no code implementations • 24 Jan 2024 • Yuling Yan, Martin J. Wainwright

In causal inference with panel data under staggered adoption, the goal is to estimate and derive confidence intervals for potential outcomes and treatment effects.

no code implementations • 10 Jan 2024 • Yaqi Duan, Martin J. Wainwright

We introduce a novel framework for analyzing reinforcement learning (RL) in continuous state-action spaces, and use it to prove fast rates of convergence in both off-line and on-line settings.

no code implementations • 14 Sep 2023 • Junhui Cai, Ran Chen, Martin J. Wainwright, Linda Zhao

In each case, we show at least three-fold gains in revenue or profit by our bandit method, as well as the interpretability of the latent factor models that are learned.

no code implementations • 5 Mar 2023 • Licong Lin, Koulik Khamaru, Martin J. Wainwright

Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals.

no code implementations • 16 Jan 2023 • Wenlong Mou, Peng Ding, Martin J. Wainwright, Peter L. Bartlett

When it is violated, the classical semi-parametric efficiency bound can easily become infinite, so that the instance-optimal risk depends on the function class used to model the regression function.

no code implementations • 7 Nov 2022 • Yaqi Duan, Martin J. Wainwright

For a given TD method applied to a well-specified model, its statistical error under trajectory data is similar to that of i. i. d.

no code implementations • 20 Oct 2022 • Eric Xia, Martin J. Wainwright

Second, by combining this meta-result with sample-size dependent guarantees for residual fitting and LSTD computation, we obtain concrete statistical guarantees that depend on the sample size along with the complexity of the function class used to fit the residuals.

no code implementations • 9 Oct 2022 • Aaditya Ramdas, Jianbo Chen, Martin J. Wainwright, Michael I. Jordan

We consider the setting where distinct agents reside on the nodes of an undirected graph, and each agent possesses p-values corresponding to one or more hypotheses local to its node.

no code implementations • 26 Sep 2022 • Wenlong Mou, Martin J. Wainwright, Peter L. Bartlett

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures.

no code implementations • 1 Jun 2022 • Andrea Zanette, Martin J. Wainwright

Such instability can be observed even with linear function approximation.

no code implementations • 6 May 2022 • Cong Ma, Reese Pathak, Martin J. Wainwright

We study the covariate shift problem in the context of nonparametric regression over a reproducing kernel Hilbert space (RKHS).

no code implementations • 24 Mar 2022 • Andrea Zanette, Martin J. Wainwright

We propose and analyze a reinforcement learning principle that approximates the Bellman equations by enforcing their validity only along an user-defined space of test functions.

no code implementations • 6 Feb 2022 • Reese Pathak, Cong Ma, Martin J. Wainwright

We study covariate shift in the context of nonparametric regression.

no code implementations • 21 Jan 2022 • Wenlong Mou, Koulik Khamaru, Martin J. Wainwright, Peter L. Bartlett, Michael I. Jordan

We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space.

no code implementations • 21 Jan 2022 • Koulik Khamaru, Eric Xia, Martin J. Wainwright, Michael I. Jordan

As a consequence, we propose a data-dependent stopping rule for instance-optimal algorithms.

no code implementations • 23 Dec 2021 • Wenlong Mou, Ashwin Pananjady, Martin J. Wainwright, Peter L. Bartlett

We then prove a non-asymptotic instance-dependent bound on a suitably averaged sequence of iterates, with a leading term that matches the local asymptotic minimax limit, including sharp dependence on the parameters $(d, t_{\mathrm{mix}})$ in the higher order terms.

no code implementations • 24 Sep 2021 • Yaqi Duan, Mengdi Wang, Martin J. Wainwright

Whereas existing worst-case theory predicts cubic scaling ($H^3$) in the effective horizon, our theory reveals that there is in fact a much wider range of scalings, depending on the kernel, the stationary distribution, and the variance of the Bellman residual error.

no code implementations • NeurIPS 2021 • Andrea Zanette, Martin J. Wainwright, Emma Brunskill

Actor-critic methods are widely used in offline reinforcement learning practice, but are not so well-understood theoretically.

