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Course

COM-406: Foundations of Data Science

Lectures in this course (89)

Explores exponential families, Bernoulli distributions, parameter estimation, and maximum entropy distributions in statistical modeling.

Covers exponential families and maximum entropy distributions under moment constraints.

Covers the exponential family of distributions and the Ising model, explaining magnetism through dipoles and spins.

Covers information measures like entropy, joint entropy, and mutual information in information theory and data processing.

Explores compression in stochastic processes through injective codes and prefix-free codes.

Explores the relationship between code word length and probability distribution, focusing on designing prefix-free codes for efficient compression.

Explores sub exponential bounds and Bernstein conditions in verifying sub exponentiality.

Explores exploration bias and generalization bound in KL divergences, emphasizing mathematical proofs and implications.

Explores the relationship between empirical risk minimization and generalization error in machine learning.

Delves into the fundamentals of reinforcement learning, discussing states, actions, rewards, policies, and neural network applications.

Covers information measures, entropy, mutual information, and data processing inequality in signal representation.

Explores variational formulation for measuring information content and divergence between probability distributions.

Discusses signal representation, focusing on mathematical expressions and inequalities in signal processing.

Covers the representation of signals and signal norms in signal processing.

Covers the representation of signals using Fourier transforms and the properties of signal vectors.

Covers signal representation and manipulation techniques in different domains.

Delves into foundational data science concepts, emphasizing theory, connections between topics, and challenges in navigating techniques.

Explores Gaussian distributions, moments, and variance calculations in probability theory.

Covers the properties of signal/data representations using Fourier transformations and matrices.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.