Hasan Abasi

On Exact Learning Monotone DNF from Membership Queries

In this paper, we study the problem of learning a monotone DNF with at most s terms of size (number of variables in each term) at most r (s term r-MDNF) from membership queries. This problem is equivalent to the problem of learning a general hypergraph using hyperedge-detecting queries, a problem motivated by applications arising in chemical reactions and genome sequencing.

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 r-SIMPLE k-PATH 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 that there is a graph G that contains an r-simple k-path and no simple path of length greater than 4logk/logr. So this, in a sense, motivates this problem especially when one’s goal is to find a short path that visits many vertices in the graph while bounding the number of visits at each vertex.

Non-adaptive Learning of a Hidden Hypergraph

We give a new deterministic algorithm that non-adaptively learns a hidden hypergraph from edge-detecting queries. All previous non-adaptive algorithms either run in exponential time or have non-optimal query complexity. We give the first polynomial time non-adaptive learning algorithm for learning hypergraph that asks an almost optimal number of queries.

Learning Boolean Halfspaces with Small Weights from Membership Queries

We consider the problem of proper learning a Boolean Halfspace with integer weights {0,1,…,t} from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks \(n^{O(t^5)}\) membership queries where the best lower bound for the number of membership queries is n t [4].

Learning boolean halfspaces with small weights from membership queries

Abstract We consider the problem of proper learning of a boolean halfspace with integer weights { 0 , 1 , … , t } , from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks n O ( t 5 ) membership queries, while the best lower bound for the number of membership queries is n Ω ( t ) [1] . In this paper we close this gap and give an adaptive proper learning algorithm with two rounds, and asking n O ( t ) membership queries. We also give a non-adaptive proper learning algorithm that asks n O ( t 3 ) membership queries.

Non-adaptive learning of a hidden hypergraph

Abstract We give a new deterministic algorithm that non-adaptively learns a hidden hypergraph from edge-detecting queries. All previous non-adaptive algorithms either run in exponential time or have non-optimal query complexity. We give the first polynomial time non-adaptive learning algorithm for learning hypergraphs that asks an almost optimal number of queries.