Quantization of Probability Distributions

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Gaussian Mixture Models & Noisy Signals

Explores Gaussian mixture models and denoising noisy signals using a probabilistic approach.

Generating Functions: Properties and Applications

Explores generating functions, Laplace transform, and their role in probability distributions.

Statistical Theory: Maximum Likelihood Estimation

Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.

Implicit Generative Models

Explores implicit generative models, covering topics like method of moments, kernel choice, and robustness of estimators.

Conditional Density and Expectation

Explores conditional density, expectations, and independence of random variables with practical examples.

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

Empirical Estimation: Distribution Estimation

Covers methods to estimate probability distributions from samples.

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Generalization Error

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.