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Physicist, Startup Founder, Blogger, Dad

Tuesday, July 17, 2018

ICML notes

It's never been a better time to work on AI/ML. Vast resources are being deployed in this direction, by corporations and governments alike. In addition to the marvelous practical applications in development, a theoretical understanding of Deep Learning may emerge in the next few years.

The notes below are to keep track of some interesting things I encountered at the meeting.

Some ML learning resources:

Metacademy
Depth First study of AlphaGo


I heard a more polished version of this talk by Elad at the Theory of Deep Learning workshop. He is trying to connect results in sparse learning (e.g., performance guarantees for L1 or threshold algos) to Deep Learning. (Video is from UCLA IPAM.)



It may turn out that the problems on which DL works well are precisely those in which the training data (and underlying generative processes) have a hierarchical structure which is sparse, level by level. Layered networks perform a kind of coarse graining (renormalization group flow): first layers filter by feature, subsequent layers by combinations of features, etc. But the whole thing can be understood as products of sparse filters, and the performance under training is described by sparse performance guarantees (ReLU = thresholded penalization?). Given the inherent locality of physics (atoms, molecules, cells, tissue; atoms, words, sentences, ...) it is not surprising that natural phenomena generate data with this kind of hierarchical structure.


Off-topic: At dinner with one of my former students and his colleague (both researchers at an AI lab in Germany), the subject of Finitism came up due to a throwaway remark about the Continuum Hypothesis.

Wikipedia
Horizons of Truth
Chaitin on Physics and Mathematics

David Deutsch:
The reason why we find it possible to construct, say, electronic calculators, and indeed why we can perform mental arithmetic, cannot be found in mathematics or logic. The reason is that the laws of physics "happen" to permit the existence of physical models for the operations of arithmetic such as addition, subtraction and multiplication.
My perspective: We experience the physical world directly, so the highest confidence belief we have is in its reality. Mathematics is an invention of our brains, and cannot help but be inspired by the objects we find in the physical world. Our idealizations (such as "infinity") may or may not be well-founded. In fact, mathematics with infinity included may be very sick, as evidenced by Godel's results, or paradoxes in set theory. There is no reason that infinity is needed (as far as we know) to do physics. It is entirely possible that there are only a (large but) finite number of degrees of freedom in the physical universe.

Paul Cohen:
I will ascribe to Skolem a view, not explicitly stated by him, that there is a reality to mathematics, but axioms cannot describe it. Indeed one goes further and says that there is no reason to think that any axiom system can adequately describe it.
This "it" (mathematics) that Cohen describes may be the set of idealizations constructed by our brains extrapolating from physical reality. But there is no guarantee that these idealizations have a strong kind of internal consistency and indeed they cannot be adequately described by any axiom system.

Monday, July 09, 2018

Game Over: Genomic Prediction of Social Mobility

The figure below shows SNP-based polygenic score and life outcome (socioeconomic index, on vertical axis) in four longitudinal cohorts, one from New Zealand (Dunedin) and three from the US. Each cohort (varying somewhat in size) has thousands of individuals, ~20k in total (all of European ancestry). The points displayed are averages over bins containing 10-50 individuals. For each cohort, the individuals have been grouped by childhood (family) social economic status. Social mobility can be predicted from polygenic score. Note that higher SES families tend to have higher polygenic scores on average -- which is what one might expect from a society that is at least somewhat meritocratic. The cohorts have not been used in training -- this is true out-of-sample validation. Furthermore, the four cohorts represent different geographic regions (even, different continents) and individuals born in different decades.

Everyone should stop for a moment and think carefully about the implications of the paragraph above and the figure below.


