arXiv subjects

Andreas Krause

Publications and source records attributed to Andreas Krause.

At least 325 records · Page 18Linked to original sources

arXiv2014

Online Submodular Maximization under a Matroid Constraint with Application to Learning Assignments

Which 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 marginal utility of each ad or information source. We show that these and other problems can be formalized as repeatedly selecting an assignment of items to positions to maximize a sequence of monotone submodular functions that arrive one by one. We present an efficient algorithm for this general problem and analyze it in the no-regret model. Our algorithm possesses strong theoretical guarantees, such as a performance ratio that converges to the optimal constant of 1 - 1/e. We empirically evaluate our algorithm on two real-world online optimization problems on the web: ad allocation with submodular utilities, and dynamically ranking blogs to detect information cascades. Finally, we present a second algorithm that handles the more general case in which the feasible sets are given by a matroid constraint, while still maintaining a 1 - 1/e asymptotic performance ratio.

cs.LG↗

arXiv2014

Near-Optimally Teaching the Crowd to Classify

How 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 natural stochastic model of the learners, modeling them as randomly switching among hypotheses based on observed feedback. We then develop STRICT, an efficient algorithm for selecting examples to teach to workers. Our solution greedily maximizes a submodular surrogate objective function in order to select examples to show to the learners. We prove that our strategy is competitive with the optimal teaching policy. Moreover, for the special case of linear separators, we prove that an exponential reduction in error probability can be achieved. Our experiments on simulated workers as well as three real image annotation tasks on Amazon Mechanical Turk show the effectiveness of our teaching algorithm.

cs.LG↗

arXiv2014

Near Optimal Bayesian Active Learning for Decision Making

How should we gather information to make effective decisions? We address Bayesian active learning and experimental design problems, where we sequentially select tests to reduce uncertainty about a set of hypotheses. Instead of minimizing uncertainty per se, we consider a set of overlapping decision regions of these hypotheses. Our goal is to drive uncertainty into a single decision region as quickly as possible. We identify necessary and sufficient conditions for correctly identifying a decision region that contains all hypotheses consistent with observations. We develop a novel Hyperedge Cutting (HEC) algorithm for this problem, and prove that is competitive with the intractable optimal policy. Our efficient implementation of the algorithm relies on computing subsets of the complete homogeneous symmetric polynomials. Finally, we demonstrate its effectiveness on two practical applications: approximate comparison-based learning and active localization using a robot manipulator.

cs.LG↗

arXiv2014

A Utility-Theoretic Approach to Privacy in Online Services

Online 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 methods to personalize services based on special knowledge about users and their context. For example, a users demographics, location, and past search and browsing may be useful in enhancing the results offered in response to web search queries. However, reasonable concerns about privacy by both users, providers, and government agencies acting on behalf of citizens, may limit access by services to such information. We introduce and explore an economics of privacy in personalization, where people can opt to share personal information, in a standing or on-demand manner, in return for expected enhancements in the quality of an online service. We focus on the example of web search and formulate realistic objective functions for search efficacy and privacy. We demonstrate how we can find a provably near-optimal optimization of the utility-privacy tradeoff in an efficient manner. We evaluate our methodology on data drawn from a log of the search activity of volunteer participants. We separately assess users' preferences about privacy and utility via a large-scale survey, aimed at eliciting preferences about peoples' willingness to trade the sharing of personal data in returns for gains in search efficiency. We show that a significant level of personalization can be achieved using a relatively small amount of information about users.

cs.AI↗

arXiv2014

Efficient Informative Sensing using Multiple Robots

The 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, these robots have bounded resources, such as limited battery or limited amounts of time to obtain measurements. Thus, careful coordination of their paths is required in order to maximize the amount of information collected, while respecting the resource constraints. In this paper, we present an efficient approach for near-optimally solving the NP-hard optimization problem of planning such informative paths. In particular, we first develop eSIP (efficient Single-robot Informative Path planning), an approximation algorithm for optimizing the path of a single robot. Hereby, we use a Gaussian Process to model the underlying phenomenon, and use the mutual information between the visited locations and remainder of the space to quantify the amount of information collected. We prove that the mutual information collected using paths obtained by using eSIP is close to the information obtained by an optimal solution. We then provide a general technique, sequential allocation, which can be used to extend any single robot planning algorithm, such as eSIP, for the multi-robot problem. This procedure approximately generalizes any guarantees for the single-robot problem to the multi-robot case. We extensively evaluate the effectiveness of our approach on several experiments performed in-field for two important environmental sensing applications, lake and river monitoring, and simulation experiments performed using several real world sensor network data sets.

