Angluin's Model Research Articles

Learning schema mappings

A schema mapping is a high-level specification of the relationship between a source schema and a target schema. Recently, a line of research has emerged that aims at deriving schema mappings automatically or semi-automatically with the help of data examples, that is, pairs consisting of a source instance and a target instance that depict, in some precise sense, the intended behavior of the schema mapping. Several different uses of data examples for deriving, refining, or illustrating a schema mapping have already been proposed and studied. In this article, we use the lens of computational learning theory to systematically investigate the problem of obtaining algorithmically a schema mapping from data examples. Our aim is to leverage the rich body of work on learning theory in order to develop a framework for exploring the power and the limitations of the various algorithmic methods for obtaining schema mappings from data examples. We focus on GAV schema mappings, that is, schema mappings specified by GAV (Global-As-View) constraints. GAV constraints are the most basic and the most widely supported language for specifying schema mappings. We present an efficient algorithm for learning GAV schema mappings using Angluin's model of exact learning with membership and equivalence queries. This is optimal, since we show that neither membership queries nor equivalence queries suffice, unless the source schema consists of unary relations only. We also obtain results concerning the learnability of schema mappings in the context of Valiant's well-known PAC (Probably-Approximately-Correct) learning model, and concerning the learnability of restricted classes of GAV schema mappings. Finally, as a byproduct of our work, we show that there is no efficient algorithm for approximating the shortest GAV schema mapping fitting a given set of examples, unless the source schema consists of unary relations only.

Randomized broadcasting in wireless mobile sensor networks

SUMMARYWireless sensor networks are a new generation of networks that need specific models and algorithms. We are interested specifically in mobile wireless sensor networks that are considered as anonymous asynchronous distributed mobile systems. As broadcast is one of the most important applications for such networks, and as it depends on the communication model, we tried to find the most suitable one to make a distributed broadcast algorithm. We adopted the population protocols, the Angluin's model of pairwise interactions of anonymous finite‐state agents, to broadcast an information. We tried to modify this model to avoid the information duplication and then calculated the complexity of the algorithm. Then, we extended the model with the rendezvous one that made the stabilization of the algorithm faster. The implementation, the simulation, and the validation of these algorithms and results have been done with Visidia. Copyright © 2012 John Wiley & Sons, Ltd.

Efficient learning algorithms yield circuit lower bounds

We describe a new approach for understanding the difficulty of designing efficient learning algorithms. We prove that the existence of an efficient learning algorithm for a circuit class C in Angluin's model of exact learning from membership and equivalence queries or in Valiant's PAC model yields a lower bound against C. More specifically, we prove that any subexponential time, deterministic exact learning algorithm for C (from membership and equivalence queries) implies the existence of a function f in EXP NP such that f ∉ C . If C is PAC learnable with membership queries under the uniform distribution or exact learnable in randomized polynomial-time, we prove that there exists a function f ∈ BPEXP (the exponential time analog of BPP ) such that f ∉ C . For C equal to polynomial-size, depth-two threshold circuits (i.e., neural networks with a polynomial number of hidden nodes), our result shows that efficient learning algorithms for this class would solve one of the most challenging open problems in computational complexity theory: proving the existence of a function in EXP NP or BPEXP that cannot be computed by circuits from C. We are not aware of any representation-independent hardness results for learning depth-2, polynomial-size neural networks with respect to the uniform distribution. Our approach uses the framework of the breakthrough result due to Kabanets and Impagliazzo showing that derandomizing BPP yields non-trivial circuit lower bounds.

Learning erasing pattern languages with queries

A pattern is a finite string of constant and variable symbols. The non-erasing language generated by a pattern is the set of all strings of constant symbols that can be obtained by substituting non-empty strings for variables. In order to build the erasing language generated by a pattern, it is also admissible to substitute the empty string. The present paper deals with the problem of learning erasing pattern languages within Angluin's model of learning with queries. Moreover, the learnability of erasing pattern languages with queries is studied when additional information is available. The results obtained are compared with previously known results in case non-erasing pattern languages have to be learned. First, when regular pattern languages have to be learned, it is shown that the learnability results for the non-erasing case remain valid, if the proper superclass of all erasing regular pattern languages is the object of learning. Second, in the general case, serious differences have been observed. For instance, it turns out that arbitrary erasing pattern languages cannot be learned in settings in which, in the non-erasing case, even polynomially many queries will suffice.

Equivalences and Separations Between Quantum and Classical Learnability

We consider quantum versions of two well-studied models of learning Boolean functions: Angluin's model of exact learning from membership queries and Valiant's probably approximately correct (PAC) model of learning from random examples. For each of these two learning models we establish a polynomial relationship between the number of quantum or classical queries required for learning. These results contrast known results that show that testing black-box functions for various properties, as opposed to learning, can require exponentially more classical queries than quantum queries. We also show that, under a widely held computational hardness assumption (the intractability of factoring Blum integers), there is a class of Boolean functions which is polynomial-time learnable in the quantum version but not the classical version of each learning model. For the model of exact learning from membership queries, we establish a stronger separation by showing that if any one-way function exists, then there is a class of functions which is polynomial-time learnable in the quantum setting but not in the classical setting. Thus, while quantum and classical learning are equally powerful from an information theory perspective, the models are different when viewed from a computational complexity perspective.

Exact learning via teaching assistants

In this paper we introduce and study a new model of exact learning called the teaching assistant model. The new ingredient in this model, as compared to Angluin's model, is that apart from the learner and teacher there is a third agent called teaching assistant. We compare the teaching assistant model with Angluin's model and show that in this model we can do a fine classification of concept classes with respect to the complexity of exact learning. In particular, we consider two algebraic concept classes, namely, permutation groups and linear spaces over finite fields. These concept classes can be seen as special subclasses of the concept class of circuits. In Angluin's exact-learning model these concept classes are, just as the concept class 3-CNF, learnable with equivalence queries but not learnable with membership queries. However, we show that in the teaching assistant model permutation groups are exactly learnable with an LWPP-assistant, and linear spaces over finite fields are exactly learnable with an SPP-assistant. As a negative result, we show that if 3-CNFs are exactly learnable with an LWPP-assistant (SPP-assistant), then NP⊆ LWPP (respectively, NP⊆ SPP ).