no code implementations • 5 Jul 2021 • Koulik Khamaru, Yash Deshpande, Tor Lattimore, Lester Mackey, Martin J. Wainwright

We propose a family of online debiasing estimators to correct these distributional anomalies in least squares estimation.

no code implementations • 28 Jun 2021 • Koulik Khamaru, Eric Xia, Martin J. Wainwright, Michael I. Jordan

Various algorithms in reinforcement learning exhibit dramatic variability in their convergence rates and ultimate accuracy as a function of the problem structure.

no code implementations • NeurIPS 2020 • Kush Bhatia, Ashwin Pananjady, Peter L. Bartlett, Anca D. Dragan, Martin J. Wainwright

Finally, we showcase the practical utility of our framework in a user study on autonomous driving, where we find that the Blackwell winner outperforms the von Neumann winner for the overall preferences.

no code implementations • 19 Jan 2021 • Cong Ma, Banghua Zhu, Jiantao Jiao, Martin J. Wainwright

Second, when the behavior policy is unknown, we analyze performance in terms of the competitive ratio, thereby revealing a fundamental gap between the settings of known and unknown behavior policies.

no code implementations • 9 Dec 2020 • Wenlong Mou, Ashwin Pananjady, Martin J. Wainwright

Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations.

no code implementations • 28 Aug 2020 • Chris Junchi Li, Wenlong Mou, Martin J. Wainwright, Michael. I. Jordan

We study the problem of solving strongly convex and smooth unconstrained optimization problems using stochastic first-order algorithms.

1 code implementation • 17 Jun 2020 • Raaz Dwivedi, Chandan Singh, Bin Yu, Martin J. Wainwright

We provide an extensive theoretical characterization of MDL-COMP for linear models and kernel methods and show that it is not just a function of parameter count, but rather a function of the singular values of the design or the kernel matrix and the signal-to-noise ratio.

no code implementations • 22 May 2020 • Nhat Ho, Koulik Khamaru, Raaz Dwivedi, Martin J. Wainwright, Michael. I. Jordan, Bin Yu

Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case.

no code implementations • NeurIPS 2020 • Reese Pathak, Martin J. Wainwright

Motivated by federated learning, we consider the hub-and-spoke model of distributed optimization in which a central authority coordinates the computation of a solution among many agents while limiting communication.

no code implementations • 7 May 2020 • Max Rabinovich, Michael. I. Jordan, Martin J. Wainwright

A line of more recent work in multiple testing has begun to investigate the tradeoffs between the FDR and FNR and to provide lower bounds on the performance of procedures that depend on the model structure.

no code implementations • 9 Apr 2020 • Wenlong Mou, Chris Junchi Li, Martin J. Wainwright, Peter L. Bartlett, Michael. I. Jordan

When the matrix $\bar{A}$ is Hurwitz, we prove a central limit theorem (CLT) for the averaged iterates with fixed step size and number of iterations going to infinity.

no code implementations • 16 Mar 2020 • Koulik Khamaru, Ashwin Pananjady, Feng Ruan, Martin J. Wainwright, Michael. I. Jordan

We address the problem of policy evaluation in discounted Markov decision processes, and provide instance-dependent guarantees on the $\ell_\infty$-error under a generative model.

no code implementations • 11 Dec 2019 • Wenlong Mou, Nhat Ho, Martin J. Wainwright, Peter L. Bartlett, Michael. I. Jordan

We study the problem of sampling from the power posterior distribution in Bayesian Gaussian mixture models, a robust version of the classical posterior.

no code implementations • 1 Oct 2019 • Wenlong Mou, Nicolas Flammarion, Martin J. Wainwright, Peter L. Bartlett

We consider the problem of sampling from a density of the form $p(x) \propto \exp(-f(x)- g(x))$, where $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth and strongly convex function and $g: \mathbb{R}^d \rightarrow \mathbb{R}$ is a convex and Lipschitz function.

no code implementations • 19 Sep 2019 • Ashwin Pananjady, Martin J. Wainwright

Markov reward processes (MRPs) are used to model stochastic phenomena arising in operations research, control engineering, robotics, and artificial intelligence, as well as communication and transportation networks.

no code implementations • 28 Aug 2019 • Wenlong Mou, Yi-An Ma, Martin J. Wainwright, Peter L. Bartlett, Michael. I. Jordan

We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order Langevin dynamics for sampling from distributions with log-concave and smooth densities.

no code implementations • 25 Jul 2019 • Wenlong Mou, Nicolas Flammarion, Martin J. Wainwright, Peter L. Bartlett

We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion.

no code implementations • 11 Jun 2019 • Martin J. Wainwright

We introduce and analyze a form of variance-reduced $Q$-learning.

