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Lecture

Logistic Regression: Cost Functions & Optimization

In course

ENG-209: Data science for engineers with Python

Ce cours propose une immersion progressive et complète dans le domaine de la Data Science à travers le langage Python. Il guide les étudiants depuis la manipulation de données brutes jusqu'à la modélisation et l'extraction de connaissances utiles à partir ...

Description

This lecture covers the concept of logistic regression, focusing on different cost functions like quadratic and absolute costs, the gradient descent algorithm, and the choice of steplength. It also explains the use of the logistic sigmoid function for probability modeling and the cross entropy cost function for optimization.

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Instructors (2)

Jean-Philippe Pellet

Olivier Verscheure

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

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).

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.

Logistic function

A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation where For values of in the domain of real numbers from to , the S-curve shown on the right is obtained, with the graph of approaching as approaches and approaching zero as approaches . The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks.

Linear model

In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning. In each case, the designation "linear" is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible.

Generalized linear model

In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.

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