nhaliday + linearity   49

Modules Matter Most | Existential Type
note comment from gasche (significant OCaml contributor) critiquing modules vs typeclasses: https://existentialtype.wordpress.com/2011/04/16/modules-matter-most/#comment-735
I also think you’re unfair to type classes. You’re right that they are not completely satisfying as a modularity tool, but your presentation make them sound bad in all aspects, which is certainly not true. The limitation of only having one instance per type may be a strong one, but it allows for a level of impliciteness that is just nice. There is a reason why, for example, monads are relatively nice to use in Haskell, while using monads represented as modules in a SML/OCaml programs is a real pain.

It’s a fact that type-classes are widely adopted and used in the Haskell circles, while modules/functors are only used for relatively coarse-gained modularity in the ML community. It should tell you something useful about those two features: they’re something that current modules miss (or maybe a trade-off between flexibility and implicitness that plays against modules for “modularity in the small”), and it’s dishonest and rude to explain the adoption difference by “people don’t know any better”.
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july 2019 by nhaliday
Subgradients - S. Boyd and L. Vandenberghe
If f is convex and x ∈ int dom f, then ∂f(x) is nonempty and bounded. To establish that ∂f(x) ≠ ∅, we apply the supporting hyperplane theorem to the convex set epi f at the boundary point (x, f(x)), ...
pdf  nibble  lecture-notes  acm  optimization  curvature  math.CA  estimate  linearity  differential  existence  proofs  exposition  atoms  math  marginal  convexity-curvature 
august 2017 by nhaliday
Missing heritability problem - Wikipedia
The "missing heritability" problem[1][2][3][4][5][6] can be defined as the fact that single genetic variations cannot account for much of the heritability of diseases, behaviors, and other phenotypes. This is a problem that has significant implications for medicine, since a person's susceptibility to disease may depend more on "the combined effect of all the genes in the background than on the disease genes in the foreground", or the role of genes may have been severely overestimated.

The 'missing heritability' problem was named as such in 2008. The Human Genome Project led to optimistic forecasts that the large genetic contributions to many traits and diseases (which were identified by quantitative genetics and behavioral genetics in particular) would soon be mapped and pinned down to specific genes and their genetic variants by methods such as candidate-gene studies which used small samples with limited genetic sequencing to focus on specific genes believed to be involved, examining the SNP kinds of variants. While many hits were found, they often failed to replicate in other studies.

The exponential fall in genome sequencing costs led to the use of GWAS studies which could simultaneously examine all candidate-genes in larger samples than the original finding, where the candidate-gene hits were found to almost always be false positives and only 2-6% replicate;[7][8][9][10][11][12] in the specific case of intelligence candidate-gene hits, only 1 candidate-gene hit replicated,[13] and of 15 neuroimaging hits, none did.[14] The editorial board of Behavior Genetics noted, in setting more stringent requirements for candidate-gene publications, that "the literature on candidate gene associations is full of reports that have not stood up to rigorous replication...it now seems likely that many of the published findings of the last decade are wrong or misleading and have not contributed to real advances in knowledge".[15] Other researchers have characterized the literature as having "yielded an infinitude of publications with very few consistent replications" and called for a phase out of candidate-gene studies in favor of polygenic scores.[16]

This led to a dilemma. Standard genetics methods have long estimated large heritabilities such as 80% for traits such as height or intelligence, yet none of the genes had been found despite sample sizes that, while small, should have been able to detect variants of reasonable effect size such as 1 inch or 5 IQ points. If genes have such strong cumulative effects - where were they? Several resolutions have been proposed, that the missing heritability is some combination of:

...

