Sunday, May 24, 2015

John Nash, dead at 86

The original title of this post was For this you won a Nobel (Memorial) Prize? But see sad news at bottom.
A Beautiful Mind: Nash went to see von Neumann a few days after he passed his generals? He wanted, he had told the secretary cockily, to discuss an idea that might be of interest to Professor von Neumann. It was a rather audacious thing for a graduate student to do. Von Neumann was a public figure, had very little contact with Princeton graduate students outside of occasional lectures, and generally discouraged them from seeking him out with their research problems. But it was typical of Nash, who had gone to see Einstein the year before with the germ of an idea.

Von Neumann was sitting at an enormous desk, looking more like a prosperous bank president than an academic in his expensive three-piece suit, silk tie, and jaunty pocket handkerchief.  He had the preoccupied air of a busy executive. At the time, he was holding a dozen consultancies, "arguing the ear off Robert Oppenheimer" over the development of the H-bomb, and overseeing the construction and programming of two prototype computers. He gestured Nash to sit down. He knew who Nash was, of course, but seemed a bit puzzled by his visit.

He listened carefully, with his head cocked slightly to one side and his fingers tapping. Nash started to describe the proof he had in mind for an equilibrium in games of more than two players. But before he had gotten out more than a few disjointed sentences, von Neumann interrupted, jumped ahead to the yet unstated conclusion of Nash's argument, and said abruptly, "That's trivial, you know. That's just a fixed point theorem." 
See also What use is game theory? Compare the excerpt below about Nash's Embedding Theorem (also of interest: Theorem proving machines).
A Beautiful Mind: Nash's theorem stated that any kind of surface that embodied a special notion of smoothness can actually be embedded in Euclidean space. He showed that you could fold the manifold like a silk handkerchief, without distorting it. Nobody would have expected Nash's theorem to be true. In fact, everyone would have expected it to be false. "It showed incredible originality," said Mikhail Gromov, the geometer whose book Partial Differential Relations builds on Nash's work. He went on:
Many of us have the power to develop existing ideas. We follow paths prepared by others. But most of us could never produce anything comparable to what Nash produced. It's like lightning striking. Psychologically the barrier he broke is absolutely fantastic. He has completely changed the perspective on partial differential equations. There has been some tendency in recent decades to move from harmony to chaos. Nash says chaos is just around the corner. 
John Conway, the Princeton mathematician who discovered surreal numbers and invented the game of Life, called Nash's result "one of the most important pieces of mathematical analysis in this century."
In writing this post, I googled "a beautiful mind" to find a link to the Amazon page. I was shocked to find a news article about the death of John Nash and his wife Alicia (both are in the photo above) yesterday in a car accident! May they rest in peace.

Saturday, May 23, 2015

Ioannidis at MSU

These videos are from an interview I did with John Ioannidis when he visited Michigan State earlier this month. The whole thing (29 min) and more short clips are available here.

Is 85% of NIH funding wasted?

Early candidate gene studies rarely replicated, but GWAS hits do.

The flyer for his talk:

Friday, May 22, 2015

Genetic architecture and predictive modeling of quantitative traits

As an experiment I recorded this video using slides from a talk I gave last week at NIH. I will be giving similar talks later this spring/summer at Human Longevity Inc. and BGI. The commonality between these institutions is that all three are on the road to accumulating a million human genomes. Who will get there first?

Recording the video was easy using Keynote, although it's a bit odd to talk to yourself for an hour. I recommend that everyone do this, in order to reach a much larger audience than can fit in a lecture hall :-)

Genetic architecture and predictive modeling of quantitative traits

I discuss the application of Compressed Sensing (L1-penalized optimization or LASSO) to genomic prediction. I show that matrices comprised of human genomes are good compressed sensors, and that LASSO applied to genomic prediction exhibits a phase transition as the sample size is varied. When the sample size crosses the phase boundary complete identification of the subspace of causal variants is possible. For typical traits of interest (e.g., with heritability ~ 0.5), the phase boundary occurs at N ~ 30s, where s (sparsity) is the number of causal variants. I give some estimates of sparsity associated with complex traits such as height and cognitive ability, which suggest s ~ 10k. In practical terms, these results imply that powerful genomic prediction will be possible for many complex traits once ~ 1 million genotypes are available for analysis.

