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Evaluating the performance of adapting trading strategies with different memory lengthsJan 05 2009We propose a prediction model based on the minority game in which traders continuously evaluate a complete set of trading strategies with different memory lengths using the strategies' past performance. Based on the chosen trading strategy they determine ... More

Building Hierarchies of Concepts via CrowdsourcingApr 27 2015Aug 01 2015Hierarchies of concepts are useful in many applications from navigation to organization of objects. Usually, a hierarchy is created in a centralized manner by employing a group of domain experts, a time-consuming and expensive process. The experts often ... More

Microstructure Effects on Daily Return Volatility in Financial MarketsNov 17 2000We simulate a series of daily returns from intraday price movements initiated by microstructure elements. Significant evidence is found that daily returns and daily return volatility exhibit first order autocorrelation, but trading volume and daily return ... More

Efficient Minimization of Decomposable Submodular FunctionsOct 26 2010Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial time. Unfortunately, ... More

Optimal Value of Information in Graphical ModelsJan 15 2014Many real-world decision making tasks require us to choose among several expensive observations. In a sensor network, for example, it is important to select the subset of sensors that is expected to provide the strongest reduction in uncertainty. In medical ... More

Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic OptimizationMar 21 2010Oct 17 2012Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, ... More

Adaptive Submodular Optimization under Matroid ConstraintsJan 24 2011Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this article, we ... More

Crowd Access Path Optimization: Diversity MattersAug 08 2015Aug 11 2015Quality assurance is one the most important challenges in crowdsourcing. Assigning tasks to several workers to increase quality through redundant answers can be expensive if asking homogeneous sources. This limitation has been overlooked by current crowdsourcing ... More

AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEsFeb 22 2019Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for ... More

Simulation of Charge Transport in Organic Semiconductors: A Time-Dependent Multiscale Method Based on Non-Equilibrium Green's FunctionsMay 20 2017In weakly interacting organic semiconductors, static and dynamic disorder often have an important impact on transport properties. Describing charge transport in these systems requires an approach that correctly takes structural and electronic fluctuations ... More

Fake News Detection in Social Networks via Crowd SignalsNov 24 2017Mar 02 2018Our work considers leveraging crowd signals for detecting fake news and is motivated by tools recently introduced by Facebook that enable users to flag fake news. By aggregating users' flags, our goal is to select a small subset of news every day, send ... More

Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEsApr 12 2018Mar 01 2019Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system ... More

Incentives for Privacy Tradeoff in Community SensingAug 19 2013Sep 14 2013Community sensing, fusing information from populations of privately-held sensors, presents a great opportunity to create efficient and cost-effective sensing applications. Yet, reasonable privacy concerns often limit the access to such data streams. How ... More

ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical SystemsFeb 17 2019Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian ... More

A Utility-Theoretic Approach to Privacy in Online ServicesJan 16 2014Online offerings such as web search, news portals, and e-commerce applications face the challenge of providing high-quality service to a large, heterogeneous user base. Recent efforts have highlighted the potential to improve performance by introducing ... More

Scalable Variational Inference in Log-supermodular ModelsFeb 23 2015Feb 24 2015We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing approximate inference ... More

Information Directed Sampling and Bandits with Heteroscedastic NoiseJan 29 2018Apr 19 2018In the stochastic bandit problem, the goal is to maximize an unknown function via a sequence of noisy evaluations. Typically, the observation noise is assumed to be independent of the evaluation point and to satisfy a tail bound uniformly on the domain; ... More

Teaching Multiple Concepts to a Forgetful LearnerMay 21 2018Oct 09 2018How can we help a forgetful learner learn multiple concepts within a limited time frame? For long-term learning, it is crucial to devise teaching strategies that leverage the underlying forgetting mechanisms of the learner. In this paper, we cast the ... More

Near-optimal Nonmyopic Value of Information in Graphical ModelsJul 04 2012A fundamental issue in real-world systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most informative subset ... More

On the Bekenstein-Hawking Entropy, Non-Commutative Branes and Logarithmic CorrectionsDec 30 2003Jun 21 2006We extend earlier work on the origin of the Bekenstein-Hawking entropy to higher-dimensional spacetimes. The mechanism of counting states is shown to work for all spacetimes associated with a Euclidean doublet $(E_1,M_1)+(E_2,M_2)$ of electric-magnetic ... More