cs.RO↗

arXiv2014

Optimal Value of Information in Graphical Models

Many 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 decision making tasks, one needs to select which tests to administer before deciding on the most effective treatment. It has been general practice to use heuristic-guided procedures for selecting observations. In this paper, we present the first efficient optimal algorithms for selecting observations for a class of probabilistic graphical models. For example, our algorithms allow to optimally label hidden variables in Hidden Markov Models (HMMs). We provide results for both selecting the optimal subset of observations, and for obtaining an optimal conditional observation plan. Furthermore we prove a surprising result: In most graphical models tasks, if one designs an efficient algorithm for chain graphs, such as HMMs, this procedure can be generalized to polytree graphical models. We prove that the optimizing value of information is $NP^{PP}$-hard even for polytrees. It also follows from our results that just computing decision theoretic value of information objective functions, which are commonly used in practice, is a #P-complete problem even on Naive Bayes models (a simple special case of polytrees). In addition, we consider several extensions, such as using our algorithms for scheduling observation selection for multiple sensors. We demonstrate the effectiveness of our approach on several real-world datasets, including a prototype sensor network deployment for energy conservation in buildings.

cs.AI↗

arXiv2013

Near-Optimal Bayesian Active Learning with Noisy Observations

We 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 observations, a greedy algorithm called generalized binary search (GBS) is known to perform near-optimally. We show that if the observations are noisy, perhaps surprisingly, GBS can perform very poorly. We develop EC2, a novel, greedy active learning algorithm and prove that it is competitive with the optimal policy, thus obtaining the first competitiveness guarantees for Bayesian active learning with noisy observations. Our bounds rely on a recently discovered diminishing returns property called adaptive submodularity, generalizing the classical notion of submodular set functions to adaptive policies. Our results hold even if the tests have non-uniform cost and their noise is correlated. We also propose EffECXtive, a particularly fast approximation of EC2, and evaluate it on a Bayesian experimental design problem involving human subjects, intended to tease apart competing economic theories of how people make decisions under uncertainty.

cs.LG↗

arXiv2013

Incentives for Privacy Tradeoff in Community Sensing

Community 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 should systems valuate and negotiate access to private information, for example in return for monetary incentives? How should they optimally choose the participants from a large population of strategic users with privacy concerns, and compensate them for information shared? In this paper, we address these questions and present a novel mechanism, SeqTGreedy, for budgeted recruitment of participants in community sensing. We first show that privacy tradeoffs in community sensing can be cast as an adaptive submodular optimization problem. We then design a budget feasible, incentive compatible (truthful) mechanism for adaptive submodular maximization, which achieves near-optimal utility for a large class of sensing applications. This mechanism is general, and of independent interest. We demonstrate the effectiveness of our approach in a case study of air quality monitoring, using data collected from the Mechanical Turk platform. Compared to the state of the art, our approach achieves up to 30% reduction in cost in order to achieve a desired level of utility.

cs.GT↗

arXiv2012

Near-optimal Nonmyopic Value of Information in Graphical Models

A 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 of variables in a graphical model. We present the first efficient randomized algorithm providing a constant factor (1-1/e-epsilon) approximation guarantee for any epsilon > 0 with high confidence. The algorithm leverages the theory of submodular functions, in combination with a polynomial bound on sample complexity. We furthermore prove that no polynomial time algorithm can provide a constant factor approximation better than (1 - 1/e) unless P = NP. Finally, we provide extensive evidence of the effectiveness of our method on two complex real-world datasets.

cs.AI↗

arXiv2012

Joint Optimization and Variable Selection of High-dimensional Gaussian Processes

Maximizing 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 Gaussian process (GP) distribution. Assuming that the unknown function only depends on few relevant variables, we show that it is possible to perform joint variable selection and GP optimization. We provide strong performance guarantees for our algorithm, bounding the sample complexity of variable selection, and as well as providing cumulative regret bounds. We further provide empirical evidence on the effectiveness of our algorithm on several benchmark optimization problems.

cs.LG↗

arXiv2012

Parallelizing Exploration-Exploitation Tradeoffs with Gaussian Process Bandit Optimization

