Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Gaussian Mixture Regression: Examples and Analysis

Description

This lecture covers the application of Gaussian Mixture Models (GMM) in regression problems, focusing on Gaussian Mixture Regression (GMR). The instructor explains how to draw the expected results of GMR on 2D distributions fitted with GMM, considering different priors and components. Various scenarios are discussed, such as the effect of using one or two components in GMR and the convergence of regression far away from components. The lecture also delves into the analytical expressions of GMR predictions, including linear regression forms and the impact of covariance matrices on the regression outcome.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (24)

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion.

Nonlinear regression

In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations. In nonlinear regression, a statistical model of the form, relates a vector of independent variables, , and its associated observed dependent variables, . The function is nonlinear in the components of the vector of parameters , but otherwise arbitrary.

Segmented regression

Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.

Logistic regression

In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination).

Related lectures (47)

Linear Regression: Statistical Inference and Regularization

Covers the probabilistic model for linear regression and the importance of regularization techniques.

Regression Analysis: Disentangling Data

Covers regression analysis for disentangling data using linear regression modeling, transformations, interpretations of coefficients, and generalized linear models.

Supervised Learning: Linear Regression

Covers supervised learning with a focus on linear regression, including topics like digit classification, spam detection, and wind speed prediction.

Regression: Linear Models

Introduces linear regression, generalized linear models, and mixed-effect models for regression analysis.

Linear Regression: Basics and Applications