1 code implementation • 29 May 2019 • Yuansi Chen, Raaz Dwivedi, Martin J. Wainwright, Bin Yu

This bound gives a precise quantification of the faster convergence of Metropolized HMC relative to simpler MCMC algorithms such as the Metropolized random walk, or Metropolized Langevin algorithm.

1 code implementation • 15 May 2019 • Martin J. Wainwright

Motivated by the study of $Q$-learning algorithms in reinforcement learning, we study a class of stochastic approximation procedures based on operators that satisfy monotonicity and quasi-contractivity conditions with respect to an underlying cone.

3 code implementations • 3 Apr 2019 • Jianbo Chen, Michael. I. Jordan, Martin J. Wainwright

We develop HopSkipJumpAttack, a family of algorithms based on a novel estimate of the gradient direction using binary information at the decision boundary.

no code implementations • 1 Feb 2019 • Raaz Dwivedi, Nhat Ho, Koulik Khamaru, Martin J. Wainwright, Michael. I. Jordan, Bin Yu

We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i. i. d.

no code implementations • 20 Dec 2018 • Dhruv Malik, Ashwin Pananjady, Kush Bhatia, Koulik Khamaru, Peter L. Bartlett, Martin J. Wainwright

We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving noise and reward feedback.

no code implementations • NeurIPS 2018 • Raaz Dwivedi, Nhật Hồ, Koulik Khamaru, Martin J. Wainwright, Michael. I. Jordan

We provide two classes of theoretical guarantees: first, we characterize the bias introduced due to the misspecification; and second, we prove that population EM converges at a geometric rate to the model projection under a suitable initialization condition.

no code implementations • 1 Oct 2018 • Raaz Dwivedi, Nhat Ho, Koulik Khamaru, Michael. I. Jordan, Martin J. Wainwright, Bin Yu

A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument.

1 code implementation • ICLR 2019 • Jianbo Chen, Le Song, Martin J. Wainwright, Michael. I. Jordan

We study instancewise feature importance scoring as a method for model interpretation.

no code implementations • 25 Jun 2018 • Cheng Mao, Ashwin Pananjady, Martin J. Wainwright

Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns.

no code implementations • ICML 2018 • Koulik Khamaru, Martin J. Wainwright

We also show that our algorithms can escape strict saddle points for a class of non-smooth functions, thereby generalizing known results for smooth functions.

no code implementations • 27 Feb 2018 • Cheng Mao, Ashwin Pananjady, Martin J. Wainwright

Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns.

3 code implementations • ICML 2018 • Jianbo Chen, Le Song, Martin J. Wainwright, Michael. I. Jordan

We introduce instancewise feature selection as a methodology for model interpretation.

1 code implementation • 8 Jan 2018 • Raaz Dwivedi, Yuansi Chen, Martin J. Wainwright, Bin Yu

Relative to known guarantees for the unadjusted Langevin algorithm (ULA), our bounds show that the use of an accept-reject step in MALA leads to an exponentially improved dependence on the error-tolerance.

no code implementations • 4 Jan 2018 • Reinhard Heckel, Max Simchowitz, Kannan Ramchandran, Martin J. Wainwright

Accordingly, we study the problem of finding approximate rankings from pairwise comparisons.

2 code implementations • 23 Oct 2017 • Yuansi Chen, Raaz Dwivedi, Martin J. Wainwright, Bin Yu

We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope.

