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Electronic Colloquium on Computational Complexity

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All reports by Author Nader Bshouty:

TR14-004 | 30th November 2013
Hasan Abasi, Nader Bshouty, Ariel Gabizon, Elad Haramaty

On $r$-Simple $k$-Path

An $r$-simple $k$-path is a {path} in the graph of length $k$ that
passes through each vertex at most $r$ times. The \simpath{r}{k}
problem, given a graph $G$ as input, asks whether there exists an
$r$-simple $k$-path in $G$. We first show that this problem is
NP-Complete. We then show ... more >>>

TR02-019 | 20th March 2002
Nader Bshouty, Lynn Burroughs

On the proper learning of axis parallel concepts

We study the proper learnability of axis parallel concept classes
in the PAC learning model and in the exact learning model with
membership and equivalence queries. These classes include union of boxes,
DNF, decision trees and multivariate polynomials.

For the {\it constant} dimensional axis parallel concepts $C$
we ... more >>>

TR98-076 | 13th November 1998
Nader Bshouty, Jeffrey J. Jackson, Christino Tamon

Attribute Efficient PAC Learning of DNF with Membership Queries under the Uniform Distribution

We study attribute efficient learning in the PAC learning model with
membership queries. First, we give an {\it attribute efficient}
PAC-learning algorithm for DNF with membership queries under the
uniform distribution. Previous algorithms for DNF have sample size
polynomial in the number of attributes $n$. Our algorithm is the
first ... more >>>

TR98-013 | 3rd March 1998
Nader Bshouty

A New Composition Theorem for Learning Algorithms

We present a new approach to the composition
of learning algorithms (in various models) for
classes of constant VC-dimension into learning algorithms for
more complicated classes.
We prove that if a class $\CC$ is learnable
in time $t$ from a hypothesis class $\HH$ of constant VC-dimension
then the class ... more >>>

TR96-059 | 12th November 1996
Shai Ben-David, Nader Bshouty, Eyal Kushilevitz

A Composition Theorem for Learning Algorithms with Applications to Geometric Concept Classes

This paper solves the open problem of exact learning
geometric objects bounded by hyperplanes (and more generally by any constant
degree algebraic surfaces) in the constant
dimensional space from equivalence queries only (i.e., in the on-line learning

We present a novel approach that allows, under ... more >>>

TR96-009 | 17th January 1996
Francesco Bergadano, Nader Bshouty, Christino Tamon, Stefano Varricchio

On Learning Branching Programs and Small Depth Circuits

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 ... more >>>

TR95-060 | 21st November 1995
Nader Bshouty

A Subexponential Exact Learning Algorithm for DNF Using Equivalence Queries

We present a $2^{\tilde O(\sqrt{n})}$ time exact learning
algorithm for polynomial size
DNF using equivalence queries only. In particular, DNF
is PAC-learnable in subexponential time under any distribution.
This is the first subexponential time
PAC-learning algorithm for DNF under any distribution.

more >>>

TR95-059 | 21st November 1995
Nader Bshouty

The Monotone Theory for the PAC-Model

We show that a DNF formula that has a CNF representation that contains
at least one ``$1/poly$-heavy''
clause with respect to a distribution $D$ is weakly learnable
under this distribution. So DNF that are not weakly
learnable under the distribution $D$ do not have
any ``$1/poly$-heavy'' clauses in any of ... more >>>

TR95-032 | 6th April 1995
Nader Bshouty, Christino Tamon

On the Fourier spectrum of monotone functions

TR95-008 | 27th January 1995
Nader Bshouty

Exact Learning Boolean Functions via the Monotone Theory

ISSN 1433-8092 | Imprint