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Wrappers For Performance Enhancement And Oblivious Decision Graphs
, 1995
"... In this doctoral dissertation, we study three basic problems in machine learning and two new hypothesis spaces with corresponding learning algorithms. The problems we investigate are: accuracy estimation, feature subset selection, and parameter tuning. The latter two problems are related and are stu ..."
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Cited by 107 (8 self)
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In this doctoral dissertation, we study three basic problems in machine learning and two new hypothesis spaces with corresponding learning algorithms. The problems we investigate are: accuracy estimation, feature subset selection, and parameter tuning. The latter two problems are related and are studied under the wrapper approach. The hypothesis spaces we investigate are: decision tables with a default majority rule (DTMs) and oblivious readonce decision graphs (OODGs).
On Learning Branching Programs and Small Depth Circuits
 Computational Learning Theory: Proc. Third European Conference. Lecture Notes in Articial Intelligence
, 1997
"... This paper studies the learnability of branching programs and small depth circuits with modular and threshold gates in both the exact and PAC learning models with and without membership queries. Some of the results extend earlier works in [GG95, ERR95, BTW95]. The main results are as follows. For ..."
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Cited by 10 (2 self)
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This paper studies the learnability of branching programs and small depth circuits with modular and threshold gates in both the exact and PAC learning models with and without membership queries. Some of the results extend earlier works in [GG95, ERR95, BTW95]. The main results are as follows. For branching programs we show the following.
On Learning Width Two Branching Programs
 In Proc. 9th Annu. Conf. on Comput. Learning Theory
, 1996
"... We prove that strict width two branching programs or SW 2 (which are width two branching programs with exactly two sinks, as defined in [BDFP86]) are properly PAC learnable under any distribution. We also observe that PAC learning monotone width two branching programs (which are width two branching ..."
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Cited by 10 (1 self)
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We prove that strict width two branching programs or SW 2 (which are width two branching programs with exactly two sinks, as defined in [BDFP86]) are properly PAC learnable under any distribution. We also observe that PAC learning monotone width two branching programs (which are width two branching programs with exactly one rejecting sink) is as hard as learning DNF formulae. This work refines both the positive and negative results in [EKR95] and answers one of the open questions in that paper. 1 Introduction Many interesting results have been found by the study of branching programs most notably by Barrington [B89] who demonstrated that a very restricted form (width five) can accept all languages contained in NC 1 . A branching program is an acyclic digraph where each node is labelled by a Boolean variable from X = fx 1 ; : : : ; x n g or the values 0 or 1. There is one designated starting node and an arbitrary number of sinks labelled with either 0 or 1. Boolean functions are comp...
Lower bounds for testing computability by small width OBDDs
 IN PROC. 8TH ANNUAL THEORY AND APPLICATIONS OF MODELS OF COMPUTATION
, 2011
"... We consider the problem of testing whether a function f: {0, 1} n → {0, 1} is computable by a readonce, width2 ordered binary decision diagram (OBDD), also known as a branching program. This problem has two variants: one where the variables must occur in a fixed, known order, and one where the v ..."
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Cited by 4 (1 self)
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We consider the problem of testing whether a function f: {0, 1} n → {0, 1} is computable by a readonce, width2 ordered binary decision diagram (OBDD), also known as a branching program. This problem has two variants: one where the variables must occur in a fixed, known order, and one where the variables are allowed to occur in an arbitrary order. We show that for both variants, any nonadaptive testing algorithm must make Ω(n) queries, and thus any adaptive testing algorithm must make Ω(log n) queries. We also consider the more general problem of testing computability by widthw OBDDs where the variables occur in a fixed order. We show that for any constant w ≥ 4, Ω(n) queries are required, resolving a conjecture of Goldreich [15]. We prove all of our lower bounds using a new technique of Blais, Brody, and Matulef [6], giving simple reductions from known hard problems in communication complexity to the testing problems at hand. Our result for width2 OBDDs provides the first example of the power of this technique for proving strong nonadaptive bounds.
