facebook/prophet

Use Negative Binomial or Poisson to handle counts data?

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#337 opened on Oct 24, 2017

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 (14 comments) (3 reactions) (0 assignees)Python (17,686 stars) (4,451 forks)batch import
enhancementhelp wanted

Description

There is a simple regression algorithm for counts data, called Poisson regression. This algorithm assumes that every regressor has a multiplicative effect. It's similar to computing the log of the data, except it works even when the data has zeroes.

It's conceivable that you could replace the Poisson distribution with the more general Negative Binomial distribution. The NB distribution is a generalization of the Poisson that allows the mean to be different from the variance. In contrast, in a Poisson distribution the mean is always the same as the variance.

The main difficulty with just changing the Normal distribution to a Negative Binomial is it's then necessary to add the constraint that $0 < \mu < \sigma^2$.

Does this seem like a good idea?

Contributor guide

Tech stack
python
Domain
datamachine learning
Issue type
research
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
4
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
half day
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
stale
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
mostly clear
Prerequisites
Poisson regressionNegative Binomial distributionPythonbasic statistics
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
30
Research direction
This issue discusses replacing the Normal distribution with Poisson or Negative Binomial for count data in Prophet. To proceed, first review the current implementation in the Prophet codebase (likely in C++ or Python). Then, explore how to model count data with a Poisson likelihood and consider the Negative Binomial extension with the constraint 0<μ<σ². Look at existing comments for suggestions, particularly the discussion about adding a parameter for dispersion. Finally, benchmark against simple Poisson regression to validate improvement.