The Experts below are selected from a list of 5289 Experts worldwide ranked by ideXlab platform
Adam R Klivans - One of the best experts on this subject based on the ideXlab platform.
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efficient algorithms for outlier robust regression
arXiv: Learning, 2018Co-Authors: Adam R Klivans, Pravesh Kothari, Raghu MekaAbstract:We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from distribution D and subsequently corrupted on some fraction of points, our algorithm outputs a linear function whose squared error is close to the squared error of the best-fitting linear function with respect to D, assuming that the marginal distribution of D over the input space is \emph{certifiably hypercontractive}. This natural property is satisfied by many well-studied distributions such as Gaussian, strongly log-concave distributions and, uniform distribution on the hypercube among others. We also give a simple statistical lower bound showing that some Distributional Assumption is necessary to succeed in this setting. These results are the first of their kind and were not known to be even information-theoretically possible prior to our work. Our approach is based on the sum-of-squares (SoS) method and is inspired by the recent applications of the method for parameter recovery problems in unsupervised learning. Our algorithm can be seen as a natural convex relaxation of the following conceptually simple non-convex optimization problem: find a linear function and a large subset of the input corrupted sample such that the least squares loss of the function over the subset is minimized over all possible large subsets.
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eigenvalue decay implies polynomial time learnability for neural networks
arXiv: Learning, 2017Co-Authors: Surbhi Goel, Adam R KlivansAbstract:We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal Assumptions under which these classes admit provably efficient algorithms. In this work we show that a natural Distributional Assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g. feed-forward networks of ReLUs). We make no Assumptions on the structure of the network or the labels. Given sufficiently-strong polynomial eigenvalue decay, we obtain {\em fully}-polynomial time algorithms in {\em all} the relevant parameters with respect to square-loss. Milder decay Assumptions also lead to improved algorithms. This is the first purely Distributional Assumption that leads to polynomial-time algorithms for networks of ReLUs, even with one hidden layer. Further, unlike prior Distributional Assumptions (e.g., the marginal distribution is Gaussian), eigenvalue decay has been observed in practice on common data sets.
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eigenvalue decay implies polynomial time learnability for neural networks
Neural Information Processing Systems, 2017Co-Authors: Surbhi Goel, Adam R KlivansAbstract:We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal Assumptions under which these classes admit provably efficient algorithms. In this work we show that a natural Distributional Assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g. feed-forward networks of ReLUs). We make no Assumptions on the structure of the network or the labels. Given sufficiently-strong eigenvalue decay, we obtain {\em fully}-polynomial time algorithms in {\em all} the relevant parameters with respect to square-loss. This is the first purely Distributional Assumption that leads to polynomial-time algorithms for networks of ReLUs. Further, unlike prior Distributional Assumptions (e.g., the marginal distribution is Gaussian), eigenvalue decay has been observed in practice on common data sets.
Surbhi Goel - One of the best experts on this subject based on the ideXlab platform.
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eigenvalue decay implies polynomial time learnability for neural networks
arXiv: Learning, 2017Co-Authors: Surbhi Goel, Adam R KlivansAbstract:We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal Assumptions under which these classes admit provably efficient algorithms. In this work we show that a natural Distributional Assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g. feed-forward networks of ReLUs). We make no Assumptions on the structure of the network or the labels. Given sufficiently-strong polynomial eigenvalue decay, we obtain {\em fully}-polynomial time algorithms in {\em all} the relevant parameters with respect to square-loss. Milder decay Assumptions also lead to improved algorithms. This is the first purely Distributional Assumption that leads to polynomial-time algorithms for networks of ReLUs, even with one hidden layer. Further, unlike prior Distributional Assumptions (e.g., the marginal distribution is Gaussian), eigenvalue decay has been observed in practice on common data sets.
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eigenvalue decay implies polynomial time learnability for neural networks
Neural Information Processing Systems, 2017Co-Authors: Surbhi Goel, Adam R KlivansAbstract:We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal Assumptions under which these classes admit provably efficient algorithms. In this work we show that a natural Distributional Assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g. feed-forward networks of ReLUs). We make no Assumptions on the structure of the network or the labels. Given sufficiently-strong eigenvalue decay, we obtain {\em fully}-polynomial time algorithms in {\em all} the relevant parameters with respect to square-loss. This is the first purely Distributional Assumption that leads to polynomial-time algorithms for networks of ReLUs. Further, unlike prior Distributional Assumptions (e.g., the marginal distribution is Gaussian), eigenvalue decay has been observed in practice on common data sets.
Bogdan Pasaniuc - One of the best experts on this subject based on the ideXlab platform.