7. Genetic effects are indeed through common SNPs acting additively, but are highly polygenic: dispersed over hundreds or thousands of variants each of small effect like a fraction of an inch or a fifth of an IQ point and with low prior probability: unexpected enough that a candidate-gene study is unlikely to select the right SNP out of hundreds of thousands of known SNPs, and GWASes up to 2010, with n<20000, would be unable to find hits which reach genome-wide statistical-significance thresholds. Much larger GWAS sample sizes, often n>100k, would be required to find any hits at all, and would steadily increase after that.
This resolution to the missing heritability problem was supported by the introduction of Genome-wide complex trait analysis (GCTA) in 2010, which demonstrated that trait similarity could be predicted by the genetic similarity of unrelated strangers on common SNPs treated additively, and for many traits the SNP heritability was indeed a substantial fraction of the overall heritability. The GCTA results were further buttressed by findings that a small percent of trait variance could be predicted in GWASes without any genome-wide statistically-significant hits by a linear model including all SNPs regardless of p-value; if there were no SNP contribution, this would be unlikely, but it would be what one expected from SNPs whose effects were very imprecisely estimated by a too-small sample. Combined with the upper bound on maximum effect sizes set by the GWASes up to then, this strongly implied that the highly polygenic theory was correct. Examples of complex traits where increasingly large-scale GWASes have yielded the initial hits and then increasing numbers of hits as sample sizes increased from n<20k to n>100k or n>300k include height,[23] intelligence,[24] and schizophrenia.
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may 2017 by nhaliday
6.896: Essential Coding Theory
- probabilistic method and Chernoff bound for Shannon coding
- probabilistic method for asymptotically good Hamming codes (Gilbert coding)
- sparsity used for LDPC codes
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february 2017 by nhaliday
Information Processing: Epistasis vs additivity
On epistasis: why it is unimportant in polygenic directional selection: http://rstb.royalsocietypublishing.org/content/365/1544/1241.short
- James F. Crow

The Evolution of Multilocus Systems Under Weak Selection: http://www.genetics.org/content/genetics/134/2/627.full.pdf
- Thomas Nagylaki

Data and Theory Point to Mainly Additive Genetic Variance for Complex Traits: http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1000008
The relative proportion of additive and non-additive variation for complex traits is important in evolutionary biology, medicine, and agriculture. We address a long-standing controversy and paradox about the contribution of non-additive genetic variation, namely that knowledge about biological pathways and gene networks imply that epistasis is important. Yet empirical data across a range of traits and species imply that most genetic variance is additive. We evaluate the evidence from empirical studies of genetic variance components and find that additive variance typically accounts for over half, and often close to 100%, of the total genetic variance. We present new theoretical results, based upon the distribution of allele frequencies under neutral and other population genetic models, that show why this is the case even if there are non-additive effects at the level of gene action. We conclude that interactions at the level of genes are not likely to generate much interaction at the level of variance.
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february 2017 by nhaliday
The infinitesimal model | bioRxiv
Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. We first review the long history of the infinitesimal model in quantitative genetics. Then we provide a definition of the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure, ... We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. In each case, by conditioning on the pedigree relating individuals in the population, we incorporate arbitrary selection and population structure. We suppose that we can observe the pedigree up to the present generation, together with all the ancestral traits, and we show, in particular, that the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order M^{-1/2}. Simulations suggest that in particular cases the convergence may be as fast as 1/M.

published version:
The infinitesimal model: Definition, derivation, and implications: https://sci-hub.tw/10.1016/j.tpb.2017.06.001

Commentary: Fisher’s infinitesimal model: A story for the ages: http://www.sciencedirect.com/science/article/pii/S0040580917301508?via%3Dihub
This commentary distinguishes three nested approximations, referred to as “infinitesimal genetics,” “Gaussian descendants” and “Gaussian population,” each plausibly called “the infinitesimal model.” The first and most basic is Fisher’s “infinitesimal” approximation of the underlying genetics – namely, many loci, each making a small contribution to the total variance. As Barton et al. (2017) show, in the limit as the number of loci increases (with enough additivity), the distribution of genotypic values for descendants approaches a multivariate Gaussian, whose variance–covariance structure depends only on the relatedness, not the phenotypes, of the parents (or whether their population experiences selection or other processes such as mutation and migration). Barton et al. (2017) call this rigorously defensible “Gaussian descendants” approximation “the infinitesimal model.” However, it is widely assumed that Fisher’s genetic assumptions yield another Gaussian approximation, in which the distribution of breeding values in a population follows a Gaussian — even if the population is subject to non-Gaussian selection. This third “Gaussian population” approximation, is also described as the “infinitesimal model.” Unlike the “Gaussian descendants” approximation, this third approximation cannot be rigorously justified, except in a weak-selection limit, even for a purely additive model. Nevertheless, it underlies the two most widely used descriptions of selection-induced changes in trait means and genetic variances, the “breeder’s equation” and the “Bulmer effect.” Future generations may understand why the “infinitesimal model” provides such useful approximations in the face of epistasis, linkage, linkage disequilibrium and strong selection.
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january 2017 by nhaliday
Selection against variants in the genome associated with educational attainment
first direct, genotypic, longitudinal evidence I think?
fulltext: https://www.dropbox.com/s/9vq5t6urtu930xe/2017-kong.pdf

