# probit regression

(30 minutes to learn)

## Summary

Probit regression is a discriminative model for classification. In this model, the binary targets are generated by sampling latent Gaussian variables whose means are linear in the inputs, and passing them through a threshold.

## Context

This concept has the prerequisites:

- binary linear classifiers (Probit regression is a binary linear classifier.)
- logistic regression (Probit regression is a variant on logistic regression.)
- probit function (Probit regression is defined in terms of the probit function.)
- gradient descent (Probit regression can be fit using gradient descent.)

## Goals

- Know what the probit regression model is

- Be able to derive the gradient descent update rules

- Understand the relationship with logistic regression:
- the two have similar activation functions
- however, probit regression is more sensitive to outliers

- Interpret the model in terms of a latent Gaussian variable and a threshold

## Core resources (read/watch one of the following)

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 9.4, "Probit regression," pages 293-295

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 4.3.5, "Probit regression," pages 210-212

## See also

- Probit regression is less robust to outliers than [logistic regression](logistic_regression) .
- Probit functions are convenient in probabilistic models because they allow for sampling algorithms which fit the latent Gaussian variables.