Linear Models
Linear models are very useful for baseline models.
3 Logistic Regression
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Category: { Machine Learning }
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References:
- Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Science & Business Media; 2013. pp. 567–567. Available: https://play.google.com/store/books/details?id=yPfZBwAAQBAJ
- Friedman J, Hastie T, Tibshirani R. Additive Logistic Regression. The Annals of Statistics. 2000. pp. 337–374. doi:10.1214/aos/1016218223
- Mehta P, Wang C-H, Day AGR, Richardson C, Bukov M, Fisher CK, et al. A high-bias, low-variance introduction to Machine Learning for physicists. Phys Rep. 2019;810: 1–124. doi:10.1016/j.physrep.2019.03.001
Summary: logistics regression is a simple model for classification
Pages: 3
2 Poisson Regression
Published:
Category: { Machine Learning }
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References:
- Fox J. Applied Regression Analysis and Generalized Linear Models. SAGE Publications; 2015. Available: https://play.google.com/store/books/details?id=cjB3BwAAQBAJ
- Rodríguez G, editor. Poisson Models for CountData. Generalized Linear Models. Available: https://data.princeton.edu/wws509/notes
- Chapter 19: Logistic and Poisson Regression by Marie Chesaniuk
- Poisson regression and non-normal loss (sklearn documentation)
- Beyond Multiple Linear Regression, Chapter 4 Poisson Regression
Summary: Poisson regression is a generalized linear model for count data.
To model a dataset that is generated from a [[Poisson distribution]] Poisson Process , we only need to model the mean $\mu$ as it is the only parameters. The simplest model we can have for some given features $X$ is a linear model. However, for count data, the effects of the predictors are often multiplicative. The next simplest model we can have is
$$ \mu = \exp\left(\beta X\right). $$
The $\exp$ makes sure that the mean is positive as this is required for count data.
Pages: 3