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**An Island of Liars is an Ensemble of Experts**

In my previous post I looked at how a group of of experts may be combined into a single, more powerful, classifier which I call NaiveBoost after the related AdaBoost . I'll illustrate how it can be used with a few examples. As before, we're face with makin...

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**Combining Expert Opinions: NaiveBoost**

In many situations we're faced with many expert opinions. How should we combine them together into one opinion, hopefully better than any single opinion? I'll demonstrate the derivation of a classifier I'll call NaiveBoost. We'll start with a simple situati...

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**Simplified Multinomial Kelly**

Here's a simplified version for optimal Kelly bets when you have multiple outcomes (e.g. horse races). The Smoczynski & Tomkins algorithm, which is explained here (or in the original paper): https://en.wikipedia.org/wiki/Kelly_criterion#Multiple_horses Let'...

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**Notes on Setting up a Titan V under Ubuntu 17.04**

I recently purchased a Titan V GPU to use for machine and deep learning, and in the process of installing the latest Nvidia driver's hosed my Ubuntu 16.04 install. I was overdue for a fresh install of Linux, anyway, so I decided to upgrade some of my drives...

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**Solving IMO 1989 #6 using Probability and Expectation**

IMO 1989 #6: A permutation \(\{x_1, x_2, \ldots , x_m\}\) of the set \(\{1, 2, \ldots , 2n\}\), where \(n\) is a positive integer, is said to have property \(P\) if \( | x_i - x_{i+1} | = n\) for at least one \(i\) in \(\{1, 2, ... , 2n-1\}\). Show that for...

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**Poisson Games and Sudden-Death Overtime**

Let's say we have a game that can be reasonably modeled as two independent Poisson processes with team \(i\) having parameter \(\lambda_i\). If one team wins in regulation with team \(i\) scoring \(n_i\), then it's well-known we have the MLE estimate \(\hat...

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**Why does Kaggle use Log-loss?**

If you're not familiar with Kaggle , it's an organization dedicated to data science competitions to both provide ways to companies to potentially do cheaper analytics, as well as to identify talented data scientists. Competitions are scored using a variety ...

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**The Kelly Criterion and a Sure Thing**

The Kelly Criterion is an alternative to standard utility theory, which seeks to maximize expected utility. Instead, the Kelly Criterion seeks to maximize expected growth . That is, if we start out with an initial bankroll \(B_0\), we seek to maximize \(\ma...

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**Prime Divisors of \(3^{32}-2^{32}\)**

Find four prime divisors < 100 for \(3^{32}-2^{32}\).

Source: British Math Olympiad, 2006.

This factors nicely as \(3^{32}-2^{32} = \left(3^{16}+2^{16}\right)\left(3^{16}-2^{16}\right)\), and we can continue factoring in this way to get \[3^{32}-2^{32} = \...

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**Highest Powers of 3 and \(\left(1+\sqrt{2}\right)^n\)**

Let \(\left(1+\sqrt{2}\right)^{2012}=a+b\sqrt{2}\), where \(a\) and \(b\) are integers. What is the greatest common divisor of \(b\) and \(81\)? Source: 2011-2012 SDML High School 2a, problem 15. Let \((1+\sqrt{2})^n = a_n + b_n \sqrt{2}\). I've thought abo...

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