A Small Cosmological Constant and Backreaction of Non-Finetuned ParametersJul 28 2000Sep 29 2003We include the backreaction on the warped geometry induced by non-finetuned parameters in a two domain-wall set-up to obtain an exponentially small Cosmological Constant $\Lambda_4$. The mechanism to suppress the Cosmological Constant involves one classical ... More

Asymptotic Dynamics of Stochastic $p$-Laplace Equations on Unbounded DomainsAug 03 2014This thesis is concerned with the asymptotic behavior of solutions of stochastic $p$-Laplace equations driven by non-autonomous forcing on $\mathbb{R}^n$. Two cases are studied, with additive and multiplicative noise respectively. Estimates on the tails ... More

The stable derived category of a noetherian schemeMar 30 2004Sep 27 2004For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect complexes. Some ... More

Deriving Auslander's formulaSep 24 2014Jun 13 2015Auslander's formula shows that any abelian category C is equivalent to the category of coherent functors on C modulo the Serre subcategory of all effaceable functors. We establish a derived version of this equivalence. This amounts to showing that the ... More

Radiation feedback on dusty clouds during Seyfert activityMar 22 2011We investigate the evolution of dusty gas clouds falling into the centre of an active Seyfert nucleus. Two-dimensional high-resolution radiation hydrodynamics simulations are performed to study the fate of single clouds and the interaction between two ... More

Safe Controller Optimization for Quadrotors with Gaussian ProcessesSep 03 2015Apr 01 2016One of the most fundamental problems when designing controllers for dynamic systems is the tuning of the controller parameters. Typically, a model of the system is used to obtain an initial controller, but ultimately the controller parameters must be ... More

Online Learning of Assignments that Maximize Submodular FunctionsAug 05 2009Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize value of information? These applications exhibit strong diminishing returns: Selection of redundant ads and ... More

Optimal DR-Submodular Maximization and Applications to Provable Mean Field InferenceMay 19 2018Nov 29 2018Mean field inference in probabilistic models is generally a highly nonconvex problem. Existing optimization methods, e.g., coordinate ascent algorithms, can only generate local optima. In this work we propose provable mean filed methods for probabilistic ... More

No-regret Bayesian Optimization with Unknown HyperparametersJan 10 2019Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate. While several BO algorithms provably converge to the global optimum of the unknown function, they assume ... More

Online Variance Reduction for Stochastic OptimizationFeb 13 2018Jun 06 2018Modern stochastic optimization methods often rely on uniform sampling which is agnostic to the underlying characteristics of the data. This might degrade the convergence by yielding estimates that suffer from a high variance. A possible remedy is to employ ... More

Strong Coresets for Hard and Soft Bregman Clustering with Applications to Exponential Family MixturesAug 21 2015May 02 2016Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means ... More

A stencil-based implementation of Parareal in the C++ domain specific embedded language STELLASep 30 2014Dec 03 2014In view of the rapid rise of the number of cores in modern supercomputers, time-parallel methods that introduce concurrency along the temporal axis are becoming increasingly popular. For the solution of time-dependent partial differential equations, these ... More

Near-Optimal Bayesian Active Learning with Noisy ObservationsOct 15 2010Dec 16 2013We tackle the fundamental problem of Bayesian active learning with noise, where we need to adaptively select from a number of expensive tests in order to identify an unknown hypothesis sampled from a known prior distribution. In the case of noise-free ... More

Online Distributed Sensor SelectionFeb 09 2010May 13 2010A key problem in sensor networks is to decide which sensors to query when, in order to obtain the most useful information (e.g., for performing accurate prediction), subject to constraints (e.g., on power and bandwidth). In many applications the utility ... More

Practical Coreset Constructions for Machine LearningMar 19 2017Jun 04 2017We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset construction ... More

No-Regret Bayesian Optimization with Unknown HyperparametersJan 10 2019Apr 01 2019Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate. While several BO algorithms provably converge to the global optimum of the unknown function, they assume ... More

Online Submodular Maximization under a Matroid Constraint with Application to Learning AssignmentsJul 03 2014Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy decreases the ... More

Near-optimal Bayesian Active Learning with Correlated and Noisy TestsMay 24 2016Jul 11 2016We consider the Bayesian active learning and experimental design problem, where the goal is to learn the value of some unknown target variable through a sequence of informative, noisy tests. In contrast to prior work, we focus on the challenging, yet ... More

Linear-time Outlier Detection via SensitivityMay 02 2016Outliers are ubiquitous in modern data sets. Distance-based techniques are a popular non-parametric approach to outlier detection as they require no prior assumptions on the data generating distribution and are simple to implement. Scaling these techniques ... More

