This lecture introduces the core concepts of dimensionality reduction.

This lecture covers the application of dimensionality reduction applied to multi-dimensional neural recordings using brain-computer interfaces with simultaneous spike recordings.

Question and Answer Session for participants in the Americas.

Question and Answer Session 2 for participants in Asia and Australia.

Question and Answer Session for participants in Africa and Europe.

This is the first of a series of tutorials on fitting models to data. In this tutorial, we start with simple linear regression, using least squares optimization.

In this tutorial, we will use a different approach to fit linear models that incorporates the random 'noise' in our data.

This tutorial discusses how to gauge how good our estimated model parameters are.

In this tutorial, we will generalize the regression model to incorporate multiple features.

This tutorial teaches users about the bias-variance tradeoff and see it in action using polynomial regression models.

This tutorial covers how to select an appropriate model based on cross-validation methods. 

This is a tutorial covering Generalized Linear Models (GLMs), which are a fundamental framework for supervised learning. In this tutorial, the objective is to model a retinal ganglion cell spike train by fitting a temporal receptive field: first with a Linear-Gaussian GLM (also known as ordinary least-squares regression model) and then with a Poisson GLM (aka "Linear-Nonlinear-Poisson" model). The data you will be using was published by Uzzell & Chichilnisky 2004.

This tutorial covers the implementation of logistic regression, a special case of GLMs used to model binary outcomes. In this tutorial, we will decode a mouse's left/right decisions from spike train data.

This tutorial covers multivariate data can be represented in different orthonormal bases.

This tutorial covers how to perform principal component analysis (PCA) by projecting the data onto the eigenvectors of its covariance matrix.

To quickly refresh your knowledge of eigenvalues and eigenvectors, you can watch this short video (4 minutes) for a geometrical explanation. For a deeper understanding, this in-depth video (17 minutes) provides an excellent basis and is beautifully illustrated.

This tutorial covers how to apply principal component analysis (PCA) for dimensionality reduction, using a classic dataset that is often used to benchmark machine learning algorithms: MNIST. We'll also learn how to use PCA for reconstruction and denoising.

You can learn more about MNIST dataset here.

This tutorial covers how dimensionality reduction can be useful for visualizing and inferring structure in your data. To do this, we will compare principal component analysis (PCA) with t-SNE, a nonlinear dimensionality reduction method.

This lecture introduces the concept of Bayesian statistics and explains why Bayesian statistics are relevant to studying the brain.

This tutorial provides an introduction to Bayesian statistics and covers developing a Bayesian model for localizing sounds based on audio and visual cues. This model will combine prior information about where sounds generally originate with sensory information about the likelihood that a specific sound came from a particular location. The resulting posterior distribution not only allows us to make optimal decision about the sound's origin, but also lets us quantify how uncertain that decision is. Bayesian techniques are therefore useful normative models: the behavior of human or animal subjects can be compared against these models to determine how efficiently they make use of information.

In this tutorial, we will use the concepts introduced in Tutorial 1 as building blocks to explore more complicated sensory integration and ventriloquism!