Napkin Folding — camdp.com
Generating exponential survival data
Posted by Cameron Davidson-Pilon at
Suppose we interested in generating exponential survival times with scale parameter \(\lambda\), and having \(\alpha\) probability of censorship, \(0 \le \alpha < 1\). This is actually, at least from what I tried, a non-trivial problem. I've derived a few algorithms: Algorithm 1 Generate \(T \sim \text{Exp}( \lambda )\). If \(\alpha = 0\), return \((T, 1)\). Solve \(\frac{ \lambda h }{ \exp (\lambda h) -1 } = \alpha \) for \(h\). Generate \(E \sim \text{TruncExp}( \lambda, h )\), where \(\text{TruncExp}\) is...
Multi-Armed Bandits
Posted by Cameron Davidson-Pilon at
Preface: This example is a (greatly modified) excerpt from the open-source book Bayesian Methods for Hackers, currently being developed on Github Adapted from an example by Ted Dunning of MapR Technologies The Multi-Armed Bandit Problem Suppose you are faced with \(N\) slot machines (colourfully called multi-armed bandits). Each bandit has an unknown probability of distributing a prize (assume for now the prizes are the same for each bandit, only the probabilities differ). Some bandits are very generous, others not so...
An algorithm to sort "Top" comments
Posted by Cameron Davidson-Pilon at
(originally posted on camdp.com) Preface: This example is a (greatly modified) excerpt from the open-source book Bayesian Methods for Hackers, currently being developed on Github ;) Why is sorting from "best" to "worst" so difficult? Consider ratings on online products: how often do you trust an average 5-star rating if there is only 1 reviewer? 2 reviewers? 3 reviewers? We implicitly understand that with such few reviewers that the average rating is not a good reflection of the true value...
Interior designing with Machine Learning
Posted by Cameron Davidson-Pilon at
(Originally on camdp.com) While designing my new apartment, I found a very cool use of machine learning. Yes, that's right, you can use machine learning in interior design. As crazy as it sounds, it is completely legitimate. The Problem I like to show off my collection of books. And with nice new bookshelves in my apartment, I wanted to display the book collection in an interesting way. I've seen organizing books by colour and gradient, a visual trick I find...