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Fast Training of Sparse Graph Neural Networks on Dense HardwareJun 27 2019Graph neural networks have become increasingly popular in recent years due to their ability to naturally encode relational input data and their ability to scale to large graphs by operating on a sparse representation of graph adjacency matrices. As we ... More

The Hanabi Challenge: A New Frontier for AI ResearchFeb 01 2019From the early days of computing, games have been important testbeds for studying how well machines can do sophisticated decision making. In recent years, machine learning has made dramatic advances with artificial agents reaching superhuman performance ... More

Super-resolution, Extremal Functions and the Condition Number of Vandermonde MatricesAug 07 2014Apr 29 2015Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely studied in the statistics, ... More

A Singly-Exponential Time Algorithm for Computing Nonnegative RankApr 30 2012Here, we give an algorithm for deciding if the nonnegative rank of a matrix $M$ of dimension $m \times n$ is at most $r$ which runs in time $(nm)^{O(r^2)}$. This is the first exact algorithm that runs in time singly-exponential in $r$. This algorithm ... More

Approximate Counting, the Lovasz Local Lemma and Inference in Graphical ModelsOct 14 2016In this paper we introduce a new approach for approximately counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula $\Phi$ with at least $k$ variables ... More

Dopamine: A Research Framework for Deep Reinforcement LearningDec 14 2018Deep reinforcement learning (deep RL) research has grown significantly in recent years. A number of software offerings now exist that provide stable, comprehensive implementations for benchmarking. At the same time, recent deep RL research has become ... More

Distributional reinforcement learning with linear function approximationFeb 08 2019Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cram\'er distance, but ... More

A penalized empirical likelihood method in high dimensionsFeb 13 2013Feb 27 2013This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is derived under ... More

Noisy Tensor Completion via the Sum-of-Squares HierarchyJan 26 2015Feb 18 2016In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to fill in its missing ... More

Beyond the Low-Degree Algorithm: Mixtures of Subcubes and Their ApplicationsMar 17 2018Feb 19 2019We introduce the problem of learning mixtures of $k$ subcubes over $\{0,1\}^n$, which contains many classic learning theory problems as a special case (and is itself a special case of others). We give a surprising $n^{O(\log k)}$-time learning algorithm ... More

A Polynomial Time Algorithm for Lossy Population RecoveryFeb 06 2013Jul 10 2013We give a polynomial time algorithm for the lossy population recovery problem. In this problem, the goal is to approximately learn an unknown distribution on binary strings of length $n$ from lossy samples: for some parameter $\mu$ each coordinate of ... More

The Paulsen Problem Made SimpleSep 13 2018The Paulsen problem is a basic problem in operator theory that was resolved in a recent tour-de-force work of Kwok, Lau, Lee and Ramachandran. In particular, they showed that every $\epsilon$-nearly equal norm Parseval frame in $d$ dimensions is within ... More

Efficiently Learning Mixtures of Mallows ModelsAug 17 2018Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population. They have a variety of applications including social choice, recommendation systems and natural language processing. Here we give the first ... More

Settling the Polynomial Learnability of Mixtures of GaussiansApr 23 2010Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We give an algorithm for this problem that has a running time, and data requirement polynomial in the dimension and the inverse ... More

Algorithms and Hardness for Robust Subspace RecoveryNov 05 2012Dec 03 2013We consider a fundamental problem in unsupervised learning called \emph{subspace recovery}: given a collection of $m$ points in $\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$ can we find ... More

Pareto Optimal Solutions for Smoothed AnalystsNov 10 2010Consider an optimization problem with $n$ binary variables and $d+1$ linear objective functions. Each valid solution $x \in \{0,1\}^n$ gives rise to an objective vector in $\R^{d+1}$, and one often wants to enumerate the Pareto optima among them. In the ... More

Spectral Methods from Tensor NetworksNov 02 2018A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not ... More

Emergence of Persistent Infection due to HeterogeneityMay 27 2016We explore the emergence of persistent infection in a patch of population, where the disease progression of the individuals is given by the SIRS model and an individual becomes infected on contact with another infected individual. We investigate the persistence ... More

Anticipating Persistent InfectionMay 04 2018We explore the emergence of persistent infection in a closed region where the disease progression of the individuals is given by the SIRS model, with an individual becoming infected on contact with another infected individual within a given range. We ... More

The Circuit Complexity of InferenceApr 11 2019Belief propagation is one of the foundations of probabilistic and causal reasoning. In this paper, we study the circuit complexity of some of the various tasks it performs. Specifically, in the broadcast tree model (which has important applications to ... More

How Robust are Reconstruction Thresholds for Community Detection?Nov 04 2015Mar 21 2016The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle et al. conjectured ... More

