Related papers: Query learning of derived $\omega$-tree languages …
We give a quasipolynomial-time algorithm for learning stochastic decision trees that is optimally resilient to adversarial noise. Given an $\eta$-corrupted set of uniform random samples labeled by a size-$s$ stochastic decision tree, our…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
The authors recently gave an $n^{O(\log\log n)}$ time membership query algorithm for properly learning decision trees under the uniform distribution (Blanc et al., 2021). The previous fastest algorithm for this problem ran in $n^{O(\log…
We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It…
The class of omega languages recognized by deterministic parity acceptors (DPAs) or deterministic Muller acceptors (DMAs) is exactly the regular omega languages. The inclusion problem is the following: given two acceptors A1 and A2,…
In this paper we study the adaptive learnability of decision trees of depth at most $d$ from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman…
An {\omega}-language is a set of infinite words over a finite alphabet X. We consider the class of recursive {\omega}-languages, i.e. the class of {\omega}-languages accepted by Turing machines with a B\"uchi acceptance condition, which is…
We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees, a rich class of high-dimensional probability distributions and a subclass of Bayesian networks, a widely-studied type of graphical model.…
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is…
We investigate the topological complexity of non Borel recognizable tree languages with regard to the difference hierarchy of analytic sets. We show that, for each integer $n \geq 1$, there is a $D_{\omega^n}({\bf \Sigma}^1_1)$-complete…
This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently…
It is well known that for a given bottom-up tree automaton it can be decided whether or not there exists deterministic top-down tree automaton that recognized the same tree language. Recently it was claimed that such a decision can be…
We give an $n^{O(\log\log n)}$-time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over $\{\pm 1\}^n$. Even in the realizable setting, the previous fastest runtime was…
Latent tree learning(LTL) methods learn to parse sentences using only indirect supervision from a downstream task. Recent advances in latent tree learning have made it possible to recover moderately high quality tree structures by training…
Tree kernels have been proposed to be used in many areas as the automatic learning of natural language applications. In this paper, we propose a new linear time algorithm based on the concept of weighted tree automata for SubTree kernel…
Machine learning on trees has been mostly focused on trees as input to algorithms. Much less research has investigated trees as output, which has many applications, such as molecule optimization for drug discovery, or hint generation for…
In this paper, we propose a novel algorithm to learn a B\"uchi automaton from a teacher who knows an $\omega$-regular language. The algorithm is based on learning a formalism named family of DFAs (FDFAs) recently proposed by Angluin and…
The RPNI algorithm (Oncina, Garcia 1992) constructs deterministic finite automata from finite sets of negative and positive example words. We propose and analyze an extension of this algorithm to deterministic $\omega$-automata with…
Decision trees and their ensembles are popular in machine learning as easy-to-understand models. Several techniques have been proposed in the literature for learning tree-based classifiers, with different techniques working well for data…
We introduce and study the weakly single-crossing domain on trees which is a generalization of the well-studied single-crossing domain in social choice theory. We design a polynomial-time algorithm for recognizing preference profiles which…