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tcs math | some mathematics & computation | tcsmath.org Reviews
https://tcsmath.org
some mathematics & computation (by James)
tcsmath.org
Entropy optimality: Matrix scaling | tcs math
http://tcsmath.org/2015/06/16/entropy-optimality-matrix-scaling
Some mathematics and computation. Author (James R. Lee). Entropy optimality: Matrix scaling. June 16, 2015. January 12, 2016. This is the first in a series of posts on the surprising power of “entropy optimality.” I have recently encountered many incarnations of this principle in a number of d ifferent settings (functional analysis, stochastic processes. Additive number theory, communication complexity. For the first post, we’ll look at a very simple but compelling example: matrix scaling. We will follow...
Entropy optimality: Chang’s Lemma | tcs math
http://tcsmath.org/2015/06/17/entropy-optimality-changs-lemma
Some mathematics and computation. Author (James R. Lee). Entropy optimality: Chang’s Lemma. June 17, 2015. June 29, 2015. In the last post. We saw how minimizing the relative entropy allowed us to obtain a “simple” feasible point of a particular polytope. We continue exploring this theme by giving a related proof of Chang’s Lemma. 11 Discrete Fourier analysis and Chang’s Lemma. Denote the finite field with. Elements. We will work over. For convenience, denote. Denote the uniform measure on. In that case,.
Primer: Lifts of polytopes and non-negative matrix factorization | tcs math
http://tcsmath.org/2015/06/20/primer-lifts-of-polytopes-and-non-negative-matrix-factorization
Some mathematics and computation. Author (James R. Lee). Primer: Lifts of polytopes and non-negative matrix factorization. June 20, 2015. June 20, 2015. In preparation for the next post on entropy optimality, we need a little background on lifts of polytopes and non-negative matrix factorization. 11 Polytopes and inequalities. Is the convex hull of a finite set of points in. Equivalently, it is a compact set defined by a family of linear inequalities. Let us give a measure of complexity for. Is the conve...
A note on the large spectrum and generalized Riesz products | tcs math
http://tcsmath.org/2015/07/01/a-note-on-the-large-spectrum-and-generalized-riesz-products
Some mathematics and computation. Author (James R. Lee). A note on the large spectrum and generalized Riesz products. July 1, 2015. July 1, 2015. I wrote a short note entitled Covering the large spectrum and generalized Riesz products. That simplifies and generalizes the approach of the first few posts on Chang’s Lemma and Bloom’s variant. Comments are encouraged, especially about references I may have missed. Entropy optimality: Quantum lifts of polytopes. September 21, 2015 at 3:15 am. Thanks very much...
Table of Contents | tcs math
http://tcsmath.org/table-of-contents
Some mathematics and computation. Author (James R. Lee). Here is a collection of posts which might have some lasting value. The Majorizing Measures Theorem. Majorizing measures: Gaussian Tools. Aram Harrow, Quantum Information, and Dvoretzky’s theorem. The Godel prize, TSP, and volume growth. Random partitions of metric spaces. The need for non-linear mappings. Open problem: Dimension reduction in. Hypercontractivity and its applications. Bloomington Summer School Recap. The pseudorandom subspace problem.
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natural language processing blog: 2014/11
http://nlpers.blogspot.com/2014_11_01_archive.html
Natural language processing blog. My biased thoughts on the fields of natural language processing (NLP), computational linguistics (CL) and related topics (machine learning, math, funding, etc.). The myth of a strong baseline. In fact, I remember back in 2005 I visited MIT and gave a talk on what eventually became the BayeSum paper. At the time I gave this talk the answer was no. In the actual paper the answer is yes. I think Regina was really on to something here, and this one question asked in ...Like ...
natural language processing blog: Some NAACL 2013 statistics on author response, review quality, etc.
http://nlpers.blogspot.com/2015/06/some-naacl-2013-statistics-on-author.html
Natural language processing blog. My biased thoughts on the fields of natural language processing (NLP), computational linguistics (CL) and related topics (machine learning, math, funding, etc.). Some NAACL 2013 statistics on author response, review quality, etc. NAACL 2015 has just passed, NAACL 2013 is long in the past. One bonus of being a program chair is that you get to have fun with data. In this post I'd like to review two pieces of data, one related to author response. Perhaps people with clear o...
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tcs math | some mathematics & computation
Some mathematics and computation. Author (James R. Lee). Entropy optimality: Analytic psd rank and John’s theorem. July 4, 2015. July 19, 2015. Recall that our goal is to sketch a proof of the following theorem, where the notation is from the last post. I will assume a knowledge of the three posts on polyhedral lifts and non-negative rank, as our argument will proceed by analogy. There exists a constant. Such that the following holds. For every. 11 Finite-dimensional operator norms. For a linear operator.
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