Near-Extremal Near-HorizonsAug 24 2018Nov 05 2018We study the behaviour of a near-extremal black hole at low energies and low temperatures and find that it can be determined from the near-horizon $AdS_2$ region. Our analysis includes charged matter and also goes beyond the $S$-wave approximation. We ... More

Information Theoretic Properties of Markov Random Fields, and their Algorithmic ApplicationsMay 31 2017Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for provably learning ... More

Learning Topic Models - Going beyond SVDApr 09 2012Apr 10 2012Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents. A number of foundational works both ... More

Nearly Complete Graphs Decomposable into Large Induced Matchings and their ApplicationsNov 01 2011Nov 08 2011We describe two constructions of (very) dense graphs which are edge disjoint unions of large {\em induced} matchings. The first construction exhibits graphs on $N$ vertices with ${N \choose 2}-o(N^2)$ edges, which can be decomposed into pairwise disjoint ... More

New Algorithms for Learning Incoherent and Overcomplete DictionariesAug 28 2013May 26 2014In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in applications such ... More

Entanglement Entropy, Relative Entropy and DualityNov 16 2018A definition for the entanglement entropy in both Abelian and non-Abelian gauge theories has been given in the literature, based on an extended Hilbert space construction. The result can be expressed as a sum of two terms, a classical term and a quantum ... More

How Many Subpopulations is Too Many? Exponential Lower Bounds for Inferring Population HistoriesNov 07 2018Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no rigorous guarantees. ... More

Learning Restricted Boltzmann Machines via Influence MaximizationMay 25 2018Nov 05 2018Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of settings, there has ... More

A renormalization group analysis of extended electronic states in 1d quasiperiodic latticesJul 07 1994We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasi-periodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. {\bf B 48}, 4192 (1993) ], within the framework of the real-space ... More

Vertex Sparsifiers and Abstract Rounding AlgorithmsJun 23 2010The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just the terminal ... More

Optimality and Sub-optimality of PCA for Spiked Random Matrices and SynchronizationSep 19 2016A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis ... More

Improved Bounds for Randomly Sampling Colorings via Linear ProgrammingOct 30 2018A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of $k$-colorings of a graph $G$ on $n$ vertices with maximum degree $\Delta$ is rapidly mixing for $k\ge\Delta+2$. In FOCS 1999, Vigoda showed that ... More

Computing a Nonnegative Matrix Factorization -- ProvablyNov 03 2011In the Nonnegative Matrix Factorization (NMF) problem we are given an $n \times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n \times r$ and $r \times m$ respectively. ... More

Extended electronic states in disordered 1-d lattices: an exampleDec 02 1993We discuss a very simple model of a 1-d disordered lattice, in which {\em all} the electronic eigenstates are extended. The nature of these states is examined from several viewpoints, and it is found that the eigenfunctions are not Bloch functions although ... More

Extended states in 1D lattices: application to quasiperiodic copper-mean chainJul 24 1993The question of the conditions under which 1D systems support extended electronic eigenstates is addressed in a very general context. Using real space renormalisation group arguments we discuss the precise criteria for determining the entire spertrum ... More

Jackiw-Teitelboim Gravity and Rotating Black HolesMay 24 2019We show that the free energy at low temperatures for near-extremal black holes is correctly obtained from the Jackiw-Teitelboim (JT) model of gravity. Our arguments apply to all black holes, including rotating ones, whose metric has a near-horizon $\mathrm{AdS}_2$ ... More

Maximum likelihood estimation of determinantal point processesJan 23 2017Jul 21 2017Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic properties of ... More

Learning Determinantal Point Processes with Moments and CyclesMar 01 2017Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are fast algorithms ... More

Optimality and Sub-optimality of PCA I: Spiked Random Matrix ModelsJul 02 2018Jul 13 2018A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical ... More

How Many Subpopulations is Too Many? Exponential Lower Bounds for Inferring Population HistoriesNov 07 2018May 08 2019Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no rigorous guarantees. ... More

Optimality and Sub-optimality of PCA for Spiked Random Matrices and SynchronizationSep 19 2016Dec 23 2016A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis ... More

Message-passing algorithms for synchronization problems over compact groupsOct 14 2016Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or SO(3). The ... More

Simple, Efficient, and Neural Algorithms for Sparse CodingMar 02 2015Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard formulation is as a ... More

Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian Mixtures and AutoencodersJun 23 2012Nov 12 2012We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees. In particular, suppose we are given samples of the form $y = Ax + \eta$ where $A$ is an unknown $n \times n$ matrix and $x$ is a random variable ... More

Provable Algorithms for Inference in Topic ModelsMay 27 2016Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference has proven ... More

Smoothed Analysis of Tensor DecompositionsNov 14 2013Jan 20 2014Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs ... More

On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse latticeDec 06 1994A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended ... More

Learning Some Popular Gaussian Graphical Models without Condition Number BoundsMay 03 2019Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension and they are ... More

Rates of estimation for determinantal point processesJun 03 2017Jul 21 2017Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic properties of ... More

