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We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps.
On the probable errors of frequency-constants
Francis Ysidro Edgeworth · 1908
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Teoria statistica delle classi e calcolo delle probabilita
C. Bonferroni · 1936
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Capital asset prices: A theory of market equilibrium under conditions of risk
William F. Sharpe · 1964
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The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets
John Lintner · 1965
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The behavior of maximum likelihood estimates under nonstandard conditions
Peter Huber · 1967
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The prediction of systematic and specific risk in common stocks
Barr Rosenberg and Walt McKibben · 1973
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James Varah · 1975
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A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity
Halbert White · 1980
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The use of subseries values for estimating the variance of a general statistic from a stationary sequence
Edward Carlstein · 1986
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A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix
Whitney Newey and Kenneth West · 1986
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Efficient estimations from a slowly convergent Robbins-Monro process
David Ruppert · 1988
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The jackknife and the bootstrap for general stationary observations
Hans Kunsch · 1989
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The practice of econometrics: classic and contemporary
Ernst Berndt · 1991
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Acceleration of stochastic approximation by averaging
Boris Polyak and Anatoli Juditsky · 1992
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A circular block-resampling procedure for stationary data
Dimitris Politis and Joseph Romano · 1992
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An introduction to the bootstrap
Bradley Efron and Robert J. Tibshirani · 1994
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Automatic lag selection in covariance matrix estimation
Whitney Newey and Kenneth West · 1994
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The stationary bootstrap
Dimitris Politis and Joseph Romano · 1994
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Bootstrap methods and their application
Anthony Christopher Davison and David Victor Hinkley · 1997
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Natural gradient works efficiently in learning
Shun-Ichi Amari · 1998
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Consistent covariance matrix estimation with spatially dependent panel data
John Driscoll and Aart Kraay · 1998
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Asymptotic statistics
Aad W. van der Vaart · 1998
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Spatial Correlations in Panel Data
Aart Kraay and John Driscoll · 1999
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The elements of statistical learning
J. Friedman, T. Hastie, and R. Tibshirani · 2001
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Bootstraps for time series
Peter Bühlmann · 2002
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The capital asset pricing model: Theory and evidence
Eugene F. Fama and Kenneth R. French · 2004
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Update of the drug resistance mutations in HIV-1: 2005
Victoria A Johnson, Francoise Brun-Vezinet, Bonaventura Clotet, Brian Conway, Daniel R. Kuritzkes, Deenan Pillay, Jonathan Schapiro, Amalio Telenti, and Douglas Richman · 2005
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Algorithmic learning in a random world: conformal prediction
Vladimir Vovk, Alexander Gammerman, and Glenn Shafer · 2005
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Genotypic predictors of human immunodeficiency virus type 1 drug resistance
Soo-Yon Rhee, Jonathan Taylor, Gauhar Wadhera, Asa Ben-Hur, Douglas L. Brutlag, and Robert W. Shafer · 2006
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Statistical inference in generalized linear mixed models: A review
F. Tuerlinckx, F. Rijmen, G. Verbeke, and P. Boeck · 2006
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Robust standard errors for panel regressions with cross-sectional dependence
Daniel Hoechle · 2007
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Covariance regularization by thresholding
Peter Bickel and Elizaveta Levina · 2008
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Asymptotic expansions of the Robbins-Monro process
Jürgen Dippon · 2008
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Edgeworth expansions for stochastic approximation theory
Jürgen Dippon · 2008
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A tutorial on conformal prediction
Glenn Shafer and Vladimir Vovk · 2008
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Simultaneous analysis of Lasso and Dantzig selector
Peter Bickel, Ya’acov Ritov, and Alexandre Tsybakov · 2009
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p p -values for high-dimensional regression
Nicolai Meinshausen, Lukas Meier, and Peter Bühlmann · 2009
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Generalized thresholding of large covariance matrices
On asymptotically optimal confidence regions and tests for high-dimensional models
Sara van de Geer, Peter Bühlmann, Ya’acov Ritov, and Ruben Dezeure · 2014