Thursday, May 21, 2015

Fifty years of twin studies

The most interesting aspect of these results is that for many traits there is no detectable non-additivity. That is, gene-gene interactions seem to be insignificant, and a simple linear genetic architecture is consistent with the results.
Meta-analysis of the heritability of human traits based on fifty years of twin studies
Nature Genetics (2015) doi:10.1038/ng.3285

Despite a century of research on complex traits in humans, the relative importance and specific nature of the influences of genes and environment on human traits remain controversial. We report a meta-analysis of twin correlations and reported variance components for 17,804 traits from 2,748 publications including 14,558,903 partly dependent twin pairs, virtually all published twin studies of complex traits. Estimates of heritability cluster strongly within functional domains, and across all traits the reported heritability is 49%. For a majority (69%) of traits, the observed twin correlations are consistent with a simple and parsimonious model where twin resemblance is solely due to additive genetic variation. The data are inconsistent with substantial influences from shared environment or non-additive genetic variation. This study provides the most comprehensive analysis of the causes of individual differences in human traits thus far and will guide future gene-mapping efforts.
See also Additivity and complex traits in mice:
You may have noticed that I am gradually collecting copious evidence for (approximate) additivity. Far too many scientists and quasi-scientists are infected by the epistasis or epigenetics meme, which is appealing to those who "revel in complexity" and would like to believe that biology is too complex to succumb to equations. ("How can it be? But what about the marvelous incomprehensible beautiful sacred complexity of Nature? But But But ...")

I sometimes explain things this way:

There is a deep evolutionary reason behind additivity: nonlinear mechanisms are fragile and often "break" due to DNA recombination in sexual reproduction. Effects which are only controlled by a single locus are more robustly passed on to offspring. ...

Many people confuse the following statements:

"The brain is complex and nonlinear and many genes interact in its construction and operation."

"Differences in brain performance between two individuals of the same species must be due to nonlinear (non-additive) effects of genes."

The first statement is true, but the second does not appear to be true across a range of species and quantitative traits.
On the genetic architecture of intelligence and other quantitative traits (p.16):
... The preceding discussion is not intended to convey an overly simplistic view of genetics or systems biology. Complex nonlinear genetic systems certainly exist and are realized in every organism. However, quantitative differences between individuals within a species may be largely due to independent linear effects of specific genetic variants. As noted, linear effects are the most readily evolvable in response to selection, whereas nonlinear gadgets are more likely to be fragile to small changes. (Evolutionary adaptations requiring significant changes to nonlinear gadgets are improbable and therefore require exponentially more time than simple adjustment of frequencies of alleles of linear effect.) One might say that, to first approximation, Biology = linear combinations of nonlinear gadgets, and most of the variation between individuals is in the (linear) way gadgets are combined, rather than in the realization of different gadgets in different individuals.

Linear models work well in practice, allowing, for example, SNP-based prediction of quantitative traits (milk yield, fat and protein content, productive life, etc.) in dairy cattle. ...

Wednesday, May 20, 2015

Imperial exams and human capital

The dangers of rent seeking and the educational signaling trap. Although the imperial examinations were probably g loaded (and hence supplied the bureaucracy with talented administrators for hundreds of years), it would have been better to examine candidates on useful knowledge, which every participant would then acquire to some degree.

See also Les Grandes Ecoles Chinoises and History Repeats.
Farewell to Confucianism: The Modernizing Effect of Dismantling China’s Imperial Examination System

Ying Bai
The Hong Kong University of Science and Technology

Imperial China employed a civil examination system to select scholar bureaucrats as ruling elites. This institution dissuaded high-performing individuals from pursuing some modernization activities, such as establishing modern firms or studying overseas. This study uses prefecture-level panel data from 1896-1910 to compare the effects of the chance of passing the civil examination on modernization before and after the abolition of the examination system. Its findings show that prefectures with higher quotas of successful candidates tended to establish more modern firms and send more students to Japan once the examination system was abolished. As higher quotas were assigned to prefectures that had an agricultural tax in the Ming Dynasty (1368-1643) of more than 150,000 stones, I adopt a regression discontinuity design to generate an instrument to resolve the potential endogeneity, and find that the results remain robust.
From the paper:
Rent seeking is costly to economic growth if “the ablest young people become rent seekers [rather] than producers” (Murphy, Shleifer, and Vishny 1991: 529). Theoretical studies suggest that if a society specifies a higher payoff for rent seeking rather than productive activities, more talent would be allocated in unproductive directions (Acemoglu 1995; Baumol 1990; Murphy, Shleifer, and Vishny 1991, 1993). This was the case in late Imperial China, when a large part of the ruling class – scholar bureaucrats – was selected on the basis of the imperial civil examination.1 The Chinese elites were provided with great incentives to invest in a traditional education and take the civil examination, and hence few incentives to study other “useful knowledge” (Kuznets 1965), such as Western science and technology.2 Thus the civil examination constituted an institutional obstacle to the rise of modern science and industry (Baumol 1990; Clark and Feenstra 2003; Huff 2003; Lin 1995).

