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Lecture

Logistic Regression: Probabilistic Interpretation

In course

ME-390: Foundations of artificial intelligence

This course provides the students with 1) a set of theoretical concepts to understand the machine learning approach; and 2) a subset of the tools to use this approach for problems arising in mechanical engineering applications. ...

Description

This lecture delves into logistic regression, continuing from the previous session. It covers the probabilistic interpretation of logistic regression, including multinomial logistic regression. The instructor discusses performance metrics, confusion matrices, and the logistic function's extension to multi-class classification. The lecture also explores K-Nearest Neighbour (KNN) for classification and regression, emphasizing the importance of feature scaling and distance metrics. The session concludes with a detailed explanation of setting hyperparameters, cross-validation, and the curse of dimensionality in KNN. Various practical examples and visualizations are used to illustrate the concepts.

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Instructor

Maryam Kamgarpour

Maryam Kamgarpour holds a Doctor of Philosophy in Engineering from the University of California, Berkeley and a Bachelor of Applied Science from University of Waterloo, Canada. Her research is on safe decision-making and control under uncertainty, game theory and mechanism design, mixed integer and stochastic optimization and control. Her theoretical research is motivated by control challenges arising in intelligent transportation networks, robotics, power grid systems and healthcare. She is the recipient of NASA High Potential Individual Award, NASA Excellence in Publication Award, and the European Union (ERC) Starting Grant.

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Statistical inference: Mathematical statistics

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).

Multinomial logistic regression

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).

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.

Binomial regression

In statistics, binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is the number of successes in a series of n independent Bernoulli trials, where each trial has probability of success p. In binomial regression, the probability of a success is related to explanatory variables: the corresponding concept in ordinary regression is to relate the mean value of the unobserved response to explanatory variables.

Cross-validation (statistics)

Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation is a resampling method that uses different portions of the data to test and train a model on different iterations. It is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice.

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