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A proximal stochastic gradient method with progressive variance reduction
Lin Xiao and Tong Zhang · 2014
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Elementary estimators for high-dimensional linear regression
Eunho Yang, Aurelie Lozano, and Pradeep Ravikumar · 2014
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Confidence intervals for low dimensional parameters in high dimensional linear models
Cun-Hui Zhang and Stephanie Zhang · 2014
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Convex optimization: Algorithms and complexity
Sébastien Bubeck · 2015
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StopWasting My Gradients: Practical SVRG
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Adam Rothman, Elizaveta Levina, and Ji Zhu · 2009
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Sharp thresholds for High-Dimensional and noisy sparsity recovery using
Martin Wainwright · 2009
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Fast global convergence rates of gradient methods for high-dimensional statistical recovery
Alekh Agarwal, Sahand Negahban, and Martin Wainwright · 2010
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Statistics for high-dimensional data: methods, theory and applications
Peter Bühlmann and Sara van de Geer · 2011
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Sparse covariance thresholding for high-dimensional variable selection
Jessie Jeng and John Daye · 2011
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Non-asymptotic analysis of stochastic approximation algorithms for machine learning
Eric Moulines and Francis R. Bach · 2011
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Reza Harikandeh, Mohamed Osama Ahmed, Alim Virani, Mark Schmidt, Jakub Konecny, and Scott Sallinen · 2015
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De-biasing the Lasso: Optimal sample size for Gaussian designs
Adel Javanmard and Andrea Montanari · 2015
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Online batch selection for faster training of neural networks
Ilya Loshchilov and Frank Hutter · 2015
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An introduction to matrix concentration inequalities
Joel Tropp · 2015
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Statistical learning with sparsity: the lasso and generalizations
R. Tibshirani, M. Wainwright, and T. Hastie · 2015
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Efficient representation of low-dimensional manifolds using deep networks
Ronen Basri and David Jacobs · 2016
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Statistical inference for model parameters in stochastic gradient descent
Xi Chen, Jason Lee, Xin Tong, and Yichen Zhang · 2016
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Deep nets for local manifold learning
Charles Chui and Hrushikesh Narhar Mhaskar · 2016
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Starting small-learning with adaptive sample sizes
Hadi Daneshmand, Aurelien Lucchi, and Thomas Hofmann · 2016
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Computer age statistical inference
B. Efron and T. Hastie · 2016
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Second-order stochastic optimization for machine learning in linear time
Naman Agarwal, Brian Bullins, and Elad Hazan · 2017
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On perturbed proximal gradient algorithms
Yves F. Atchadé, Gersende Fort, and Eric Moulines · 2017
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Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chains
Aymeric Dieuleveut, Alain Durmus, and Francis Bach · 2017
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On Scalable Inference with Stochastic Gradient Descent
Yixin Fang, Jinfeng Xu, and Lei Yang · 2017
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Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity
Sébastien Gadat and Fabien Panloup · 2017
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Statistical consistency and asymptotic normality for high-dimensional robust
Po-Ling Loh · 2017
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Support recovery without incoherence: A case for nonconvex regularization
Po-Ling Loh and Martin Wainwright · 2017
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Empirical Analysis of the Hessian of Over-Parametrized Neural Networks
Levent Sagun, Utku Evci, V. Ugur Guney, Yann Dauphin, and Leon Bottou · 2017
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Asymptotic and finite-sample properties of estimators based on stochastic gradients
Panos Toulis and Edoardo M. Airoldi · 2017
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High-Dimensional Statistics: A Non-Asymptotic Viewpoint
Martin J. Wainwright · 2017
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Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
Han Xiao, Kashif Rasul, and Roland Vollgraf · 2017
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Panning for gold:‘model-x’knockoffs for high dimensional controlled variable selection
Emmanuel Candes, Yingying Fan, Lucas Janson, and Jinchi Lv · 2018
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Statistical sparse online regression: A diffusion approximation perspective
Jianqing Fan, Wenyan Gong, Chris Junchi Li, and Qiang Sun · 2018
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False Discovery Rate Control via Debiased Lasso
Adel Javanmard and Hamid Javadi · 2018
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Statistical inference using SGD
Tianyang Li, Liu Liu, Anastasios Kyrillidis, and Constantine Caramanis · 2018
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Weijie Su and Yuancheng Zhu · 2018
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