2/17/23, 3:13 PM Bike Rides and the Poisson Model — Data Mininghttps://pantelis.github.io/data-mining/aiml-common/assignments/mle/poisson-regression-1/index.html 1/1Bike Rides and the Poisson...

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2/17/23, 3:13 PM Bike Rides and the Poisson Model — Data Mining https://pantelis.github.io/data-mining/aiml-common/assignments/mle/poisson-regression-1/index.html 1/1 Bike Rides and the Poisson Model Contents Maximum Likelihood I Maximum Likelihood II To help the urban planners, you are called to model the daily bike rides in NYC using this dataset. The dataset contains date, day of the week, high and low temp, precipitation and bike ride couunts as columns. Maximum Likelihood I The obvious choice in distributions is the Poisson distribution which depends only on one parameter, λ, which is the average number of occurrences per interval. We want to estimate this parameter using Maximum Likelihood Estimation. Implement a Gradient Descent algorithm from scratch that will estimate the Poisson distribution according to the Maximum Likelihood criterion. Plot the estimated mean vs iterations to showcase convergence towards the true mean. References: 1. This blog post. 2. This blog post and note the negative log likelihood function. Maximum Likelihood II A colleague of yours suggest that the parameter must be itself dependent on the weather and other factors since people bike when its not raining. Assume that you model as where is one of the example features and is a set of parameters. Train the model with SGD with this assumption and compare the MSE of the predictions with the Maximum Likelihood I approach. You may want to use this partial derivative of the log likelihood function # Code here λ λ λi = exp(w T xi) xi w # By Pantelis Monogioudis, Ph.D © Copyright 2023. https://gist.github.com/sachinsdate/c17931a3f000492c1c42cf78bf4ce9fe/archive/7a5131d3f02575668b3c7e8c146b6a285acd2cd7.zip https://en.wikipedia.org/wiki/Poisson_distribution https://towardsdatascience.com/the-poisson-process-everything-you-need-to-know-322aa0ab9e9a https://towardsdatascience.com/understanding-maximum-likelihood-estimation-fa495a03017a http://home.cc.umanitoba.ca/~godwinrt/7010/poissonregression.pdf