Epidemiological and genetic association studies show that genetics play an important role in the attainment of education. Here, we investigate the effect of this genetic component on the reproductive history of 109,120 Icelanders and the consequent impact on the gene pool over time. We show that an educational attainment polygenic score, POLY_EDU, constructed from results of a recent study is associated with delayed reproduction (P < 10^−100) and fewer children overall. _The effect is stronger for women and remains highly significant after adjusting for educational attainment._ Based on 129,808 Icelanders born between 1910 and 1990, we find that the average POLY_EDU has been declining at a rate of ∼0.010 standard units per decade, which is substantial on an evolutionary timescale. Most importantly, because POLY_EDU only captures a fraction of the overall underlying genetic component the latter could be declining at a rate that is two to three times faster.

- POLY_EDU has negative effect on RS for men, while EDU itself (or just controlling for POLY_EDU?) has positive effect
- also has some trends for height (0) and schizophrenia (-)

Natural selection making 'education genes' rarer, says Icelandic study: https://www.reddit.com/r/slatestarcodex/comments/5opugw/natural_selection_making_education_genes_rarer/
Gwern pretty pessimistic
http://www.smithsonianmag.com/smart-news/study-shows-genes-associated-education-are-declining-180961836/

http://andrewgelman.com/2017/07/30/iceland-education-gene-trend-kangaroo/

The Marching Morons: https://westhunt.wordpress.com/2017/01/22/the-marching-morons/
There’s a new paper out on how the frequency of variants that affect educational achievement (which also affect IQ) have been changing over time in Iceland. Naturally, things are getting worse.

We don’t have all those variants identified yet, but from the fraction we do know and the rate of change, they estimate that genetic potential for IQ is dropping about 0.30 point per decade – 3 points per century, about a point a generation. In Iceland.

Sounds reasonable, in the same ballpark as demography-based estimates.

It would be interesting to look at moderately recent aDNA and see when this trend started – I doubt if has been going on very long. [ed.: I would guess since the demographic transition/industrial revolution, though, right?]

This is the most dangerous threat the human race faces.

Paper Review: Icelandic Dysgenics: http://www.unz.com/akarlin/paper-review-icelandic-dysgenics/
The main mechanism was greater age at first child, not total number of children (i.e. the clever are breeding more slowly).
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january 2017 by nhaliday
Books, 2016 | West Hunter
1. The Peloponnesian War
2 The Empire of the Steppes
3. The Columbian Exchange
4. Breaking the Maya Code
5. War Before Civilization
6. The Discourses (Machiavelli)
7. Introduction to Algorithms
8. Rare Earth
9. The Wizard War
10. Night comes to the Cretaceous
11. Microbe Hunters
12. The Youngest Science
13. Plagues and Peoples
14. Project Orion
15. Extraordinary Popular Delusions and the Madness of Crowds
16. Godstalk, P. C. Hodgell
17. Footfall, Larry Niven and Jerry Pournelle
18. On Stranger Tides, Tim Powers
19. His Share of Glory, Cyril Kornbluth
20. Herodotus
21. The Secret History, Procopius

https://westhunt.wordpress.com/2016/12/04/books-2016/#comment-85575
Mukherjee is a moron. Next question?

He’s suggested that gene interactions are real important in IQ [epistatic rather than additive effects] but he is incorrect. If new to the field, it could take as much as an afternoon to find that out.
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december 2016 by nhaliday

bundles : abstractpatterns

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