Results 1  10
of
46
Learning mixtures of submodular shells with application to document summarization
, 2012
"... We introduce a method to learn a mixture of submodular “shells” in a largemargin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular function. A mixture of such shells can then also be so instantia ..."
Abstract

Cited by 30 (9 self)
 Add to MetaCart
We introduce a method to learn a mixture of submodular “shells” in a largemargin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular function. A mixture of such shells can then also be so instantiated to produce a more complex submodular function. What our algorithm learns are the mixture weights over such shells. We provide a risk bound guarantee when learning in a largemargin structuredprediction setting using a projected subgradient method when only approximate submodular optimization is possible (such as with submodular function maximization). We apply this method to the problem of multidocument summarization and produce the best results reported so far on the widely used NIST DUC05 through DUC07 document summarization corpora.
Maximizing the Contact Opportunity for Vehicular Internet Access
 In Proc. of IEEE INFOCOM
, 2010
"... Abstract—With increasing popularity of media enabled handhelds, the need for high datarate services for mobile users is evident. Largescale Wireless LANs (WLANs) can provide such a service, but they are expensive to deploy and maintain. Open WLAN accesspoints (APs), on the other hand, need no new ..."
Abstract

Cited by 26 (2 self)
 Add to MetaCart
(Show Context)
Abstract—With increasing popularity of media enabled handhelds, the need for high datarate services for mobile users is evident. Largescale Wireless LANs (WLANs) can provide such a service, but they are expensive to deploy and maintain. Open WLAN accesspoints (APs), on the other hand, need no new deployments, but can offer only opportunistic services with no guarantees on short term throughput. In contrast, a carefully planned sparse deployment of roadside WiFi provides an economically scalable infrastructure with quality of service assurance to mobile users. In this paper, we propose to study deployment techniques for providing roadside WiFi services. In particular, we present a new metric, called Contact Opportunity, as a characterization of a roadside WiFi network. Informally, the contact opportunity for a given deployment measures the fraction of distance or time that a mobile user is in contact with some AP when moving through a certain path. Such a metric is closely related to the quality of data service that a mobile user might experience while driving through the system. We then present an efficient deployment method that maximizes the worst case contact opportunity under a budget constraint. We further show how to extend this concept and the deployment techniques to a more intuitive metric – the average throughput – by taking various dynamic elements into account. Simulations over a real road network and experimental results show that our approach achieves more than 200 % higher minimum contact opportunity, 30%100 % higher average contact opportunity and a significantly improved distribution of average throughput compared with two commonly used algorithms. I.
Selecting observations against adversarial objectives
 In Advances in Neural Information Processing Systems
, 2007
"... In many applications, one has to actively select among a set of expensive observations before making an informed decision. Often, we want to select observations which performwell when evaluated with an objective function chosen by an adversary. Examples include minimizing the maximum posterior var ..."
Abstract

Cited by 25 (9 self)
 Add to MetaCart
(Show Context)
In many applications, one has to actively select among a set of expensive observations before making an informed decision. Often, we want to select observations which performwell when evaluated with an objective function chosen by an adversary. Examples include minimizing the maximum posterior variance in Gaussian Process regression, robust experimental design, and sensor placement for outbreak detection. In this paper, we present the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for the case where the possible objective functions exhibit submodularity, an intuitive diminishing returns property. Moreover, we prove that better approximation algorithms do not exist unless NPcomplete problems admit efficient algorithms. We evaluate our algorithm on several realworld problems. For Gaussian Process regression, our algorithm compares favorably with stateoftheart heuristics described in the geostatistics literature, while being simpler, faster and providing theoretical guarantees. For robust experimental design, our algorithm performs favorably compared to SDPbased algorithms. 1
Uncertaintydriven view planning for underwater inspection
 In Proc. IEEE Int. Conf. Robotics and Automation
, 2012
"... Abstract — We discuss the problem of inspecting an underwater structure, such as a submerged ship hull, with an autonomous underwater vehicle (AUV). In such scenarios, the goal is to construct an accurate 3D model of the structure and to detect any anomalies (e.g., foreign objects or deformations). ..."
Abstract

Cited by 17 (6 self)
 Add to MetaCart
(Show Context)
Abstract — We discuss the problem of inspecting an underwater structure, such as a submerged ship hull, with an autonomous underwater vehicle (AUV). In such scenarios, the goal is to construct an accurate 3D model of the structure and to detect any anomalies (e.g., foreign objects or deformations). We propose a method for constructing 3D meshes from sonarderived point clouds that provides watertight surfaces, and we introduce uncertainty modeling through nonparametric Bayesian regression. Uncertainty modeling provides novel cost functions for planning the path of the AUV to minimize a metric of inspection performance. We draw connections between the resulting cost functions and submodular optimization, which provides insight into the formal properties of active perception problems. In addition, we present experimental trials that utilize profiling sonar data from ship hull inspection. I.
Interactive Submodular Set Cover
, 2010
"... We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover. Applications include advertising in social networks with hidden information. We give an approximation gu ..."
Abstract

