Lectures related to The cross-nested logit model

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Linear Combinations: Moment-Generating Functions

Explores moment-generating functions, linear combinations, and normality of random variables.

Generating Functions: Properties and Applications

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

Red bus/Blue bus paradox

Explores the Red bus/Blue bus paradox, nested logit models, and multivariate extreme value models in transportation.

Exponential Family Models: Statistical Inference

Covers exponential family models and their statistical properties, including canonical statistics and cumulant-generating functions.

Moment Generating Function and Multivariate Normal Distribution

Explores moment generating functions and multivariate normal distributions in probability and statistics.

Continuous Random Variables: Basics

Explores continuous random variables, cdf, pdf, convolution, and sum of dice.

Gaussian Vectors: Properties and Distributions

Explains multivariate Gaussian distribution properties and moment generating functions for random vectors.

Multivariate Normal Distribution

Covers the multivariate normal distribution, moment-generating function, and combinatorics.

Common Distributions: Moment Generating Functions

Explores common probability distributions, special distributions, and entropy concepts.

Gaussian Random Vectors

Explores Gaussian vectors, moment generating functions, independence, density functions, affine transformations, and quadratic forms.

Spherical Symmetry in Statistical Mechanics

Explores spherical symmetry in statistical mechanics and its role in phase transitions.

Regular Exponential Family Models

Explores regular exponential family models, unifying distributions like Poisson, binomial, and normal under a common framework.

Elementary Distributions Factsheet

Covers elementary distributions like Bernoulli, Binomial, Geometric, Negative Binomial, Poisson, and Multinomial.

Calculations of Expectation

Covers the calculation of expectation and variance for different types of random variables, including discrete and continuous ones.

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Linear Models: Least Squares

Explores linear models, least squares, Gaussian vectors, and model selection methods.

Derivation of the logit model MOOC: Introduction to Discrete Choice Models

Explains the derivation of the logit model in choice models, covering error terms, choice sets, and availability conditions.

Astrophysical Fluids & Plasmas

Explores astrophysical fluids, plasmas, MHD, turbulence, and plasma oscillations, including Faraday rotation for measuring cosmic magnetic fields.

Epidemics and Bootstrap Percolation in Square Lattice

Explores epidemics spread models and Bootstrap Percolation in square lattice networks, focusing on the Kolmogorov equation and probability generating functions.