Dueling AlgorithmsJan 14 2011We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two players, whose ... More

Electric and Magnetic response in dielectric dark states for low loss subwavelength optical meta atomsApr 22 2016Created surfaces or meta surfaces, composed of appropriately shaped sub-wavelength structures, namely, meta-atoms, control light at wavelength scales. Historically, meta surfaces have used radiating metallic resonators as wavelength inclusions. However, ... More

Hybrid scheme for factorization: Factoring 551 using a 3-qubit NMR quantum adiabatic processorNov 03 2016Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorization. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the factors of a given ... More

A Polynomial-time Approximation Scheme for Fault-tolerant Distributed StorageJul 13 2013We consider a problem which has received considerable attention in systems literature because of its applications to routing in delay tolerant networks and replica placement in distributed storage systems. In abstract terms the problem can be stated as ... More

Can Women Break the Glass Ceiling?: An Analysis of #MeToo Hashtagged Posts on TwitterJun 03 2019In October 2017, there happened the uprising of an unprecedented online movement on social media by women across the world who started publicly sharing their untold stories of being sexually harassed along with the hashtag #MeToo (or some variants of ... More

Realization of an all-dielectric zero-index optical metamaterialJul 18 2013Metamaterials offer unprecedented flexibility for manipulating the optical properties of matter, including the ability to access negative index, ultra-high index and chiral optical properties. Recently, metamaterials with near-zero refractive index have ... More

Robust Estimators in High Dimensions without the Computational IntractabilityApr 21 2016We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning and theoretical ... More

Being Robust (in High Dimensions) Can Be PracticalMar 02 2017Mar 13 2018Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in theoretical computer ... More

Robust Estimators in High Dimensions without the Computational IntractabilityApr 21 2016Mar 15 2019We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning and theoretical ... More

Robustly Learning a Gaussian: Getting Optimal Error, EfficientlyApr 12 2017Nov 05 2017We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve estimation error ... More

A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique ProblemApr 11 2016Apr 12 2016We prove that with high probability over the choice of a random graph $G$ from the Erd\H{o}s-R\'enyi distribution $G(n,1/2)$, the $n^{O(d)}$-time degree $d$ Sum-of-Squares semidefinite programming relaxation for the clique problem will give a value of ... More

A Practical Algorithm for Topic Modeling with Provable GuaranteesDec 19 2012Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model inference have been based on a maximum likelihood objective. Efficient algorithms exist that approximate ... More

The role of crystallographic orientation of martensitic variants on cleavage crack propagationJun 30 2016Jul 18 2016Cleavage crack propagation has been investigated in a low-carbon lath-martensitic steel using electron back-scattered diffraction technique. The ability of different martensitic boundaries within prior-austenite grain, such as sub-block, block and packet ... More

Hybrid scheme for factorization: Factoring 551 using a 3-qubit NMR quantum adiabatic processorNov 03 2016Nov 16 2016Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorization. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the factors of a given ... More

MEAM potentials for Al, Si, Mg, Cu, and Fe alloysJul 04 2011Mar 08 2012A set of Modified Embedded Atom Method (MEAM) potentials for the interactions between Al, Si, Mg, Cu, and Fe was developed from a combination of each element's MEAM potential in order to study metal alloying. Previously published MEAM parameters of single ... More

Melting tungsten nanoparticles: a molecular dynamics studyMay 11 2007We report a molecular dynamics simulation of melting of tungsten (W) nanoparticles. The modified embedded atom method (MEAM) interatomic potentials are used to describe the interaction between tungsten atoms. The melting temperature of unsupported tungsten ... More

Metasurface polarization splitterOct 13 2016Polarization beam splitters, devices that separate the two orthogonal polarizations of light into different propagation directions, are one of the most ubiquitous optical elements. However, traditionally polarization splitters rely on bulky optical materials, ... More

A multi-objective optimization procedure to develop modified-embedded-atom-method potentials: an application to magnesiumAug 01 2007We have developed a multi-objective optimization (MOO) procedure to construct modified-embedded-atom-method (MEAM) potentials with minimal manual fitting. This procedure has been applied successfully to develop a new MEAM potential for magnesium. The ... More

Site occupancy and magnetic properties of Al-substituted M-type strontium hexaferriteApr 09 2015Apr 27 2015We use first-principles total-energy calculations based on density functional theory to study the site occupancy and magnetic properties of Al-substituted $M$-type strontium hexaferrite SrFe$_{12-x}$Al$_{x}$O$_{19}$ with $x=0.5$ and $x=1.0$. We find that ... More

Beating the random assignment on constraint satisfaction problems of bounded degreeMay 13 2015Aug 11 2015We show that for any odd $k$ and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $\frac{1}{2} + \Omega(1/\sqrt{D})$ fraction of constraints, where $D$ is a bound ... More