1 code implementation • NeurIPS 2017 • Aaditya Ramdas, Fanny Yang, Martin J. Wainwright, Michael. I. Jordan

In the online multiple testing problem, p-values corresponding to different null hypotheses are observed one by one, and the decision of whether or not to reject the current hypothesis must be made immediately, after which the next p-value is observed.

1 code implementation • 29 Sep 2017 • Aaditya Ramdas, Jianbo Chen, Martin J. Wainwright, Michael. I. Jordan

We propose a linear-time, single-pass, top-down algorithm for multiple testing on directed acyclic graphs (DAGs), where nodes represent hypotheses and edges specify a partial ordering in which hypotheses must be tested.

no code implementations • 1 Sep 2017 • Nihar B. Shah, Sivaraman Balakrishnan, Martin J. Wainwright

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise.

no code implementations • 19 Jul 2017 • Ashwin Pananjady, Cheng Mao, Vidya Muthukumar, Martin J. Wainwright, Thomas A. Courtade

We show that when the assignment of items to the topology is arbitrary, these permutation-based models, unlike their parametric counterparts, do not admit consistent estimation for most comparison topologies used in practice.

no code implementations • NeurIPS 2017 • Yuting Wei, Fanny Yang, Martin J. Wainwright

Early stopping of iterative algorithms is a widely-used form of regularization in statistics, commonly used in conjunction with boosting and related gradient-type algorithms.

1 code implementation • NeurIPS 2017 • Jianbo Chen, Mitchell Stern, Martin J. Wainwright, Michael. I. Jordan

We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response.

1 code implementation • NeurIPS 2017 • Fanny Yang, Aaditya Ramdas, Kevin Jamieson, Martin J. Wainwright

We propose an alternative framework to existing setups for controlling false alarms when multiple A/B tests are run over time.

no code implementations • 24 Apr 2017 • Ashwin Pananjady, Martin J. Wainwright, Thomas A. Courtade

The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems.

no code implementations • 18 Mar 2017 • Aaditya Ramdas, Rina Foygel Barber, Martin J. Wainwright, Michael. I. Jordan

There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision.

1 code implementation • ICML 2017 • Yuchen Zhang, Percy Liang, Martin J. Wainwright

For learning two-layer convolutional neural networks, we prove that the generalization error obtained by a convexified CNN converges to that of the best possible CNN.

no code implementations • NeurIPS 2016 • Chi Jin, Yuchen Zhang, Sivaraman Balakrishnan, Martin J. Wainwright, Michael Jordan

Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical Gaussians.

no code implementations • 9 Aug 2016 • Ashwin Pananjady, Martin J. Wainwright, Thomas A. Courtade

Consider a noisy linear observation model with an unknown permutation, based on observing $y = \Pi^* A x^* + w$, where $x^* \in \mathbb{R}^d$ is an unknown vector, $\Pi^*$ is an unknown $n \times n$ permutation matrix, and $w \in \mathbb{R}^n$ is additive Gaussian noise.

no code implementations • 30 Jun 2016 • Nihar B. Shah, Sivaraman Balakrishnan, Martin J. Wainwright

The task of aggregating and denoising crowd-labeled data has gained increased significance with the advent of crowdsourcing platforms and massive datasets.

no code implementations • 28 Jun 2016 • Reinhard Heckel, Nihar B. Shah, Kannan Ramchandran, Martin J. Wainwright

We first analyze a sequential ranking algorithm that counts the number of comparisons won, and uses these counts to decide whether to stop, or to compare another pair of items, chosen based on confidence intervals specified by the data collected up to that point.

no code implementations • 6 May 2016 • Maxim Rabinovich, Aaditya Ramdas, Michael. I. Jordan, Martin J. Wainwright

These results show that it is possible for empirical expectations of functions to concentrate long before the underlying chain has mixed in the classical sense, and we show that the concentration rates we achieve are optimal up to constants.

no code implementations • 25 Mar 2016 • Horia Mania, Aaditya Ramdas, Martin J. Wainwright, Michael. I. Jordan, Benjamin Recht

This paper studies the use of reproducing kernel Hilbert space methods for learning from permutation-valued features.

