Bayesian histograms for rare event classification

Bayesian histograms for rare event classification(dionhaefner.github.io)

74 points by dionhaefner 4 years ago | 6 comments

clircle 4 years ago |

A very odd method where logistic regression would have sufficed. I would have done something like

    library(mgcv)
    gam(y ~ s(x), data, family = binomial)

to do a wiggly logistic regression, and avoid the binning issue entirely.

You can do it Bayesianly if you like, but I don't see why we should discretize the data into buckets.

And what am I supposed to take away from the normalized histogram?

dionhaefner 4 years ago | |

Yes that would probably work! GAMs are a bit of a black box to me so I find it hard to reason about them. I think my method is a bit simpler and it’s more straightforward to get uncertainties, but certainly less elegant than a smooth solution.

contravariant 4 years ago |

Calling this Bayesian seems a bit like wishful thinking at the moment, you could just as easily have called it frequentist as the main mechanism is merging adjacent bins based on a p-value.

A truly Bayesian approach would require specifying a likelihood function for the data based on the choice of bins and turning this into a posterior distribution on the choice (and number) of bins.

Calculating the maximum likelihood estimate for the simplest such likelihood function (samples within a bin are uniform + the number of bins is geometrically distributed) can be done with a vaguely similar algorithm, but simply merging adjacent bins greedily is almost certainly biasing the result right now.

dionhaefner 4 years ago | |

I basically determine p via Bayesian inference within every bin (via a conjugate beta prior for p which gives a beta posterior). If that’s not Bayesian then I don’t know what is :)

Yes the pruning can be done with a frequentist method too. Yes you can come up with smarter / more statistically sound ways to construct these binnings. Do they work on >1e9 data points?

CrazyStat 4 years ago |

Interesting. You've invented something like the Optional Polya Tree [1], except from a bottom up instead of top down construction.

[1] https://www.researchgate.net/publication/47278398_Optional_P...

rossdavidh 4 years ago |

While I haven't tried it out yet, I have to say I very much like the idea, and the article is very clear and well-written. Nicely done!