This paper identifies the negative incentive effect of the civil exam on modernization by exploring the impact of the system’s abolition in 1904-05. The main empirical difficulty is that the abolition was universal, with no regional variation in policy implementation. To better understand the modernizing effect of the system’s abolition, I employ a simple conceptual framework that incorporates two choices open to Chinese elites: to learn from the West and pursue some modernization activities or to invest in preparing for the civil examination. In this model, the elites with a greater chance of passing the examination would be less likely to learn from the West; they would tend to pursue more modernization activities after its abolition. Accordingly, the regions with a higher chance of passing the exam should be those with a larger increase in modernization activities after the abolition, which makes it possible to employ a difference-in-differences (DID) method to identify the causal effect of abolishing the civil examination on modernization.

I exploit the variation in the probability of passing the examination among prefectures – an administrative level between the provincial and county levels. To control the regional composition of successful candidates, the central government of the Qing dynasty (1644-1911) allocated a quota of successful candidates to each prefecture.3 In terms of the chances of individual participants – measured by the ratio of quotas to population – there were great inequalities among the regions (Chang 1955). To measure the level of modernization activities in a region, I employ (1) the number of newly modern private firms (per million inhabitants) above a designated size that has equipping steam engine or electricity as a proxy for the adoption of Western technology and (2) the number of new Chinese students in Japan – the most import host country of Chinese overseas students (per million inhabitants) as a proxy of learning Western science. Though the two measures might capture other things, for instance entrepreneurship or human capital accumulation, the two activities are both intense in modern science and technology, and thus employed as the proxies of modernization. ...
From Credentialism and elite employment:
Evaluators relied so intensely on “school” as a criterion of evaluation not because they believed that the content of elite curricula better prepared students for life in their firms – in fact, evaluators tended to believe that elite and, in particular, super-elite instruction was “too abstract,” “overly theoretical,” or even “useless” compared to the more “practical” and “relevant” training offered at “lesser” institutions – but rather due to the strong cultural meanings and character judgments evaluators attributed to admission and enrollment at an elite school. I discuss the meanings evaluators attributed to educational prestige in their order of prevalence among respondents. ...

Saturday, May 16, 2015

The Grisly Folk

H.G. Wells on the first encounters between modern humans and Neanderthals. See also The Neanderthal problem and Neanderthals dumb?
The Grisly Folk: ... But one may doubt if the first human group to come into the grisly land was clever enough to solve the problems of the new warfare. Maybe they turned southward again to the gentler regions from which they had come, and were killed by or mingled with their own brethren again. Maybe they perished altogether in that new land of the grisly folk into which they had intruded. Yet the truth may be that they even held their own and increased. If they died there were others of their kind to follow them and achieve a better fate.

That was the beginning of a nightmare age for the little children of the human tribe. They knew they were watched.

Their steps were dogged. The legends of ogres and man-eating giants that haunt the childhood of the world may descend to us from those ancient days of fear. And for the Neandertalers it was the beginning of an incessant war that could end only in extermination.

The Neandertalers, albeit not so erect and tall as men, were the heavier, stronger creatures, but they were stupid, and they went alone or in twos and threes; the menfolk were swifter, quicker-witted, and more social — when they fought they fought in combination. They lined out and surrounded and pestered and pelted their antagonists from every side. They fought the men of that grisly race as dogs might fight a bear. They shouted to one another what each should do, and the Neandertaler had no speech; he did not understand. They moved too quickly for him and fought too cunningly.

Many and obstinate were the duels and battles these two sorts of men fought for this world in that bleak age of the windy steppes, thirty or forty thousand years ago. The two races were intolerable to each other. They both wanted the eaves and the banks by the rivers where the big flints were got. They fought over the dead mammoths that had been bogged in the marshes, and over the reindeer stags that had been killed in the rutting season. When a human tribe found signs of the grisly folk near their cave and squatting place, they had perforce to track them down and kill them; their own safety and the safety of their little ones was only to be secured by that killing. The Neandertalers thought the little children of men fair game and pleasant eating. ...
Razib Khan discusses other examples from this genre.

