Related papers: Structure learning in polynomial time: Greedy algo…
We define and study greedy matchings in vertex-ordered bipartite graphs. It is shown that each vertex-ordered bipartite graph has a unique greedy matching. The proof uses (a weak form of) Newman's lemma. The vertex ordering is called a…
Score-based approaches in the structure learning task are thriving because of their scalability. Continuous relaxation has been the key reason for this advancement. Despite achieving promising outcomes, most of these methods are still…
We investigate at decision trees that incorporate both traditional queries based on one attribute and queries based on hypotheses about the values of all attributes. Such decision trees are similar to ones studied in exact learning, where…
We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity,…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
Identifying causal relations among multi-variate time series is one of the most important elements towards understanding the complex mechanisms underlying the dynamic system. It provides critical tools for forecasting, simulations and…
Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…
Learning the structure of Directed Acyclic Graphs (DAGs) presents a significant challenge due to the vast combinatorial search space of possible graphs, which scales exponentially with the number of nodes. Recent advancements have redefined…
Causal discovery is a crucial initial step in establishing causality from empirical data and background knowledge. Numerous algorithms have been developed for this purpose. Among them, the score-matching method has demonstrated superior…
The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model…
We study the problem of reducing test-time acquisition costs in classification systems. Our goal is to learn decision rules that adaptively select sensors for each example as necessary to make a confident prediction. We model our system as…
Main approaches for learning Bayesian networks can be classified as constraint-based, score-based or hybrid methods. Although high-dimensional consistency results are available for constraint-based methods like the PC algorithm, such…
The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it take Omega(n^2) time,…
Mainly motivated by the problem of modelling directional dependence relationships for multivariate count data in high-dimensional settings, we present a new algorithm, called learnDAG, for learning the structure of directed acyclic graphs…
Structural learning of directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. We propose a new Gaussian DAG model for dependent data which assumes the observations…
Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…
A Bayesian network is a probabilistic graphical model that consists of a directed acyclic graph (DAG), where each node is a random variable and attached to each node is a conditional probability distribution (CPD). A Bayesian network can be…
Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is…
The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a…
Learning graphical conditional independence structures is an important machine learning problem and a cornerstone of causal discovery. However, the accuracy and execution time of learning algorithms generally struggle to scale to problems…