Generalized Linear Models Steve S Ml Notes

Leo Migdal
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generalized linear models steve s ml notes

Three cases when Poisson Regression should be applied: a. When there is an exponential relationship between x and y b. When the increase in X leads to an increase in the variance of Y c. When Y is a discrete variable and must be positive Let’s create a glm model with conditions below a. The relationship between x and y is an exponential relationship b.

The variance of y is constant when x increases c. y can be either discret or continuous variable and also can be negative ```python from numpy.random import uniform, normal import numpy as np np.set_printoptions(precision=4) Generalized Linear Models (GLMs) are a class of regression models that can be used to model a wide range of relationships between a response variable and one or more predictor variables. Unlike traditional linear regression models, which assume a linear relationship between the response and predictor variables, GLMs allow for more flexible, non-linear relationships by using a different underlying statistical distribution. The following article discusses the Generalized linear models (GLMs) which explains how Linear regression and Logistic regression are a member of a much broader class of models.

GLMs can be used to construct the models for regression and classification problems by using the type of distribution which best describes the data or labels given for training the model. Below given are some types of datasets and the corresponding distributions which would help us in constructing the model for a particular type of data (The term data specified here refers to the output... To understand GLMs we will begin by defining exponential families. Exponential families are a class of distributions whose probability density function(PDF) can be molded into the following form: P(y;\eta) = b(y)exp(\eta^T * T(y) - a(\eta))\hspace{1mm}\\ \small \eta - Natural\hspace{1mm} parameter\hspace{1mm} (can\hspace{1mm} be\hspace{1mm} a \hspace{1mm}scalar... Proof - Bernoulli distribution is a member of the exponential family. P(y;\phi) = \phi^y * (1-\phi)^{(1-y)}\\ \hspace{1cm}= exp(log(\phi^y * (1-\phi)^{(1-y)}))\\ \hspace{1cm}= exp(y * log(\phi) + (1-y) * log(1-\phi))\\ \hspace{1cm}= exp(y * log(\phi/1-\phi)) + log(1-\phi))\hspace{1mm}- Eq 2

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You’ve already scratched the surface of what generalized linear models are meant to address if you’ve ever constructed a linear regression model in Python and wondered, “This works great, but what if my data... In essence, linear regression develops into a generalized linear model (GLM). Even if your data doesn’t match the assumptions of a traditional straight-line model, you can still use this adaptable framework to describe relationships between variables. Consider it a powerful extension that allows you greater flexibility while maintaining interpretability. Because real-world data is messy. Sometimes your target variable is binary (yes/no), sometimes it’s a count (like the number of clicks), and sometimes it’s highly skewed (like insurance claims).

A standard linear regression assumes the outcome is continuous and normally distributed, which just doesn’t hold up in many of these cases. That’s where GLMs come in. These models give you the tools to work with all sorts of outcome variables, using the right mathematical assumptions behind the scenes. And the best part? They still give you those nice, clean coefficients you can interpret and explain to your team or client. Here are just a few problems GLMs are made for:

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You’ve Already Scratched The Surface Of What Generalized Linear Models

You’ve already scratched the surface of what generalized linear models are meant to address if you’ve ever constructed a linear regression model in Python and wondered, “This works great, but what if my data... In essence, linear regression develops into a generalized linear model (GLM). Even if your data doesn’t match the assumptions of a traditional straight-line model, you can still use this ad...