no code implementations • 22 Mar 2016 • Nihar B. Shah, Sivaraman Balakrishnan, Martin J. Wainwright

Second, we show that a regularized least squares estimator can achieve a poly-logarithmic adaptivity index, thereby demonstrating a $\sqrt{n}$-gap between optimal and computationally achievable adaptivity.

no code implementations • 2 Mar 2016 • Ahmed El Alaoui, Xiang Cheng, Aaditya Ramdas, Martin J. Wainwright, Michael. I. Jordan

Together, these properties show that $p = d+1$ is an optimal choice, yielding a function estimate $\hat{f}$ that is both smooth and non-degenerate, while remaining maximally sensitive to $P$.

no code implementations • 30 Dec 2015 • Nihar B. Shah, Martin J. Wainwright

We consider data in the form of pairwise comparisons of n items, with the goal of precisely identifying the top k items for some value of k < n, or alternatively, recovering a ranking of all the items.

no code implementations • 27 Dec 2015 • Fanny Yang, Sivaraman Balakrishnan, Martin J. Wainwright

By exploiting this characterization, we provide non-asymptotic finite sample guarantees on the Baum-Welch updates, guaranteeing geometric convergence to a small ball of radius on the order of the minimax rate around a global optimum.

no code implementations • 25 Nov 2015 • Yuchen Zhang, Jason D. Lee, Martin J. Wainwright, Michael. I. Jordan

For loss functions that are $L$-Lipschitz continuous, we present algorithms to learn halfspaces and multi-layer neural networks that achieve arbitrarily small excess risk $\epsilon>0$.

no code implementations • 19 Oct 2015 • Nihar B. Shah, Sivaraman Balakrishnan, Adityanand Guntuboyina, Martin J. Wainwright

On the other hand, unlike in the BTL and Thurstone models, computing the minimax-optimal estimator in the stochastically transitive model is non-trivial, and we explore various computationally tractable alternatives.

no code implementations • 10 Sep 2015 • Yudong Chen, Martin J. Wainwright

We provide a simple set of conditions under which projected gradient descent, when given a suitable initialization, converges geometrically to a statistically useful solution.

no code implementations • 29 May 2015 • Yun Yang, Martin J. Wainwright, Michael. I. Jordan

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints.

no code implementations • 9 May 2015 • Mert Pilanci, Martin J. Wainwright

We also describe extensions of our methods to programs involving convex constraints that are equipped with self-concordant barriers.

no code implementations • 6 May 2015 • Nihar B. Shah, Sivaraman Balakrishnan, Joseph Bradley, Abhay Parekh, Kannan Ramchandran, Martin J. Wainwright

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others.

no code implementations • 11 Mar 2015 • Yuchen Zhang, Martin J. Wainwright, Michael. I. Jordan

In this paper, we show that the slow rate is intrinsic to a broad class of M-estimators.

no code implementations • 5 Feb 2015 • Yuchen Zhang, Martin J. Wainwright, Michael. I. Jordan

We study the following generalized matrix rank estimation problem: given an $n \times n$ matrix and a constant $c \geq 0$, estimate the number of eigenvalues that are greater than $c$.

no code implementations • 25 Jan 2015 • Yun Yang, Mert Pilanci, Martin J. Wainwright

Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces.

no code implementations • 17 Dec 2014 • Po-Ling Loh, Martin J. Wainwright

We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and $\ell_\infty$-bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex.

no code implementations • 3 Nov 2014 • Mert Pilanci, Martin J. Wainwright

We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint.

no code implementations • 9 Aug 2014 • Sivaraman Balakrishnan, Martin J. Wainwright, Bin Yu

Leveraging this characterization, we then provide non-asymptotic guarantees on the EM and gradient EM algorithms when applied to a finite set of samples.

no code implementations • 5 May 2014 • John C. Duchi, Michael. I. Jordan, Martin J. Wainwright, Yuchen Zhang

Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines.

no code implementations • 29 Apr 2014 • Mert Pilanci, Martin J. Wainwright

We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a lower-dimensional problem.

no code implementations • 29 Apr 2014 • Geoffrey Schiebinger, Martin J. Wainwright, Bin Yu

