Christopher Long
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"Tick, clong, tick, clong, tick, clong, went the night." - Thurber
"Tick, clong, tick, clong, tick, clong, went the night." - Thurber

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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...
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... Add a comment... Post has attachment 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 ... Add a comment... Post has attachment 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... Add a comment... Post has attachment Prime Divisors of \(3^{32}-2^{32}$$
Find four prime divisors < 100 for $$3^{32}-2^{32}$$.
This factors nicely as $$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} = \...
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...