Related papers: Learning pseudo-Boolean k-DNF and Submodular Funct…

We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube $\{0,1\}^n$. Our main result is the following structural theorem: any submodular function is…

Since its introduction by Valiant in 1984, PAC learning of DNF expressions remains one of the central problems in learning theory. We consider this problem in the setting where the underlying distribution is uniform, or more generally, a…

We give two results on PAC learning DNF formulas using membership queries in the challenging "distribution-free" learning framework, where learning algorithms must succeed for an arbitrary and unknown distribution over $\{0,1\}^n$. (1) We…

Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…

We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of $\tilde{O}(s^{3}/\epsilon + s^{2}/\epsilon^{2})$, where $s$ is the size of DNF formula and $\epsilon$ is the PAC error…

Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…

This paper revisits the problem of learning a k-CNF Boolean function from examples in the context of online learning under the logarithmic loss. In doing so, we give a Bayesian interpretation to one of Valiant's celebrated PAC learning…

An interesting classical result due to Jackson allows polynomial-time learning of the function class DNF using membership queries. Since in most practical learning situations access to a membership oracle is unrealistic, this paper explores…

In 1992 Blum and Rudich [BR92] gave an algorithm that uses membership and equivalence queries to learn $k$-term DNF formulas over $\{0,1\}^n$ in time $\textsf{poly}(n,2^k)$, improving on the naive $O(n^k)$ running time that can be achieved…

We are interested in computing $k$ most preferred models of a given d-DNNF circuit $C$, where the preference relation is based on an algebraic structure called a monotone, totally ordered, semigroup $(K, \otimes, <)$. In our setting, every…

We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time. Our result…

We start with an overview of a class of submodular functions called SCMMs (sums of concave composed with non-negative modular functions plus a final arbitrary modular). We then define a new class of submodular functions we call {\em deep…

$k$-submodular functions, introduced by Huber and Kolmogorov, are functions defined on $\{0, 1, 2, \dots, k\}^n$ satisfying certain submodular-type inequalities. $k$-submodular functions typically arise as relaxations of NP-hard problems,…

We give a "regularity lemma" for degree-d polynomial threshold functions (PTFs) over the Boolean cube {-1,1}^n. This result shows that every degree-d PTF can be decomposed into a constant number of subfunctions such that almost all of the…

The theorem states that: Every Boolean function can be $\epsilon -approximated$ by a Disjunctive Normal Form (DNF) of size $O_{\epsilon}(2^{n}/\log{n})$. This paper will demonstrate this theorem in detail by showing how this theorem is…

Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…

We show that all non-negative submodular functions have high {\em noise-stability}. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on $\{-1,1\}^n$ (for any constant…

In 1992 Mansour proved that every size-$s$ DNF formula is Fourier-concentrated on $s^{O(\log\log s)}$ coefficients. We improve this to $s^{O(\log\log k)}$ where $k$ is the read number of the DNF. Since $k$ is always at most $s$, our bound…

This paper proposes algorithms for learning two-level Boolean rules in Conjunctive Normal Form (CNF, i.e. AND-of-ORs) or Disjunctive Normal Form (DNF, i.e. OR-of-ANDs) as a type of human-interpretable classification model, aiming for a…

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…