Archive

Archive for the ‘Mathematics’ Category

Fast Portfolio re-Balancing as a Fractional Linear Program

August 12th, 2010 John Mount No comments

Fast Portfolio re-Balancing as a Fractional Linear Program is an example of the kind of work we have done encoding client problems (in this case optimal portfolio selection) as optimization problems (so we can use purchased software to solve them). Its a bit mathy- but we are excited we got permission to share this. Read more…

What Did Theorists Do Before The Age Of Big Data?

August 2nd, 2010 John Mount 1 comment

We have been living in the age of “big data” for some time now. This is an age where incredible things can be accomplished through the effective application of statistics and machine learning at large scale (for example see: “The Unreasonable Effectiveness of Data” Alon Halevy, Peter Norvig, Fernando Pereira, IEEE Intelligent Systems (2009)). But I have gotten to thinking about the period before this. The period before we had easy access to so much data, before most computation was aggregation and before we accepted numerical analysis style convergence as “efficient.” A small problem I needed to solve (as part of a bigger project) reminded me what theoretical computer scientists did then: we worried about provable worst case efficiency.

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Gradients via Reverse Accumulation

July 14th, 2010 John Mount No comments

We extend the ideas of from Automatic Differentiation with Scala to include the reverse accumulation. Reverse accumulation is a non-obvious improvement to automatic differentiation that can in many cases vastly speed up calculations of gradients. Read more…

Automatic Differentiation with Scala

June 14th, 2010 John Mount 5 comments

This article is a worked-out exercise in applying the Scala type system to solve a small scale optimization problem. For this article we supply complete Scala source code (under a GPLv3 license) and some design discussion. Read more…

Algorithmic Movie (with texture)

April 27th, 2010 John Mount No comments

We would like to share a new algorithmic movie we have created.

Since the mid 90′s we have been dabbling off and on with a combination of algorithmic and genetic art (see: What is “Genetic Art?” or try running the Java code directly in your browser). Every once in a while we return to the project and generate something we would like to share.

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SIGACT Review of: Combinatorics the Rota Way

April 20th, 2010 John Mount No comments

SIGACT News review of: Combinatorics the Rota Way. Also found on Professor Gasarch’s page and ACM SIGACT News Volume 41, Issue 2 (paywall)

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“Easy” Portfolio Allocation

January 14th, 2010 John Mount Comments off

This is an elementary mathematical finance article. This means if you know some math (linear algebra, differential calculus) you can find a quick solution to a simple finance question. The topic was inspired by a recent article in The American Mathematical Monthly (Volume 117, Number 1 January 2010, pp. 3-26): “Find Good Bets in the Lottery, and Why You Shouldn’t Take Them” by Aaron Abrams and Skip Garibaldi which said optimal asset allocation is now an undergraduate exercise. That may well be, but there are a lot of people with very deep mathematical backgrounds that have yet to have seen this. We will fill in the details here. The style is terse, but the content should be about what you would expect from one day of lecture in a mathematical finance course.

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The Local to Global Principle

November 11th, 2009 John Mount Comments off

We describe the “the local to global principle.” It is a principle used to break algorithmic problem solving into two distinct phases (local criticism followed by global solution) and is an aid both in the design and in the application of algorithms. Instead of giving a formal definition of the principle we quickly define it and discuss a few examples and methods. We have produced both a stand-alone PDF (more legible) and a HTML/blog form (more skimable).
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Google AdSense Channels IDs and the Cramer Rao Inequality

October 19th, 2009 John Mount 2 comments

“Comparing Apples and Oranges: Two Examples of the Limits of Statistical Inference, With an Application to Google Advertising Markets” is our analysis of Google AdSense Channel IDs and our use of the Cramer Rao bound to show that these IDs fundamentally limit what participants in the Google online advertising market can measure (and therefore in turn limit what these players can do).
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A Discrete Model Gauging Market Efficiency

September 8th, 2009 John Mount 4 comments

New paper: A Discrete Model Gauging Market Efficiency PDF

We highly recommend reading the PDF version, but please find below a HTML translation of the paper.

We follow up on some interesting work from the literature and explore some conditions that allow large predatory traders to dominate markets.

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