Gradient Descent and Linear Regression

We implement linear regression using gradient descent, a general optimization technique which in this case can find the global minimum.

Text Classification with Naive Bayes and NLTK

In the last post we talked about the theoretical side of naive Bayes in text classification. Here we will implement the model in Python, both from …

Bayesian Inference for the Poisson Model

This lecture discusses Bayesian inference for the Poisson model, including conjugate prior specification, a different way to specify a "non-informative" prior, and relevant posterior summaries.

Naive Bayes

We talk about one of the simplest classification methods, naive Bayes classifiers, and its applications in text classification. It's not really machine learning as we only need a single pass through the data to compute necessary values.

Bayesian Inference for the Binomial Model

The general procedure for Bayesian analysis. We use two different prior models and compare the resulting posteriors (visually and mathematically).

Frequentist Inference

A simple problem in the binomial setting solved under the frequentist view of statistics.

Introduction to Bayesian Statistics

First lecture of the course, and a brief history of Bayesian statistics.

Conditional Heteroscedastic Models

Introducing volatility to our time series models. The properties and building procedures of ARCH and GARCH models are discussed.

Eigenvalues and Eigenvectors

Probably the most important lecture in this course -- we start from the calculation of eigenvalues and eigenvectors, and move on to related topics such as the eigendecomposition, singular value decomposition, and the Moore-Penrose inverse.

Spectral Analysis

We talk about a method that helps us find the periodicity of a time series -- the spectral density.