Caption from the PNAS paper.
Fig. 4. Education polygenic score associations with social attainment for Add Health Study, WLS, Dunedin Study, and HRS participants with low-, middle-, and high-socioeconomic status (SES) social origins. The figure plots polygenic score associations with socioeconomic attainment for Add Health Study (A), Dunedin Study (B), WLS (C), and HRS (D) participants who grew up in low-, middle-, and high-SES households. For the figure, low- middle-, and high-SES households were defined as the bottom quartile, middle 50%, and top quartile of the social origins score distributions for the Add Health Study, WLS, and HRS. For the Dunedin Study, low SES was defined as a childhood NZSEI of two or lower (20% of the sample), middle SES was defined as childhood NZSEI of three to four (63% of the sample), and high SES was defined as childhood NZSEI of five or six (17% of the sample). Attainment is graphed in terms of socioeconomic index scores for the Add Health Study, Dunedin Study, and WLS and in terms of household wealth in the HRS. Add Health Study and WLS socioeconomic index scores were calculated from Hauser and Warren (34) occupational income and occupational education scores. Dunedin Study socioeconomic index scores were calculated similarly, according to the Statistics New Zealand NZSEI (38). HRS household wealth was measured from structured interviews about assets. All measures were z-transformed to have mean = 0, SD = 1 for analysis. The individual graphs show binned scatterplots in which each plotted point reflects average x and y coordinates for a bin of 50 participants for the Add Health Study, WLS, and HRS and for a bin of 10 participants for the Dunedin Study. The red regression lines are plotted from the raw data. The box-and-whisker plots at the bottom of the graphs show the distribution of the education polygenic score for each childhood SES category. The blue diamond in the middle of the box shows the median; the box shows the interquartile range; and the whiskers show upper and lower bounds defined by the 25th percentile minus 1.5× the interquartile range and the 75th percentile plus 1.5× the interquartile range, respectively. The vertical line intersecting the x axis shows the cohort average polygenic score. The figure illustrates three findings observed consistently across cohorts: (i) participants who grew up in higher-SES households tended to have higher socioeconomic attainment independent of their genetics compared with peers who grew up in lower-SES households; (ii) participants’ polygenic scores were correlated with their social origins such that those who grew up in higher-SES households tended to have higher polygenic scores compared with peers who grew up in lower-SES households; (iii) participants with higher polygenic scores tended to achieve higher levels of attainment across strata of social origins, including those born into low-SES families.

The paper:
Genetic analysis of social-class mobility in five longitudinal studies, Belsky et al.

PNAS July 9, 2018. 201801238; published ahead of print July 9, 2018. https://doi.org/10.1073/pnas.1801238115

A summary genetic measure, called a “polygenic score,” derived from a genome-wide association study (GWAS) of education can modestly predict a person’s educational and economic success. This prediction could signal a biological mechanism: Education-linked genetics could encode characteristics that help people get ahead in life. Alternatively, prediction could reflect social history: People from well-off families might stay well-off for social reasons, and these families might also look alike genetically. A key test to distinguish biological mechanism from social history is if people with higher education polygenic scores tend to climb the social ladder beyond their parents’ position. Upward mobility would indicate education-linked genetics encodes characteristics that foster success. We tested if education-linked polygenic scores predicted social mobility in >20,000 individuals in five longitudinal studies in the United States, Britain, and New Zealand. Participants with higher polygenic scores achieved more education and career success and accumulated more wealth. However, they also tended to come from better-off families. In the key test, participants with higher polygenic scores tended to be upwardly mobile compared with their parents. Moreover, in sibling-difference analysis, the sibling with the higher polygenic score was more upwardly mobile. Thus, education GWAS discoveries are not mere correlates of privilege; they influence social mobility within a life. Additional analyses revealed that a mother’s polygenic score predicted her child’s attainment over and above the child’s own polygenic score, suggesting parents’ genetics can also affect their children’s attainment through environmental pathways. Education GWAS discoveries affect socioeconomic attainment through influence on individuals’ family-of-origin environments and their social mobility.

Note Added from comments: Plots would look much noisier if not for averaging many individuals into single point. Keep in mind that socioeconomic success depends on a lot more than just cognitive ability, or even cognitive ability + conscientiousness.

But, underlying predictor correlates ~0.35 with actual educational attainment, IIRC. That is, the polygenic score predicts EA about as well as standardized tests predict success in schooling.

This means you can at least use it to identify outliers: just as a very high/low test score (SAT, ACT, GRE) does not *guarantee* success/failure in school, nevertheless the signal is useful for selection = admissions.

Friday, July 06, 2018

Seven Years, Two Tweets

Is anyone keeping score?

See On the Genetic Architecture of Cognitive Ability (2014) and Nautilus Magazine: Super Intelligent Humans.



Thursday, July 05, 2018

Cognitive ability predicted from fMRI (Caltech Neuroscience)

Caltech researchers used elastic net (L1 and L2 penalization) to train a predictor using cognitive scores and fMRI data from ~900 individuals. The predictor captures about 20% of variance in intelligence; the score correlates a bit more than 0.45 with actual intelligence. This may validate earlier work by Korean researchers in 2015, although the Korean group claimed much higher predictive correlations.

