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Photo Credit This article by Christopher Tong has got a lot of love from people I followed on Twitter, so I decided to read it. It was very enlightening. But to be honest, I don’t fully understand quite a few arguments made by this article, probably because I lack the experience of more rigorous scientific experiments and research. Nonetheless, I think writing down the parts I find interesting and put it into a blog post would be beneficial for myself and other potential readers. Hopefully, it makes it easier to reflect on these materials later. ...

Photo Credit We’ve discussed what quantile regression is and how does it work in Part 1. In this Part 2 we’re going to explore how to train quantile regression models in deep learning models and gradient boosting trees. Source Code The source code to this post is provided in this repository: ceshine/quantile-regression-tensorflow. It is a fork of strongio/quantile-regression-tensorflow, with following modifcations: Use the example dataset from the scikit-learn example. The TensorFlow implementation is mostly the same as in strongio/quantile-regression-tensorflow. ...

Photo Credit I’m starting to think prediction interval[1] should be a required output of every real-world regression model. You need to know the uncertainty behind each point estimation. Otherwise the predictions are often not actionable. For example, consider historical sales of an item under a certain circumstance are (10000, 10, 50, 100). Standard least squares method gives you an estimate of 2540. If you restock based on that prediction, you’re likely going to significantly overstock 75% of the time. The prediction is almost useless. But if you estimate the quantiles of the data distribution, the estimated 5th, 50th, and 95th percentiles are 16, 75, 8515, which are much more informative than the 2540 single estimation. It is also the idea of quantile regression. ...