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Reshef, Yakir

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Reshef

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Yakir

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Reshef, Yakir
Author's Publications: search.filters.isAuthorOfPublication.04a0b3ee-a380-4643-85f2-3c8d824bf61e

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    On Extractors and Exposure-Resilient Functions for Sublogarithmic Entropy
    (Wiley-Blackwell, 2013) Reshef, Yakir; Vadhan, Salil
    We study resilient functions and exposure-resilient functions in the low-entropy regime. A resilient function (a.k.a. deterministic extractor for oblivious bit-fixing sources) maps any distribution on n -bit strings in which k bits are uniformly random and the rest are fixed into an output distribution that is close to uniform. With exposure-resilient functions, all the input bits are random, but we ask that the output be close to uniform conditioned on any subset of n - k input bits. In this paper, we focus on the case that k is sublogarithmic in n. We simplify and improve an explicit construction of resilient functions for k sublogarithmic in n due to Kamp and Zuckerman (SICOMP 2006), achieving error exponentially small in k rather than polynomially small in k. Our main result is that when k is sublogarithmic in n, the short output length of this construction (O(log k) output bits) is optimal for extractors computable by a large class of space-bounded streaming algorithms. Next, we show that a random function is a resilient function with high probability if and only if k is superlogarithmic in n, suggesting that our main result may apply more generally. In contrast, we show that a random function is a static (resp. adaptive) exposure-resilient function with high probability even if k is as small as a constant (resp. loglog n). No explicit exposure-resilient functions achieving these parameters are known.
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    Reference-based phasing using the Haplotype Reference Consortium panel
    (2016) Loh, Po-Ru; Danecek, Petr; Palamara, Pier Francesco; Fuchsberger, Christian; Reshef, Yakir; Finucane, Hilary; Schoenherr, Sebastian; Forer, Lukas; McCarthy, Shane; Abecasis, Goncalo R; Durbin, Richard; Price, Alkes
    Haplotype phasing is a fundamental problem in medical and population genetics. Phasing is generally performed via statistical phasing within a genotyped cohort, an approach that can attain high accuracy in very large cohorts but attains lower accuracy in smaller cohorts. Here, we instead explore the paradigm of reference-based phasing. We introduce a new phasing algorithm, Eagle2, that attains high accuracy across a broad range of cohort sizes by efficiently leveraging information from large external reference panels (such as the Haplotype Reference Consortium, HRC) using a new data structure based on the positional Burrows-Wheeler transform. We demonstrate that Eagle2 attains a ≈20x speedup and ≈10% increase in accuracy compared to reference-based phasing using SHAPEIT2. On European-ancestry samples, Eagle2 with the HRC panel achieves >2x the accuracy of 1000 Genomes-based phasing. Eagle2 is open source and freely available for HRC-based phasing via the Sanger Imputation Service and the Michigan Imputation Server.
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    Publication
    Cleaning up the record on the maximal information coefficient and equitability
    (Proceedings of the National Academy of Sciences, 2014) Reshef, David; Reshef, Yakir; Mitzenmacher, Michael; Sabeti, Pardis
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    Functionally informed fine-mapping and polygenic localization of complex trait heritability
    (Springer Science and Business Media LLC, 2020-11-16) Weissbrod, Omer; Hormozdiari, Farhad; Benner, Christian; Cui, Ran; Ulirsch, Jacob; Gazal, Steven; Schoech, Armin; van de Geijn, Bryce; Reshef, Yakir; Márquez-Luna, Carla; O’Connor, Luke; Pirinen, Matti; Finucane, Hilary; Price, Alkes
    Fine-mapping aims to identify causal variants impacting complex traits. We propose PolyFun, a computationally scalable framework to improve fine-mapping accuracy by leveraging functional annotations across the entire genome-not just genome-wide-significant loci-to specify prior probabilities for fine-mapping methods such as SuSiE or FINEMAP. In simulations, PolyFun + SuSiE and PolyFun + FINEMAP were well calibrated and identified >20% more variants with a posterior causal probability >0.95 than identified in their nonfunctionally informed counterparts. In analyses of 49 UK Biobank traits (average n = 318,000), PolyFun + SuSiE identified 3,025 fine-mapped variant-trait pairs with posterior causal probability >0.95, a >32% improvement versus SuSiE. We used posterior mean per-SNP heritabilities from PolyFun + SuSiE to perform polygenic localization, constructing minimal sets of common SNPs causally explaining 50% of common SNP heritability; these sets ranged in size from 28 (hair color) to 3,400 (height) to 2 million (number of children). In conclusion, PolyFun prioritizes variants for functional follow-up and provides insights into complex trait architectures.