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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

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

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

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

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

Structured Variational Inference in Unstable Gaussian Process State Space ModelsJul 16 2019Gaussian processes are expressive, non-parametric statistical models that are well-suited to learn nonlinear dynamical systems. However, large-scale inference in these state space models is a challenging problem. In this paper, we propose CBF-SSM a scalable ... 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

Learning-based Model Predictive Control for Safe Exploration and Reinforcement LearningJun 27 2019Reinforcement learning has been successfully used to solve difficult tasks in complex unknown environments. However, these methods typically do not provide any safety guarantees during the learning process. This is particularly problematic, since reinforcement ... 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

Mixed-Variable Bayesian OptimizationJul 02 2019The optimization of expensive to evaluate, black-box, mixed-variable functions, i.e. functions that have continuous and discrete inputs, is a difficult and yet pervasive problem in science and engineering. In Bayesian optimization (BO), special cases ... More

Adaptive Sequence SubmodularityFeb 15 2019Jun 20 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 a certain order (e.g., guiding an agent through a series of states). Not ... 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

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

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

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 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

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

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

Learning Implicit Generative Models Using Differentiable Graph TestsSep 04 2017Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base measure, and ... 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

Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic OptimizationMar 21 2010Dec 06 2017Solving 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

Stochastic Bandits with Context DistributionsJun 06 2019We introduce a novel stochastic contextual bandit model, where at each step the adversary chooses a distribution over a context set. The learner observes only the context distribution while the exact context realization remains hidden. This allows for ... More

Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian OptimizationMar 03 2017In practice, the parameters of control policies are often tuned manually. This is time-consuming and frustrating. Reinforcement learning is a promising alternative that aims to automate this process, yet often requires too many experiments to be practical. ... 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

Reinforced Imitation: Sample Efficient Deep Reinforcement Learning for Map-less Navigation by Leveraging Prior DemonstrationsMay 18 2018Aug 31 2018This work presents a case study of a learning-based approach for target driven map-less navigation. The underlying navigation model is an end-to-end neural network which is trained using a combination of expert demonstrations, imitation learning (IL) ... 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

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

Energy conserving Anisotropic Anhysteretic Magnetic Modelling for Finite Element AnalysisDec 20 2012To model ferromagnetic material in finite element analysis a correct description of the constitutive relationship (BH-law) must be found from measured data. This article proposes to use the energy density function as a centrepiece. Using this function, ... 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

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

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

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

Safe Controller Optimization for Quadrotors with Gaussian ProcessesSep 03 2015Aug 16 2017One 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

Streaming Non-monotone Submodular Maximization: Personalized Video Summarization on the FlyJun 12 2017Dec 26 2017The need for real time analysis of rapidly producing data streams (e.g., video and image streams) motivated the design of streaming algorithms that can efficiently extract and summarize useful information from massive data "on the fly". Such problems ... 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

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

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

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

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

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

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

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

Observation of strontium segregation in LaAlO$_{3}$/SrTiO$_{3}$ and NdGaO$_{3}$/SrTiO$_{3}$ oxide heterostructures by X-ray photoemission spectroscopyJan 31 2014LaAlO$_{3}$ and NdGaO$_{3}$ thin films of different thickness have been grown by pulsed laser deposition on TiO$_2$-terminated SrTiO$_{3}$ single crystals and investigated by soft X-ray photoemission spectroscopy. The surface sensitivity of the measurements ... 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

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

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

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

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

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

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

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

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

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

Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in RoboticsFeb 14 2016Mar 02 2018Robotic 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

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

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

Mathematical Notions vs. Human Perception of Fairness: A Descriptive Approach to Fairness for Machine LearningFeb 13 2019Jun 28 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

Mathematical Notions vs. Human Perception of Fairness: A Descriptive Approach to Fairness for Machine LearningFeb 13 2019Aug 19 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

Pullback Attractors of Non-autonomous Stochastic Degenerate Parabolic Equations on Unbounded DomainsSep 05 2013This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R^n. We first establish the asymptotic compactness of the equation in L^2(R^n) and then prove the existence and uniqueness of non-autonomous ... More

Bökstedt periodicity and quotients of DVRsJul 08 2019In this note we compute the topological Hochschild homology of quotients of DVRs. Along the way we give a short argument for B\"okstedt periodicity and generalizations over various other bases. Our strategy also gives a very efficient way to redo the ... More

Improved model for transmission probabilities of membrane bellows based on TPMC simulationsJul 31 2018Many complex vacuum systems include edge-welded bellows. Their simulation in the molecular flow regime with a Test Particle Monte Carlo (TPMC) code, such as MolFlow+, can take considerable amounts of computing power and time. Therefore we investigated ... More

The variety of subadditive functions for finite group schemesApr 05 2016For a finite group scheme, the subadditive functions on finite dimensional representations are studied. It is shown that the projective variety of the cohomology ring can be recovered from the equivalence classes of subadditive functions. Using Crawley-Boevey's ... More

A simple protocol for certifying graph states and applications in quantum networksJan 15 2018We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see for example how it can be used to for measurement ... More

Schauder Bases Having Many Good Block Basic SequencesJul 27 2019In the study of asymptotic geometry in Banach spaces, a basic sequence which gives rise to a spreading model has been called a good sequence. It is well known that every normalized basic sequence in a Banach space has a subsequence which is good. We investigate ... More

Acyclicity versus total acyclicity for complexes over noetherian ringsJun 14 2005Jun 13 2006It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is equivalent, as a triangulated category, to the homotopy category of injective modules. Restricted to compact objects, this statement ... More

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

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

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

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

Learning Generative Models across Incomparable SpacesMay 14 2019May 15 2019Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), ... 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

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

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

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

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

Learning Generative Models across Incomparable SpacesMay 14 2019Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), ... More

Guarantees for Greedy Maximization of Non-submodular Functions with ApplicationsMar 06 2017May 14 2019We 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

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

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

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

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

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

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

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

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 Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian ProcessesMar 15 2016Aug 16 2017Control 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

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