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local genetic correlation gives insights into the shared genetic architecture of complex traits
American Journal of Human Genetics, 2017Co-Authors: Huwenbo Shi, Nicholas Mancuso, Sarah Spendlove, Bogdan PasaniucAbstract:Although genetic correlations between complex traits provide valuable insights into epidemiological and etiological studies, a precise quantification of which genomic regions disproportionately contribute to the genome-wide correlation is currently lacking. Here, we introduce ρ-HESS, a technique to quantify the correlation between pairs of traits due to genetic variation at a small region in the genome. Our approach requires GWAS summary data only and makes no Distributional Assumption on the causal variant effect sizes while accounting for linkage disequilibrium (LD) and overlapping GWAS samples. We analyzed large-scale GWAS summary data across 36 quantitative traits, and identified 25 genomic regions that contribute significantly to the genetic correlation among these traits. Notably, we find 6 genomic regions that contribute to the genetic correlation of 10 pairs of traits that show negligible genome-wide correlation, further showcasing the power of local genetic correlation analyses. Finally, we report the distribution of local genetic correlations across the genome for 55 pairs of traits that show putative causal relationships.
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local genetic correlation gives insights into the shared genetic architecture of complex traits
bioRxiv, 2016Co-Authors: Huwenbo Shi, Nicholas Mancuso, Sarah Spendlove, Bogdan PasaniucAbstract:Although genetic correlations between complex traits provide valuable insights into epidemiological and etiological studies, a precise quantification of which genomic regions contribute to the genome-wide genetic correlation is currently lacking. Here, we introduce ρ-HESS, a technique to quantify the correlation between pairs of traits due to genetic variation at a small region in the genome. Our approach only requires GWAS summary data and makes no Distributional Assumption on the causal variant effects sizes while accounting for linkage disequilibrium (LD) and overlapping GWAS samples. We analyzed large-scale GWAS summary data across 35 complex traits, and identified 27 genomic regions that contribute significantly to the genetic correlation among these traits. Notably, we find 7 genomic regions that contribute to the genetic correlation of 12 pairs of traits that show negligible genome-wide correlation, further showcasing the power of local genetic correlation analyses. Finally, we leverage the distribution of local genetic correlations across the genome to assign putative direction of causality for 15 pairs of traits.
Huwenbo Shi - One of the best experts on this subject based on the ideXlab platform.
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local genetic correlation gives insights into the shared genetic architecture of complex traits
American Journal of Human Genetics, 2017Co-Authors: Huwenbo Shi, Nicholas Mancuso, Sarah Spendlove, Bogdan PasaniucAbstract:Although genetic correlations between complex traits provide valuable insights into epidemiological and etiological studies, a precise quantification of which genomic regions disproportionately contribute to the genome-wide correlation is currently lacking. Here, we introduce ρ-HESS, a technique to quantify the correlation between pairs of traits due to genetic variation at a small region in the genome. Our approach requires GWAS summary data only and makes no Distributional Assumption on the causal variant effect sizes while accounting for linkage disequilibrium (LD) and overlapping GWAS samples. We analyzed large-scale GWAS summary data across 36 quantitative traits, and identified 25 genomic regions that contribute significantly to the genetic correlation among these traits. Notably, we find 6 genomic regions that contribute to the genetic correlation of 10 pairs of traits that show negligible genome-wide correlation, further showcasing the power of local genetic correlation analyses. Finally, we report the distribution of local genetic correlations across the genome for 55 pairs of traits that show putative causal relationships.
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local genetic correlation gives insights into the shared genetic architecture of complex traits
bioRxiv, 2016Co-Authors: Huwenbo Shi, Nicholas Mancuso, Sarah Spendlove, Bogdan PasaniucAbstract:Although genetic correlations between complex traits provide valuable insights into epidemiological and etiological studies, a precise quantification of which genomic regions contribute to the genome-wide genetic correlation is currently lacking. Here, we introduce ρ-HESS, a technique to quantify the correlation between pairs of traits due to genetic variation at a small region in the genome. Our approach only requires GWAS summary data and makes no Distributional Assumption on the causal variant effects sizes while accounting for linkage disequilibrium (LD) and overlapping GWAS samples. We analyzed large-scale GWAS summary data across 35 complex traits, and identified 27 genomic regions that contribute significantly to the genetic correlation among these traits. Notably, we find 7 genomic regions that contribute to the genetic correlation of 12 pairs of traits that show negligible genome-wide correlation, further showcasing the power of local genetic correlation analyses. Finally, we leverage the distribution of local genetic correlations across the genome to assign putative direction of causality for 15 pairs of traits.
Chihyuck Jun - One of the best experts on this subject based on the ideXlab platform.
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a new exponentially weighted moving average sign chart using repetitive sampling
Journal of Process Control, 2014Co-Authors: Muhammad Aslam, Muhammad Azam, Chihyuck JunAbstract:Abstract In this paper, a new nonparametric control chart based on the exponentially weighted moving average (EWMA) sign statistic is proposed using repetitive sampling. The control chart is proposed to effectively detect the process mean shift away from the target value without the Distributional Assumption on the quality characteristic. The proposed control chart is based on two pairs of upper and lower control limits having different control coefficients. The in-control and the out-of-control average run lengths of the proposed control chart are evaluated through the Monte Carlo simulation. The proposed control chart is shown to be more efficient than the existing EWMA sign control chart in terms of the average run length.