Safe Exploration in Finite Markov Decision Processes with Gaussian ProcessesJun 15 2016In classical reinforcement learning, when exploring an environment, agents accept arbitrary short term loss for long term gain. This is infeasible for safety critical applications, such as robotics, where even a single unsafe action may cause system failure. ... More

Mathematical Notions vs. Human Perception of Fairness: A Descriptive Approach to Fairness for Machine LearningFeb 13 2019Fairness for Machine Learning has received considerable attention, recently. Various mathematical formulations of fairness have been proposed, and it has been shown that it is impossible to satisfy all of them simultaneously. The literature so far has ... More

Multi-Player Bandits: The Adversarial CaseFeb 21 2019We consider a setting where multiple players sequentially choose among a common set of actions (arms). Motivated by a cognitive radio networks application, we assume that players incur a loss upon colliding, and that communication between players is not ... More

Safe Convex Learning under Uncertain ConstraintsMar 11 2019We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as personalized ... More

Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in RoboticsFeb 14 2016Robotics algorithms typically depend on various parameters, the choice of which significantly affects the robot's performance. While an initial guess for the parameters may be obtained from dynamic models of the robot, parameters are usually tuned manually ... More

Inferring Networks of Diffusion and InfluenceJun 01 2010Oct 23 2011Information diffusion and virus propagation are fundamental processes taking place in networks. While it is often possible to directly observe when nodes become infected with a virus or adopt the information, observing individual transmissions (i.e., ... More

Magnetohydrodynamic stability of broad line region cloudsJul 03 2012Aug 16 2012Hydrodynamic stability has been a longstanding issue for the cloud model of the broad line region in active galactic nuclei. We argue that the clouds may be gravitationally bound to the supermassive black hole. If true, stabilisation by thermal pressure ... More

Actively Learning Hemimetrics with Applications to Eliciting User PreferencesMay 23 2016May 27 2016Motivated by an application of eliciting users' preferences, we investigate the problem of learning hemimetrics, i.e., pairwise distances among a set of $n$ items that satisfy triangle inequalities and non-negativity constraints. In our application, the ... More

Noisy Submodular Maximization via Adaptive Sampling with Applications to Crowdsourced Image Collection SummarizationNov 23 2015Dec 01 2015We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of clicks or ... More

Learning to Use Learners' AdviceFeb 16 2017Feb 17 2017In this paper, we study a variant of the framework of online learning using expert advice with limited/bandit feedback. We consider each expert as a learning entity, seeking to more accurately reflecting certain real-world applications. In our setting, ... More

Parallelizing Exploration-Exploitation Tradeoffs with Gaussian Process Bandit OptimizationJun 27 2012Can one parallelize complex exploration exploitation tradeoffs? As an example, consider the problem of optimal high-throughput experimental design, where we wish to sequentially design batches of experiments in order to simultaneously learn a surrogate ... More

Stability of Cloud Orbits in the Broad Line Region of Active Galactic NucleiJul 01 2010Oct 11 2010We investigate the global dynamic stability of spherical clouds in the Broad Line Region (BLR) of Active Galactic Nuclei (AGN), exposed to radial radiation pressure, gravity of the central black hole (BH), and centrifugal forces assuming the clouds adapt ... More

Safe Exploration in Finite Markov Decision Processes with Gaussian ProcessesJun 15 2016Nov 15 2016In classical reinforcement learning, when exploring an environment, agents accept arbitrary short term loss for long term gain. This is infeasible for safety critical applications, such as robotics, where even a single unsafe action may cause system failure. ... More

Differentiable Submodular MaximizationMar 05 2018Jun 14 2018We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial nature, submodular ... More

Scalable k-Means Clustering via Lightweight CoresetsFeb 27 2017Jun 06 2018Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive data sets. While ... More

Joint Optimization and Variable Selection of High-dimensional Gaussian ProcessesJun 27 2012Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from a high-dimensional ... More

Unsupervised Imitation LearningJun 19 2018We introduce a novel method to learn a policy from unsupervised demonstrations of a process. Given a model of the system and a set of sequences of outputs, we find a policy that has a comparable performance to the original policy, without requiring access ... More

The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical SystemsAug 02 2018Oct 01 2018Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since the learned policy ... More

Bounding Inefficiency of Equilibria in Continuous Actions Games using Submodularity and CurvatureMar 03 2019Games with continuous strategy sets arise in several machine learning problems (e.g. adversarial learning). For such games, simple no-regret learning algorithms exist in several cases and ensure convergence to coarse correlated equilibria (CCE). The efficiency ... More

Linear versus set valued Kronecker representationsJun 06 2016A set valued representation of the Kronecker quiver is nothing but a quiver. We apply the forgetful functor from vector spaces to sets and compare linear with set valued representations of the Kronecker quiver.

Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian ProcessesMar 15 2016Oct 05 2016Control theory can provide useful insights into the properties of controlled, dynamic systems. One important property of nonlinear systems is the region of attraction (ROA), a safe subset of the state space in which a given controller renders an equilibrium ... More

Galactic winds - How to launch galactic outflows in typical Lyman-break galaxiesJun 13 2013We perform hydrodynamical simulations of a young galactic disc embedded in a hot gaseous halo using parameters typical for Lyman break galaxies (LBGs). We take into account the (static) gravitational potentials due to a dark matter halo, a stellar bulge ... More

Time parallel gravitational collapse simulationSep 04 2015Dec 28 2016This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar field. To account for the shrinking of the spatial domain in ... More

Information-Directed Exploration for Deep Reinforcement LearningDec 18 2018Efficient exploration remains a major challenge for reinforcement learning. One reason is that the variability of the returns often depends on the current state and action, and is therefore heteroscedastic. Classical exploration strategies such as upper ... More

Learning User Preferences to Incentivize Exploration in the Sharing EconomyNov 17 2017Nov 24 2017We study platforms in the sharing economy and discuss the need for incentivizing users to explore options that otherwise would not be chosen. For instance, rental platforms such as Airbnb typically rely on customer reviews to provide users with relevant ... More

Learning to Compensate Photovoltaic Power Fluctuations from Images of the Sky by Imitating an Optimal PolicyNov 13 2018The energy output of photovoltaic (PV) power plants depends on the environment and thus fluctuates over time. As a result, PV power can cause instability in the power grid, in particular when increasingly used. Limiting the rate of change of the power ... More

Discrete Sampling using Semigradient-based Product MixturesJul 04 2018Jul 09 2018We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and Ising models. ... More

Lazier Than Lazy GreedySep 28 2014Nov 28 2014Is it possible to maximize a monotone submodular function faster than the widely used lazy greedy algorithm (also known as accelerated greedy), both in theory and practice? In this paper, we develop the first linear-time algorithm for maximizing a general ... More

Training Gaussian Mixture Models at Scale via CoresetsMar 23 2017Jan 15 2018How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good ... More

Uniform Deviation Bounds for Unbounded Loss Functions like k-MeansFeb 27 2017Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we ... More

Continuous DR-submodular Maximization: Structure and AlgorithmsNov 04 2017Dec 16 2017DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others. DR-submodularity ... More

Guarantees for Greedy Maximization of Non-submodular Functions with ApplicationsMar 06 2017Jun 13 2017We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for maximizing submodular ... More

Algorithms for Learning Sparse Additive Models with Interactions in High DimensionsMay 02 2016May 08 2017A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}\phi_{l}(x_l)$ where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll d$. Assuming $\phi$'s, $\mathcal{S}$ ... More

Bond and site color-avoiding percolation in scale free networksJul 23 2018Sep 12 2018Recently the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one vulnerability ... More

Adaptive Sequence SubmodularityFeb 15 2019In many machine learning applications, one needs to interactively select a sequence of items (e.g., recommending movies based on a user's feedback) or make sequential decisions in certain orders (e.g., guiding an agent through a series of states). Not ... More

Radiatively enhanced elasticity and turbulence in clumpy tori of Active Galactic NucleiNov 25 2009Jul 01 2010The paper assumes radiation forces proportional to distance between equal temperature clouds. However, we assume there are clouds in any direction. The forces then cancel almost entirely, besides small velocity effects. Therefore, the presented theory ... More

Fairness Behind a Veil of Ignorance: A Welfare Analysis for Automated Decision MakingJun 13 2018Jan 11 2019We draw attention to an important, yet largely overlooked aspect of evaluating fairness for automated decision making systems---namely risk and welfare considerations. Our proposed family of measures corresponds to the long-established formulations of ... More

Horizontally Scalable Submodular MaximizationMay 31 2016A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances that can fit in ... More

Efficient Online Learning for Optimizing Value of Information: Theory and Application to Interactive TroubleshootingMar 16 2017Jul 17 2017We consider the optimal value of information (VoI) problem, where the goal is to sequentially select a set of tests with a minimal cost, so that one can efficiently make the best decision based on the observed outcomes. Existing algorithms are either ... More