On the Hardness of Approximating the Minimum Consistent OBDD Problem
, 1996
"... . Ordered binary decision diagrams (OBDD, for short) represent Boolean functions as directed acyclic graphs. The minimum consistent OBDD problem is, given an incomplete truth table of a function, to find the smallest OBDD that is consistent with the truth table with respect to a fixed variable o ..."
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Cited by 4 (0 self)
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. Ordered binary decision diagrams (OBDD, for short) represent Boolean functions as directed acyclic graphs. The minimum consistent OBDD problem is, given an incomplete truth table of a function, to find the smallest OBDD that is consistent with the truth table with respect to a fixed variable ordering. We show that this problem is NPhard, and prove that there is a constant ffl ? 0 such that no polynomial time algorithm can approximate the minimum consistent OBDD within the ratio n ffl unless P=NP, where n is the number of variables. This result suggests that OBDDs are unlikely to be polynomial time learnable in PAClearning model. Furthermore, we give a polynomial time learnable subclass of OBDDs representing symmetric functions. 1 Introduction For a class of representations of languages, the minimum consistent problem is to find a representation that is as small size as possible and is consistent with given positive and negative examples. The computational complexity o...
The Isomorphism Problem for OneTimeOnly Branching Programs and Arithmetic Circuits
, 1997
"... We investigate the computational complexity of the isomorphism problem for onetimeonly branching programs (1BPI): on input of two onetimeonly branching programs B 0 and B 1 , decide whether there exists a permutation of the variables of B 1 such that it becomes equivalent to B 0 . ..."
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Cited by 1 (0 self)
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We investigate the computational complexity of the isomorphism problem for onetimeonly branching programs (1BPI): on input of two onetimeonly branching programs B 0 and B 1 , decide whether there exists a permutation of the variables of B 1 such that it becomes equivalent to B 0 .
Testing Computability by Width Two OBDDs
"... Property testing is concerned with deciding whether an object (e.g. a graph or a function) has a certain property or is “far ” (for some definition of far) from every object with that property. In this paper we give lower and upper bounds for testing functions for the property of being computable by ..."
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Cited by 1 (1 self)
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Property testing is concerned with deciding whether an object (e.g. a graph or a function) has a certain property or is “far ” (for some definition of far) from every object with that property. In this paper we give lower and upper bounds for testing functions for the property of being computable by a readonce width2 Ordered Binary Decision Diagram (OBDD), also known as a branching program, where the order of the variables is known. Width2 OBDDs generalize two classes of functions that have been studied in the context of property testing linear functions (over GF (2)) and monomials. In both these cases membership can be tested in time that is linear in 1/ɛ. Interestingly, unlike either of these classes, in which the query complexity of the testing algorithm does not depend on the number, n, of variables in the tested function, we show that (onesided error) testing for computability by a width2 OBDD requires Ω(log(n)) queries, and give an algorithm (with onesided error) that tests for this property and performs Property testing is concerned with deciding whether an object (e.g. a graph or a function) has a certain property or is “far ” (for some definition of far) from every object with that property [RS96,
Testing Computability by WidthTwo OBDDs Where the Variable Order is Unknown
"... Property testing is concerned with deciding whether an object (e.g. a graph or a function) has a certain property or is “far ” (for a prespecified distance measure) from every object with that property. In this work we design and analyze an algorithm for testing functions for the property of being c ..."
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Cited by 1 (1 self)
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Property testing is concerned with deciding whether an object (e.g. a graph or a function) has a certain property or is “far ” (for a prespecified distance measure) from every object with that property. In this work we design and analyze an algorithm for testing functions for the property of being computable by a readonce width2 Ordered Binary Decision Diagram (OBDD), also known as a branching program, where the order of the variables is not known to us. That is, we must accept a function f if there exists an order of the variables according to which a width2 OBDD can compute f. The query complexity of our algorithm is Õ(log n)poly(1/ɛ). In previous work (in Proceedings of RANDOM, 2009) we designed an algorithm for testing computability by an OBDD with a fixed order, which is known to the algorithm. Thus, we extend our knowledge concerning testing of functions that are characterized by their computability using simple computation devices and in the process gain some insight concerning these devices. 1