As a corollary we control the fraction of samples mislabeled by spectral clustering under finite mixtures with nonparametric components.

no code implementations • 7 Dec 2013 • John C. Duchi, Michael. I. Jordan, Martin J. Wainwright, Andre Wibisono

We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients.

no code implementations • NeurIPS 2013 • Yuchen Zhang, John Duchi, Michael. I. Jordan, Martin J. Wainwright

We establish minimax risk lower bounds for distributed statistical estimation given a budget $B$ of the total number of bits that may be communicated.

no code implementations • NeurIPS 2013 • John Duchi, Martin J. Wainwright, Michael. I. Jordan

We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician.

no code implementations • 15 Jun 2013 • Garvesh Raskutti, Martin J. Wainwright, Bin Yu

The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm.

no code implementations • 22 May 2013 • Yuchen Zhang, John C. Duchi, Martin J. Wainwright

We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression.

no code implementations • NeurIPS 2013 • Po-Ling Loh, Martin J. Wainwright

We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions.

no code implementations • NeurIPS 2012 • Po-Ling Loh, Martin J. Wainwright

We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph.

no code implementations • NeurIPS 2012 • Yuchen Zhang, Martin J. Wainwright, John C. Duchi

The first algorithm is an averaging method that distributes the $N$ data samples evenly to $m$ machines, performs separate minimization on each subset, and then averages the estimates.

no code implementations • NeurIPS 2012 • Andre Wibisono, Martin J. Wainwright, Michael. I. Jordan, John C. Duchi

We consider derivative-free algorithms for stochastic optimization problems that use only noisy function values rather than gradients, analyzing their finite-sample convergence rates.

no code implementations • NeurIPS 2012 • Alekh Agarwal, Sahand Negahban, Martin J. Wainwright

We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse.

no code implementations • NeurIPS 2012 • John C. Duchi, Michael. I. Jordan, Martin J. Wainwright

We study statistical risk minimization problems under a privacy model in which the data is kept confidential even from the learner.

no code implementations • NeurIPS 2011 • Po-Ling Loh, Martin J. Wainwright

On the statistical side, we provide non-asymptotic bounds that hold with high probability for the cases of noisy, missing, and/or dependent data.

no code implementations • NeurIPS 2011 • Miles E. Lopes, Laurent J. Jacob, Martin J. Wainwright

We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we propose a new test statistic for the two-sample test of means that integrates a random projection with the classical Hotelling T^2 statistic.

no code implementations • NeurIPS 2010 • Alekh Agarwal, Sahand Negahban, Martin J. Wainwright

Many statistical $M$-estimators are based on convex optimization problems formed by the weighted sum of a loss function with a norm-based regularizer.

no code implementations • NeurIPS 2010 • Alekh Agarwal, Martin J. Wainwright, John C. Duchi

The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication.

no code implementations • NeurIPS 2009 • Garvesh Raskutti, Bin Yu, Martin J. Wainwright

components from some distribution $\mP$, we determine tight lower bounds on the minimax rate for estimating the regression function with respect to squared $\LTP$ error.

no code implementations • NeurIPS 2009 • Sahand Negahban, Bin Yu, Martin J. Wainwright, Pradeep K. Ravikumar

The estimation of high-dimensional parametric models requires imposing some structure on the models, for instance that they be sparse, or that matrix structured parameters have low rank.

no code implementations • NeurIPS 2009 • Alekh Agarwal, Martin J. Wainwright, Peter L. Bartlett, Pradeep K. Ravikumar

The extensive use of convex optimization in machine learning and statistics makes such an understanding critical to understand fundamental computational limits of learning and estimation.

no code implementations • NeurIPS 2008 • Sahand Negahban, Martin J. Wainwright

We consider the following instance of transfer learning: given a pair of regression problems, suppose that the regression coefficients share a partially common support, parameterized by the overlap fraction $\overlap$ between the two supports.

no code implementations • NeurIPS 2007 • Alan S. Willsky, Erik B. Sudderth, Martin J. Wainwright

Variational methods are frequently used to approximate or bound the partition or likelihood function of a Markov random field.

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