theorem, and learn how loss functions and maximum likelihood guide training.

Learn how a population includes all data and how sampling yields a representative sample to train models, with random versus biased approaches guiding data collection.

The lecture explains the expected value, showing how to compute it from sample points by multiplying values by their probabilities, and why it reflects the center of mass of data.

Explore variance as a measure of data spread and covariance as a measure of how features relate, guiding data cleaning, redundancy reduction, and prep for methods like PCA.

Explore how nature follows a normal distribution, represented by mu and sigma, with variance shaping the curve. Recognize that central limit theorem offers practical shortcuts when data is normal.

Explore the central limit theorem and why averaging many data points leads to a normal distribution. See how this intuition underpins machine learning by explaining why averages yield stable data.

Learn conditional probability by calculating the probability of a given b using the intersection over b formula. See how this underpins Bayes theorem and helps minimize loss in optimization.

Learn Bayes theorem to compute probabilities like p(A|B) and p(B|A), relate A∩B, and update predictions and model parameters through iteration to improve machine learning optimization.

Explain maximum likelihood estimation by modeling data probability given theta. Update theta via Bayes theorem and select theta star by argmax of the data likelihood.

Explore linear algebra's role in machine learning for calculating, updating, and representing models, covering scalars, vectors, matrices, tensors, operations, rank, linear dependence, eigenvalues, eigenvectors, decompositions, and principal component analysis.

Explore scalar, vector, matrix, and tensor concepts, from single numbers to multi-dimensional arrays, and see how tensors power image data and gpu computations.

Master matrix operations, including addition, subtraction, and multiplication, with dimension compatibility a n×m and b z×k, yielding c n×k. See how multiply weights and inputs drive computations, with bias.

Explore rank as the number of independent rows, distinguishing independent from dependent vectors, and learn row echelon form and row operations to reveal and remove redundant information in matrices.

Explore eigenvectors and eigenvalues as invariant directions of a matrix, guiding data reduction with principal component analysis and the determinant-based method to compute them.

Explore how principal component analysis uses covariance and variance to identify eigenvectors and eigenvalues, select top components, and reduce dimensionality.

Explore calculus tailored for machine learning, blending normal, matrix, and vector calculus; learn derivatives and gradients essential for working with vectors and matrices.

Learn how derivatives capture changes with respect to another variable, extending to multi-dimensional inputs. Define gradients as partial derivatives that show how each input influences the output.

Compute the mean squared error loss between y and y dash, then update theta via gradient descent with a learning rate to minimize that loss, as captured by backpropagation.

Apply the chain rule to compute dz/dt by multiplying dz/dx, dx/dy, and dy/dt, when z relates to x, x to y, and y to t.

Explore how backpropagation updates model parameters through gradients, loss, and activation functions to introduce non-linearity, improve predictions, and train deep learning systems from intuition to implementation.

Explore how gradient descent uses the loss curve and its slope dl/dtheta to descend from any starting point toward local minima, and how local minima differ from global minima.

Learn how convexity guarantees a local and global minimum, enabling gradient descent to reduce loss to its lowest value, unlike concave models that cannot reach high accuracy.

Explore Python basics like dynamic typing, variables, zero-indexed lists, and pandas. Leverage NumPy for arrays, dot products and matrix multiplication, and gradient descent with MSE loss to update weights.

Explore the history from the perceptron to deep learning and transformers, compare neural networks, SVMs, decision trees, and regressions, and review training basics, regularization, standardization, and ensembles.

Explain how ai, ml, and deep learning relate as a hierarchical, interconnected family, with IoT devices as ai examples, and how training algorithms power classical ml methods.

Explore supervised, unsupervised, and reinforcement learning, comparing input-output data and environment-driven feedback. See real-world examples from images, games, and stock markets.

Differentiate regression from classification by linking continuous outputs to regression and discrete outputs to classification, using analog versus digital signal analogies to show when to predict numbers or categories.

Explore how training, validation, and test sets separate learning from memorization in neural networks, and how weights, biases, and hyperparameters (theta, lambda) are tuned during validation.

Prevent overfitting by stopping training when validation loss rises, and apply regularization methods like L2 (ridge) or L1 (lasso) to penalize large weights and improve generalization.

Learn how one-hot encoding converts categorical features like climate into separate binary features, avoiding arbitrary ordering and handling multiple categories per instance.

Learn linear regression as a foundational method, minimize mean squared error with gradient descent to update weights and biases, and note its limits with non-linear and multivariate data.

Evaluate machine learning models using a confusion matrix, detailing true/false positives and negatives, and compare accuracy, precision, recall, and F1 score with spam and cancer examples.

Explore how a decision tree asks questions to predict health outcomes using features such as age, city, and BMI. Build a simple if-else tree with root and branches.

Learn how decision trees train by building the tree and test by traversing it. Understand how information gain or gini impurity guides root node selection and helps curb overfitting.

Explain entropy and information gain, show how to compute them for features, and illustrate constructing a decision tree by selecting the highest information gain at each split.

Explore Gini impurity in decision trees, learn to compute Gini for a node, apply weighted averages, and compare its effectiveness with information gain for optimal splits.

Understand how ensembles like bagging and boosting address the problem of large decision trees with many features and the associated computational and memory demands, including potential hallucinations.

Discover how bagging improves accuracy by creating multiple data sets, training diverse decision trees, and combining outputs by voting or averaging, exemplified by the random forest model.

Boosting is sequential, building an ensemble of models that focus on previously wrong outputs by increasing the weight of misclassified data points, while keeping the total weight one.