Lecture

Regularization in Machine Learning

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the concepts of overfitting, regularization, and cross-validation in machine learning. It explains how to handle nonlinear data, polynomial curve fitting, feature expansion, kernel functions, and kernelized algorithms. The instructor discusses the importance of model complexity, k-Nearest Neighbors, and the impact of different k values on training and test errors. The lecture also delves into cross-validation methods like leave-one-out and k-fold, highlighting their advantages and drawbacks. It concludes with demonstrations on ridge regression, kernel ridge regression, and the incorporation of regularization in logistic regression and support vector machines.

Official source

Ontological neighbourhood

Statistics

Data analysis: Cross-validation, Regression analysis

Related concepts (32)

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.

Regularized least squares

Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting solution. RLS is used for two main reasons. The first comes up when the number of variables in the linear system exceeds the number of observations. In such settings, the ordinary least-squares problem is ill-posed and is therefore impossible to fit because the associated optimization problem has infinitely many solutions.

Ridge regression

Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. It is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters.

Bayesian linear regression

Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often labelled ) conditional on observed values of the regressors (usually ).

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 (64)

Machine Learning Fundamentals: Regularization and Cross-validation

Explores overfitting, regularization, and cross-validation in machine learning, emphasizing the importance of feature expansion and kernel methods.

Nonlinear ML Algorithms

Introduces nonlinear ML algorithms, covering nearest neighbor, k-NN, polynomial curve fitting, model complexity, overfitting, and regularization.

Overfitting, Cross-validation & Regularization

Explores model complexity, overfitting, and the role of cross-validation and regularization in machine learning.

Cross-Validation: Techniques and Applications

Explores cross-validation, overfitting, regularization, and regression techniques in machine learning.

Cross-validation & Regularization