Press release:
In a new study, researchers from Caltech, Cedars-Sinai Medical Center, and the University of Salerno show that their new computing tool can predict a person's intelligence from functional magnetic resonance imaging (fMRI) scans of their resting state brain activity. Functional MRI develops a map of brain activity by detecting changes in blood flow to specific brain regions. In other words, an individual's intelligence can be gleaned from patterns of activity in their brain when they're not doing or thinking anything in particular—no math problems, no vocabulary quizzes, no puzzles.

"We found if we just have people lie in the scanner and do nothing while we measure the pattern of activity in their brain, we can use the data to predict their intelligence," says Ralph Adolphs (PhD '92), Bren Professor of Psychology, Neuroscience, and Biology, and director and Allen V. C. Davis and Lenabelle Davis Leadership Chair of the Caltech Brain Imaging Center.

To train their algorithm on the complex patterns of activity in the human brain, Adolphs and his team used data collected by the Human Connectome Project (HCP), a scientific endeavor funded by the National Institutes of Health (NIH) that seeks to improve understanding of the many connections in the human brain. Adolphs and his colleagues downloaded the brain scans and intelligence scores from almost 900 individuals who had participated in the HCP, fed these into their algorithm, and set it to work.

After processing the data, the team's algorithm was able to predict intelligence at statistically significant levels across these 900 subjects, says Julien Dubois (PhD '13), a postdoctoral fellow at Cedars-Sinai Medical Center. But there is a lot of room for improvement, he adds. The scans are coarse and noisy measures of what is actually happening in the brain, and a lot of potentially useful information is still being discarded.

"The information that we derive from the brain measurements can be used to account for about 20 percent of the variance in intelligence we observed in our subjects," Dubois says. "We are doing very well, but we are still quite far from being able to match the results of hour-long intelligence tests, like the Wechsler Adult Intelligence Scale,"

Dubois also points out a sort of philosophical conundrum inherent in the work. "Since the algorithm is trained on intelligence scores to begin with, how do we know that the intelligence scores are correct?" The researchers addressed this issue by extracting a more precise estimate of intelligence across 10 different cognitive tasks that the subjects had taken, not only from an IQ test. ...
Paper:
A distributed brain network predicts general intelligence from resting-state human neuroimaging data

Individual people differ in their ability to reason, solve problems, think abstractly, plan and learn. A reliable measure of this general ability, also known as intelligence, can be derived from scores across a diverse set of cognitive tasks. There is great interest in understanding the neural underpinnings of individual differences in intelligence, since it is the single best predictor of long-term life success, and since individual differences in a similar broad ability are found across animal species. The most replicated neural correlate of human intelligence to date is total brain volume. However, this coarse morphometric correlate gives no insights into mechanisms; it says little about function. Here we ask whether measurements of the activity of the resting brain (resting-state fMRI) might also carry information about intelligence. We used the final release of the Young Adult Human Connectome Project dataset (N=884 subjects after exclusions), providing a full hour of resting-state fMRI per subject; controlled for gender, age, and brain volume; and derived a reliable estimate of general intelligence from scores on multiple cognitive tasks. Using a cross-validated predictive framework, we predicted 20% of the variance in general intelligence in the sampled population from their resting-state fMRI data. Interestingly, no single anatomical structure or network was responsible or necessary for this prediction, which instead relied on redundant information distributed across the brain.

Tuesday, July 03, 2018

In the land of the Gene Titans

Apologies for the lack of posts recently. I've been traveling and busy with meetings. For my own recollection, here is a partial list of places I've been in the past weeks.

Illumina (San Diego)
Ancestry (~10M genomes! San Francisco)
23andMe (~5M genomes! Mountain View)
OpenAI (machines beat pro human teams in complex Dota 2 game! San Francisco)
Affymetrix (Santa Clara)
Healdsburg, Sonoma (Talk at meeting of Oligarchs :-)
Soros Fund Management (Talk at leadership retreat, Museum of Arts and Design, NYC)


These GeneTitans are part of the Affy lab that did all of the genotyping for the UK Biobank project. The footprint for this kind of lab is shockingly small: ~6k samples per week per machine and ~10 machines means millions of individual genotypes per year. Illumina produces similar arrays/readers and a hundred square meters of lab space is enough to process millions of samples per year for DTC genomics companies like 23andMe and Ancestry.

We may have a lab like this soon at MSU ;-)

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