Can 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 function mapping stimulus to response and identify the maximum of the function. We formalize the task as a multi-armed bandit problem, where the unknown payoff function is sampled from a Gaussian process (GP), and instead of a single arm, in each round we pull a batch of several arms in parallel. We develop GP-BUCB, a principled algorithm for choosing batches, based on the GP-UCB algorithm for sequential GP optimization. We prove a surprising result; as compared to the sequential approach, the cumulative regret of the parallel algorithm only increases by a constant factor independent of the batch size B. Our results provide rigorous theoretical support for exploiting parallelism in Bayesian global optimization. We demonstrate the effectiveness of our approach on two real-world applications.

cs.LG↗

arXiv2011

Inferring Networks of Diffusion and Influence

Information 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., who infects whom, or who influences whom) is typically very difficult. Furthermore, in many applications, the underlying network over which the diffusions and propagations spread is actually unobserved. We tackle these challenges by developing a method for tracing paths of diffusion and influence through networks and inferring the networks over which contagions propagate. Given the times when nodes adopt pieces of information or become infected, we identify the optimal network that best explains the observed infection times. Since the optimization problem is NP-hard to solve exactly, we develop an efficient approximation algorithm that scales to large datasets and finds provably near-optimal networks. We demonstrate the effectiveness of our approach by tracing information diffusion in a set of 170 million blogs and news articles over a one year period to infer how information flows through the online media space. We find that the diffusion network of news for the top 1,000 media sites and blogs tends to have a core-periphery structure with a small set of core media sites that diffuse information to the rest of the Web. These sites tend to have stable circles of influence with more general news media sites acting as connectors between them.

cs.DS↗

arXiv2011

Adaptive Submodular Optimization under Matroid Constraints

Many 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 extend this classic result to a general class of adaptive optimization problems under partial observability, where each choice can depend on observations resulting from past choices. Specifically, we prove that a natural adaptive greedy algorithm provides a $1/(p+1)$ approximation for the problem of maximizing an adaptive monotone submodular function subject to $p$ matroid constraints, and more generally over arbitrary $p$-independence systems. We illustrate the usefulness of our result on a complex adaptive match-making application.

cs.DS↗

arXiv2010

Efficient Minimization of Decomposable Submodular Functions

Many 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, state-of-the-art algorithms for general submodular minimization are intractable for larger problems. In this paper, we introduce a novel subclass of submodular minimization problems that we call decomposable. Decomposable submodular functions are those that can be represented as sums of concave functions applied to modular functions. We develop an algorithm, SLG, that can efficiently minimize decomposable submodular functions with tens of thousands of variables. Our algorithm exploits recent results in smoothed convex minimization. We apply SLG to synthetic benchmarks and a joint classification-and-segmentation task, and show that it outperforms the state-of-the-art general purpose submodular minimization algorithms by several orders of magnitude.

cs.LG↗

arXiv2010

Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design

Many 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 the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GP-UCB compares favorably with other heuristical GP optimization approaches.

cs.LG↗

arXiv2010

Online Distributed Sensor Selection

A 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 function is not known a priori, must be learned from data, and can even change over time. Furthermore for large sensor networks solving a centralized optimization problem to select sensors is not feasible, and thus we seek a fully distributed solution. In this paper, we present Distributed Online Greedy (DOG), an efficient, distributed algorithm for repeatedly selecting sensors online, only receiving feedback about the utility of the selected sensors. We prove very strong theoretical no-regret guarantees that apply whenever the (unknown) utility function satisfies a natural diminishing returns property called submodularity. Our algorithm has extremely low communication requirements, and scales well to large sensor deployments. We extend DOG to allow observation-dependent sensor selection. We empirically demonstrate the effectiveness of our algorithm on several real-world sensing tasks.

cs.LG↗

arXiv2009

Online Learning of Assignments that Maximize Submodular Functions

Which 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 information sources decreases their marginal utility. We show that these and other problems can be formalized as repeatedly selecting an assignment of items to positions to maximize a sequence of monotone submodular functions that arrive one by one. We present an efficient algorithm for this general problem and analyze it in the no-regret model. Our algorithm possesses strong theoretical guarantees, such as a performance ratio that converges to the optimal constant of 1-1/e. We empirically evaluate our algorithm on two real-world online optimization problems on the web: ad allocation with submodular utilities, and dynamically ranking blogs to detect information cascades.

cs.LG↗

arXiv2009

Evaluating the performance of adapting trading strategies with different memory lengths

We 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 their prediction of the movement for the following time period of a single asset. We find empirically using stocks from the S&P500 that our prediction model yields a high success rate of over 51.5% and produces higher returns than a buy-and-hold strategy. Even when taking into account trading costs we find that using the predictions will generate superior investment portfolios.

q-fin.PM↗