The ravages of time

These make me happy and sad at the same time.

Monday, May 11, 2015

New kids on the blockchain

WSJ reports on institutional interest in blockchain technologies.
WSJ: Nasdaq OMX Group Inc. is testing a new use of the technology that underpins the digital currency bitcoin, in a bid to transform the trading of shares in private companies.

The experiment joins a slew of financial-industry forays into bitcoin-related technology. If the effort is deemed successful, Nasdaq wants to use so-called blockchain technology in its stock market, one of the world’s largest, and potentially shake up systems that have facilitated the trading of financial assets for decades. ...

The blockchain is maintained, updated and verified by a vast global network of independently owned computers known as “miners” that collectively work to prove the ledger’s authenticity.

In theory, this decentralized system for verifying information means transactions need no longer be channeled through banks, clearinghouses and other middlemen. Advocates say this “trustless” structure means direct transfers of ownership can occur over the blockchain almost instantaneously without the risk of default or manipulation by an intermediating third party.

One idea is that encrypted, digital representations of share certificates could be inserted into minute bitcoin transactions known as “Satoshis,” facilitating an immediate, verifiable transfer of stock ownership from seller to buyer.

Still, bitcoin-based settlement remains untested in the real world. Regulators worry about the anonymous status of the bitcoin miners that collectively manage the system. It is conceivable that bad actors might one day take over the mining network and destroy the integrity of its verification system, some say.

... Real-time settlement has been a goal of regulators and investors alike as it would reduce the risk of counterparty failure and free up billions of dollars of capital that is sidelined during that wait period.

Oliver Bussmann, chief investment officer of Swiss bank UBS AG, last year said the blockchain was the biggest disrupting force in the financial sector, meaning its success could potentially have far-reaching ramifications for banks, trading houses and others. His bank has since established a special blockchain lab to study uses of the technology.

Nasdaq named Fredrik Voss, a vice president, as its new “blockchain technology evangelist” to lead efforts to increase use of the technology.
See my earlier discussion Crypto-currencies, Bitcoin and Blockchain. For these kind of applications I think miners should not be the primary mechanism for blockchain verification. The bank / exchange should do it themselves and then post a large bounty (e.g., $50 million dollars) to any miner who finds an error in the publicly available blockchain. Of course, in these scenarios it would be nice to have more functionality than just transfers (which is all Bitcoin can do now). It would be trivial to encode options, derivatives contracts, conditional agreements, etc. in the blockchain. See Ethereum.
7. One interesting scenario is for a country (Singapore? Denmark?) or large financial entity (Goldman, JPM, Visa) to issue its own crypto currency, managing the blockchain itself but leaving it in the public domain so that third parties (including regulators) can verify transactions. Confidence in this kind of "Institutional Coin" (IC) would be high from the beginning. An IC with Ethereum-like capabilities could revolutionize the financial industry. In place of an opaque web of counterparty relationships leading to systemic risk, the IC blockchain would be easily audited by machine. Regulators would require that the IC authority know its customers, so pseudonymity would only be partial.

Saturday, May 09, 2015

Our Kids and Coming Apart

Nick Lemann reviews Our Kids: The American Dream in Crisis by Robert D. Putnam. At the descriptive level, Putnam's conclusions seem very similar to those of Charles Murray in Coming Apart.

Of course, description is much easier to obtain than causality.
NYBooks: ... By the logic of the book, access to social capital ought to be strongly associated with going to college and doing well there—otherwise, why stress it so strongly? The syllogism would be: social capital leads to educational attainment, which leads to mobility. But for his classmates, Putnam reports, academic achievement was the factor most predictive of college attendance, and the link between such achievement and parental encouragement (of the kind he has copiously praised in the main body of the book) was only “modestly important,” and “much weaker” than the link between class rank and college attendance. Not only that:
No other measure of parental affluence or family structure or neighborhood social capital (or indeed anything else we had measured)—none of the factors that this book has shown are so important in producing today’s opportunity gap—had any appreciable effect on college attendance or other educational attainment.
In the methods appendix, Putnam refers readers to his website for more detail on his findings about his classmates. There, he writes:
No measure of parental resources adds any predictive power whatsoever—not parental occupational status, not parental unemployment, not family economic insecurity during high school, not homeownership, not neighborhood characteristics, and not family structure…. Parental education, parental encouragement, and class rank were all modestly predictive of extracurricular participation, but holding constant those variables, extracurricular participation itself was unrelated to college-going.
So is it really the case that Putnam has shown that strong social capital once produced individual opportunity—let alone that the deterioration of social capital has produced what he calls the opportunity gap? The passages I just quoted seem to indicate that the strong association between social capital and opportunity that is Putnam’s core assertion has not been proven. Putnam doesn’t define “social capital” precisely enough to rigorously test its effects, even on as small and unrepresentative a sample as the one in his survey, and he doesn’t attempt to test its effects precisely in the present. It could even be that, rather than social capital generating prosperity, prosperity might generate social capital, which would mean Putnam has been showing us the effects of inequality, not the causes.
It seems possible to me that:

1. American society has become increasingly meritocratic in the last 50 years, with advancement more and more dependent on largely heritable attributes such as cognitive ability, conscientiousness, future time orientation, etc. Consequently, gaps between different SES groups have become more and more difficult to remediate.

2. External forces, such as automation and global economic competition, have placed a larger and larger premium on attributes such as those listed above, leaving Americans of below average ability at a severe disadvantage.

The consequences of these observations are exacerbated by an increasingly winner take all economic system.

If these points are correct, then Our Kids and Coming Apart are documenting consequences, not causes.

See also Income, Wealth and IQ , US Economic Mobility and Random microworlds: the mystery of nonshared environment.

Friday, May 08, 2015

Rockhold winning and losing

I was surprised at how easily Luke Rockhold beat Lyoto Machida a few weeks ago. Once it went to the ground Rockhold completely dominated the fight.

If you're a grappler you might enjoy this video of Rockhold getting destroyed by a much smaller Rustam Chsiev at Grappler's Quest. Unbelievable how physical this match was. Luke could do nothing to Chsiev.

Thursday, May 07, 2015

Peter Visscher: Genomics, Big Data, Medicine, and Complex Traits

Another good talk from the Genomics, Big Data, and Medicine Seminar Series at the Icahn School of Medicine (Mt. Sinai). Peter starts his talk by discussing height as a classical model trait, giving credit to Galton for first investigating heritability and related ideas, and noting the approximate additivity of genetic effects. @16min, state of the art genomic prediction of height from GIANT collaboration.

Interestingly, Visscher is Dutch for Fisher -- as in Ronald Fisher (the father of population genetics and early pioneer in statistics).

See Maxwell's demon and genetic engineering.
Ronald Fisher on positive alleles for intelligence, in Mendelism and Biometry (1911):

Suppose we knew, for example, 20 pairs of mental characters [loci in the genome]. These would combine in over a million pure mental types; [some of] these would naturally occur rather less frequently than once in a billion; or in a country like England about once in 20,000 generations [assuming the positive variants are somewhat rare]; it will give some idea as to the excellence of the best of these types when we consider that the Englishmen from Shakespeare to Darwin have occurred within 10 generations; the thought of a race of men combining the illustrious qualities of these giants, and breeding true to them, is almost too overwhelming, but such a race will inevitably arise in whatever country first sees the inheritance of mental characters elucidated.

Sunday, May 03, 2015

Replication is hard; understanding what that means is even harder

Bad news for psychology -- only 39 of 100 published findings were replicated in a recent coordinated effort.
Nature | News: An ambitious effort to replicate 100 research findings in psychology ended last week — and the data look worrying. Results posted online on 24 April, which have not yet been peer-reviewed, suggest that key findings from only 39 of the published studies could be reproduced. ...
The article goes on:
But the situation is more nuanced than the top-line numbers suggest (See graphic, 'Reliability test'). Of the 61 non-replicated studies, scientists classed 24 as producing findings at least “moderately similar” to those of the original experiments, even though they did not meet pre-established criteria, such as statistical significance, that would count as a successful replication.  [ Yeah, right. ]
This makes me suspect bounded cognition -- humans trusting their post hoc stories and intuition instead of statistical criteria chosen before planned replication attempts.

The most tragic thing about Ioannidis's work on low replication rates and wasted research funding is that while medical researchers might pay lip service to his results (which are highly cited), they typically have not actually grasped the implications for their own work. In particular, they typically have not updated their posteriors to reflect the low reliability of research results, even in the top journals.

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