nhaliday + embeddings   30

CS 731 Advanced Artificial Intelligence - Spring 2011
- statistical machine learning
- sparsity in regression
- graphical models
- exponential families
- variational methods
- dimensionality reduction, eg, PCA
- Bayesian nonparametrics
- compressive sensing, matrix completion, and Johnson-Lindenstrauss
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january 2017 by nhaliday
Ethnic fractionalization and growth | Dietrich Vollrath
Garett Jones did a podcast with The Economics Detective recently on the costs of ethnic diversity. It is particularly worth listening to given that racial identity has re-emerged as a salient element of politics. A quick summary - and the link above includes a nice write-up of relevant sources - would be that diversity within workplaces does not appear to improve outcomes (however those outcomes are measured).

At the same time, there is a parallel literature, touched on in the podcast, about ethnic diversity (or fractionalization, as it is termed in that literature) and economic growth. But one has to be careful drawing a bright line between the two literatures. It does not follow that the results for workplace diversity imply the results regarding economic growth. And this is because the growth results, to the extent that you believe they are robust, all operate through political systems.

So here let me walk through some of the core empirical relationships that have been found regarding ethnic fractionalization and economic growth, and then talk about why you need to take care with over-interpreting them. This is not a thorough literature review, and I realize there are other papers in the same vein. What I’m after is characterizing the essential results.


- objection about sensitivity of measure to definition of clusters seems dumb to me (point is to fix definitions than compare different polities. as long as direction and strength of correlation is fairly robust to changes in clustering, this is a stupid critique)
- also, could probably define a less arbitrary notion of fractionalization (w/o fixed clustering or # of clusters) if using points in a metric/vector/euclidean space (eg, genomes)
- eg, A Generalized Index of Ethno-Linguistic Fractionalization: http://www-3.unipv.it/webdept/prin/workpv02.pdf
So like -E_{A, B ~ X} d(A, B). Or maybe -E_{A, B ~ X} f(d(A, B)) for f an increasing function (in particular, f(x) = x^2).

Note that E ||A - B|| = Θ(E ||E[A] - A||), and E ||A - B||^2 = 2Var A,
for A, B ~ X, so this is just quantifying deviation from mean for Euclidean spaces.

In the case that you have a bunch of difference clusters w/ centers equidistant (so n+1 in R^n), measures p_i, and internal variances σ_i^2, you get E ||A - B||^2 = -2∑_i p_i^2σ_i^2 - ∑_{i≠j} p_ip_j(1 + σ_i^2 + σ_j^2) = -2∑_i p_i^2σ_i^2 - ∑_{i≠j} p_ip_j(1 + σ_i^2 + σ_j^2) = -∑_i p_i^2(1 + 2σ_i^2) - ∑_i 2p_i(1-p_i)σ_i^2
(inter-center distance scaled to 1 wlog).
(in general, if you allow _approximate_ equidistance, you can pack in exp(O(n)) clusters via JL lemma)
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december 2016 by nhaliday
Information Processing: Thought vectors and the dimensionality of the space of concepts
If we trained a deep net to translate sentences about Physics from Martian to English, we could (roughly) estimate the "conceptual depth" of the subject. We could even compare two different subjects, such as Physics versus Art History.
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december 2016 by nhaliday

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