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

Lecture

Decision Rules: Maximum a Posteriori Decision

In course

EE-311: Fundamentals of machine learning

Ce cours présente une vue générale des techniques d'apprentissage automatique, passant en revue les algorithmes, le formalisme théorique et les protocoles expérimentaux. ...

Description

This lecture covers the possible decision rules based on likelihood ratios, focusing on the maximum a posteriori decision. It explains how to select the class with the highest probability given an observation, emphasizing the concept of posterior maximization. The lecture also introduces the concept of true likelihood ratio and its calculation, highlighting its importance in decision-making processes.

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

Instructors (2)

François Fleuret

Michael Stefan Daniel Liebling

Official source

Related concepts (16)

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

Likelihood-ratio test

In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models, specifically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods. If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error. Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero.

Likelihood principle

In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density function considered as a function of its distributional parameterization argument.

Maximum a posteriori estimation

In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior distribution (that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Related lectures (46)

Likelihood Ratio Test: Hypothesis Testing

Covers the Likelihood Ratio Test and hypothesis testing methods using Maximum Likelihood Estimators.

Linear Regression: Statistical Inference Perspective

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

Likelihood Ratio Test: Detection & Estimation

Covers the likelihood ratio test for detection and estimation in statistical analysis.

Detection & Estimation

Covers binary classification, hypothesis testing, likelihood ratio tests, and decision rules.

Discriminant Analysis: Bayes Rule