Cited by 17 (4 self)
 Add to MetaCart
(Show Context)
We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover. Applications include advertising in social networks with hidden information. We give an approximation guarantee for a novel greedy algorithm and give a hardness of approximation result which matches up to constant factors. We also discuss negative results for simpler approaches and present encouraging early experimental results.
Simultaneous learning and covering with adversarial noise
 In ICML
, 2011
"... We study simultaneous learning and covering problems: submodular set cover problems that depend on the solution to an active (query) learning problem. The goal is to jointly minimize the cost of both learning and covering. We extend recent work in this setting to allow for a limited amount of advers ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
(Show Context)
We study simultaneous learning and covering problems: submodular set cover problems that depend on the solution to an active (query) learning problem. The goal is to jointly minimize the cost of both learning and covering. We extend recent work in this setting to allow for a limited amount of adversarial noise. Certain noisy query learning problems are a special case of our problem. Crucial to our analysis is a lemma showing the logical OR of two submodular cover constraints can be reduced to a single submodular set cover constraint. Combined with known results, this new lemma allows for arbitrary monotone circuits of submodular cover constraints to be reduced to a single constraint. As an example practical application, we present a movie recommendation website that minimizes the total cost of learning what the user wants to watch and recommending a set of movies. 1. Background Consider a movie recommendation problem where we want to recommend to a user a small set of movies to watch. Assume first that we already have some model of the user’s taste in movies (for example learned from the user’s ratings history or stated genre preferences). In this case, we can pose the recommendation problem as an optimization problem: using the model, we can design an objective function F (S) which measures the quality of a set of movie recommendations S ⊆ V. Our goal is then to maximize F (S) subject to a constraint on the size or cost of S (e.g. S  ≤ k). Alternatively
Label Selection on Graphs
, 2009
"... We investigate methods for selecting sets of labeled vertices for use in predicting the labels of vertices on a graph. We specifically study methods which choose a single batch of labeled vertices (i.e. offline, non sequential methods). In this setting, we find common graph smoothness assumptions di ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
(Show Context)
We investigate methods for selecting sets of labeled vertices for use in predicting the labels of vertices on a graph. We specifically study methods which choose a single batch of labeled vertices (i.e. offline, non sequential methods). In this setting, we find common graph smoothness assumptions directly motivate simple label selection methods with interesting theoretical guarantees. These methods bound prediction error in terms of the smoothness of the true labels with respect to the graph. Some of these bounds give new motivations for previously proposed algorithms, and some suggest new algorithms which we evaluate. We show improved performance over baseline methods on several real world data sets.
Submodular Optimization with Submodular Cover and Submodular Knapsack Constraints
, 2013
"... We investigate two new optimization problems — minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of realworld appl ..."
Abstract

Cited by 14 (8 self)
 Add to MetaCart
(Show Context)
We investigate two new optimization problems — minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of realworld applications in machine learning including sensor placement and data subset selection, which require maximizing a certain submodular function (like coverage or diversity) while simultaneously minimizing another (like cooperative cost). These problems are often posed as minimizing the difference between submodular functions [9, 25] which is in the worst case inapproximable. We show, however, that by phrasing these problems as constrained optimization, which is more natural for many applications, we achieve a number of bounded approximation guarantees. We also show that both these problems are closely related and an approximation algorithm solving one can be used to obtain an approximation guarantee for the other. We provide hardness results for both problems thus showing that our approximation factors are tight up to logfactors. Finally, we empirically demonstrate the performance and good scalability properties of our algorithms.
Algorithms for approximate minimization of the difference between submodular functions, with applications
, 2012
"... We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the pe ..."
Abstract

Cited by 12 (11 self)
 Add to MetaCart
(Show Context)
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the periteration cost of our algorithms is much less than [30], and our algorithms can be used to efficiently minimize a difference between submodular functions under various combinatorial constraints, a problem not previously addressed. We provide computational bounds and a hardness result on the multiplicative inapproximability of minimizing the difference between submodular functions. We show, however, that it is possible to give worstcase additive bounds by providing a polynomial time computable lowerbound on the minima. Finally we show how a number of machine learning problems can be modeled as minimizing the difference between submodular functions. We experimentally show the validity of our algorithms by testing them on the problem of feature selection with submodular cost features.
Graphbased Submodular Selection for Extractive Summarization
, 2009
"... We propose a novel approach for unsupervised extractive summarization. Our approach builds a semantic graph for the document to be summarized. Summary extraction is then formulated as optimizing submodular functions defined on the semantic graph. The optimization is theoretically guaranteed to be n ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
(Show Context)
We propose a novel approach for unsupervised extractive summarization. Our approach builds a semantic graph for the document to be summarized. Summary extraction is then formulated as optimizing submodular functions defined on the semantic graph. The optimization is theoretically guaranteed to be nearoptimal under the framework of submodularity. Extensive experiments on the ICSI meeting summarization task on both human transcripts and automatic speech recognition (ASR) outputs show that the graphbased submodular selection approach consistently outperforms the maximum marginal relevance (MMR) approach, a conceptbased approach using integer linear programming (ILP), and a recursive graphbased ranking algorithm using Google’s PageRank.