Safe Model-based Reinforcement Learning with Stability GuaranteesMay 23 2017Nov 13 2017Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world systems. As ... More

Learning-based Model Predictive Control for Safe ExplorationMar 22 2018Nov 07 2018Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in safety-critical, real-world ... More

Learning Sparse Additive Models with Interactions in High DimensionsApr 18 2016A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is referred to as a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}\phi_{l}(x_l)$, where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll d$. Assuming $\phi_l$'s ... More

Near-Optimally Teaching the Crowd to ClassifyFeb 10 2014Mar 07 2014How should we present training examples to learners to teach them classification rules? This is a natural problem when training workers for crowdsourcing labeling tasks, and is also motivated by challenges in data-driven online education. We propose a ... More

Information Gathering with Peers: Submodular Optimization with Peer-Prediction ConstraintsNov 17 2017Nov 24 2017We study a problem of optimal information gathering from multiple data providers that need to be incentivized to provide accurate information. This problem arises in many real world applications that rely on crowdsourced data sets, but where the process ... More

Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional SubspacesFeb 08 2019Bayesian optimization is known to be difficult to scale to high dimensions, because the acquisition step requires solving a non-convex optimization problem in the same search space. In order to scale the method and keep its benefits, we propose an algorithm ... More

Efficient Informative Sensing using Multiple RobotsJan 15 2014The need for efficient monitoring of spatio-temporal dynamics in large environmental applications, such as the water quality monitoring in rivers and lakes, motivates the use of robotic sensors in order to achieve sufficient spatial coverage. Typically, ... More

Guaranteed Non-convex Optimization: Submodular Maximization over Continuous DomainsJun 17 2016Sep 20 2016Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation guarantees. ... More

Algorithms for Learning Sparse Additive Models with Interactions in High DimensionsMay 02 2016A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}\phi_{l}(x_l)$ where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll d$. Assuming $\phi$'s, $\mathcal{S}$ ... More

Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set EstimationOct 24 2016We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a ... More

Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental DesignDec 21 2009Jun 09 2010Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve ... More

Stochastic Submodular Maximization: The Case of Coverage FunctionsNov 05 2017Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic continuous optimization, ... More

Coordinated Online Learning With Applications to Learning User PreferencesFeb 09 2017We study an online multi-task learning setting, in which instances of related tasks arrive sequentially, and are handled by task-specific online learners. We consider an algorithmic framework to model the relationship of these tasks via a set of convex ... More

Submodularity on Hypergraphs: From Sets to SequencesFeb 26 2018Mar 15 2018In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a large volume ... More

Information-Directed Exploration for Deep Reinforcement LearningDec 18 2018Mar 25 2019Efficient exploration remains a major challenge for reinforcement learning. One reason is that the variability of the returns often depends on the current state and action, and is therefore heteroscedastic. Classical exploration strategies such as upper ... More

Online Variance Reduction with MixturesMar 29 2019Adaptive importance sampling for stochastic optimization is a promising approach that offers improved convergence through variance reduction. In this work, we propose a new framework for variance reduction that enables the use of mixtures over predefined ... More

Dimensions of triangulated categories via Koszul objectsFeb 07 2008Apr 15 2009Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation ... More

Distributed Submodular MaximizationNov 03 2014Jun 27 2016Many large-scale machine learning problems--clustering, non-parametric learning, kernel machines, etc.--require selecting a small yet representative subset from a large dataset. Such problems can often be reduced to maximizing a submodular set function ... More

Time parallel gravitational collapse simulationSep 04 2015Apr 24 2016This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar field. To account for the shrinking of the spatial domain in ... More

Tradeoffs for Space, Time, Data and Risk in Unsupervised LearningMay 02 2016Faced with massive data, is it possible to trade off (statistical) risk, and (computational) space and time? This challenge lies at the heart of large-scale machine learning. Using k-means clustering as a prototypical unsupervised learning problem, we ... More

Guaranteed Non-convex Optimization: Submodular Maximization over Continuous DomainsJun 17 2016Mar 01 2017Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation guarantees. ... More

A Moral Framework for Understanding of Fair ML through Economic Models of Equality of OpportunitySep 10 2018Nov 27 2018We map the recently proposed notions of algorithmic fairness to economic models of Equality of opportunity (EOP)---an extensively studied ideal of fairness in political philosophy. We formally show that through our conceptual mapping, many existing definition ... More