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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 4 (2 self)
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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
Query Learning and Certificates in Lattices
"... Abstract. We provide an abstract version, in terms of lattices, of the Horn query learning algorithm of Angluin, Frazier, and Pitt. To validate it, we develop a proof that is independent of the propositional Horn logic structure. We also construct a certificate set for the class of lattices that gen ..."
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Cited by 2 (2 self)
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Abstract. We provide an abstract version, in terms of lattices, of the Horn query learning algorithm of Angluin, Frazier, and Pitt. To validate it, we develop a proof that is independent of the propositional Horn logic structure. We also construct a certificate set for the class of lattices that generalizes and improves an earlier certificate construction and that relates very clearly with the new proof. 1
Active Learning and Submodular Functions
, 2012
"... Active learning is a machine learning setting where the learning algorithm decides what data is labeled. Submodular functions are a class of set functions for which many optimization problems have efficient exact or approximate algorithms. We examine their connections. • We propose a new class of in ..."
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Active learning is a machine learning setting where the learning algorithm decides what data is labeled. Submodular functions are a class of set functions for which many optimization problems have efficient exact or approximate algorithms. We examine their connections. • We propose a new class of interactive submodular optimization problems which connect and generalize submodular optimization and active learning over a finite query set. We derive greedy algorithms with approximately optimal worstcase cost. These analyses apply to exact learning, approximate learning, learning in the presence of adversarial noise, and applications that mix learning and covering. • We consider active learning in a batch, transductive setting where the learning algorithm selects a set of examples to be labeled at once. In this setting we derive new error bounds which use symmetric submodular functions for regularization, and we give algorithms which approximately minimize these bounds. • We consider a repeated active learning setting where the learning algorithm solves a sequence of related learning problems. We propose an approach to this problem based on a new online prediction version of submodular set cover. A common
25th Annual Conference on Learning Theory Computational Bounds on Statistical Query Learning
"... We study the complexity of learning in Kearns ’ wellknown statistical query (SQ) learning model (Kearns, 1993). A number of previous works have addressed the definition and estimation of the informationtheoretic bounds on the SQ learning complexity, in other words, bounds on the query complexity. ..."
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We study the complexity of learning in Kearns ’ wellknown statistical query (SQ) learning model (Kearns, 1993). A number of previous works have addressed the definition and estimation of the informationtheoretic bounds on the SQ learning complexity, in other words, bounds on the query complexity. Here we give the first strictly computational upper and lower bounds on the complexity of several types of learning in the SQ model. As it was already observed, the known characterization of distributionspecific SQ learning (Blum, et al. 1994) implies that for weak learning over a fixed distribution, the query complexity and computational complexity are essentially the same. In contrast, we show that for both distributionspecific and distributionindependent (strong) learning there exists a concept class of polynomial query complexity that is not efficiently learnable unless RP = NP. We then prove that our distributionspecific lower bound is essentially tight by showing that for every concept class C of polynomial query complexity there exists a polynomial time algorithm that given access to random points from any distribution D and an NP oracle, can SQ learn C over D. We also consider a restriction of the SQ model, the correlational statistical query (CSQ) model (Bshouty and Feldman, 2001; Feldman, 2008) of learning which is closelyrelated to Valiant’s model of evolvability (Valiant, 2007). We show a similar separation result for distributionindependent CSQ learning under a stronger assumption: there exists a concept class of polynomial CSQ query complexity which is not efficiently learnable unless every problem in W[P] has a randomized fixed parameter tractable algorithm.