Data Classification: Gaussian Mixture Models

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Topic Models: Understanding Latent Structures

Explores topic models, Gaussian mixture models, Latent Dirichlet Allocation, and variational inference in understanding latent structures within data.

Linear Regression: Statistical Inference Perspective

Explores linear regression from a statistical inference perspective, covering probabilistic models, ground truth, labels, and maximum likelihood estimators.

Gaussian Mixture Models & Noisy Signals

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

Clustering & Density Estimation

Covers dimensionality reduction, clustering, and density estimation techniques, including PCA, K-means, GMM, and Mean Shift.

Gaussian Mixture Model: EM final form

Explains the E-step and M-step calculations in the Gaussian Mixture Model, including the pseudocode of the EM algorithm.

Sampling: conditional maximum likelihood estimation

Covers Conditional Maximum Likelihood estimation, contribution to likelihood, and MEV model application in choice-based samples.

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.

Estimation Methods

Covers various methods for estimating model parameters, such as method of moments and maximum likelihood estimation.

Fisher Information, Cramér-Rao Inequality, MLE

Explains Fisher information, Cramér-Rao inequality, and MLE properties, including invariance and asymptotics.