相关论文: Near-Optimal Learning of Tree-Structured Distribut…

We show that $n$-variable tree-structured Ising models can be learned computationally-efficiently to within total variation distance $\epsilon$ from an optimal $O(n \ln n/\epsilon^2)$ samples, where $O(\cdot)$ hides an absolute constant…

We consider the problem of learning a tree-structured Ising model from data, such that subsequent predictions computed using the model are accurate. Concretely, we aim to learn a model such that posteriors $P(X_i|X_S)$ for small sets of…

We provide high probability finite sample complexity guarantees for hidden non-parametric structure learning of tree-shaped graphical models, whose hidden and observable nodes are discrete random variables with either finite or countable…

The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both…

We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first…

Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…

This paper considers structure learning from data with $n$ samples of $p$ variables, assuming that the structure is a forest, using the Chow-Liu algorithm. Specifically, for incomplete data, we construct two model selection algorithms that…

We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…

We consider the problem of learning underlying tree structure from noisy, mixed data obtained from a linear model. To achieve this, we use the expectation maximization algorithm combined with Chow-Liu minimum spanning tree algorithm. This…

We consider the task of learning the maximum-likelihood polytree from data. Our first result is a performance guarantee establishing that the optimal branching (or Chow-Liu tree), which can be computed very easily, constitutes a good…

We extend the Chow-Liu algorithm for general random variables while the previous versions only considered finite cases. In particular, this paper applies the generalization to Suzuki's learning algorithm that generates from data forests…

The Chow-Liu algorithm (IEEE Trans.~Inform.~Theory, 1968) has been a mainstay for the learning of tree-structured graphical models from i.i.d.\ sampled data vectors. Its theoretical properties have been well-studied and are well-understood.…

The seminal work of Chow and Liu (1968) shows that approximation of a finite probabilistic system by Markov trees can achieve the minimum information loss with the topology of a maximum spanning tree. Our current paper generalizes the…

Chow and Liu (1968) studied the problem of learning a maximumlikelihood Markov tree. We generalize their work to more complexMarkov networks by considering the problem of learning a maximumlikelihood Markov network of bounded complexity. We…

We consider the problem of modeling discrete-valued vector time series data using extensions of Chow-Liu tree models to capture both dependencies across time and dependencies across variables. Conditional Chow-Liu tree models are…

Accurate knowledge of power grid topology is a prerequisite for effective state estimation and grid stability. While data-driven methods for topology reconstruction exist, the minimum requirements for measurement quality, specifically…

The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual…

Given a graph $G=(V,E)$, a $\beta$-ruling set is a subset $S\subseteq V$ that is i) independent, and ii) every node $v\in V$ has a node of $S$ within distance $\beta$. In this paper we present almost optimal distributed algorithms for…

We design fast algorithms for repeatedly sampling from strongly Rayleigh distributions, which include random spanning tree distributions and determinantal point processes. For a graph $G=(V, E)$, we show how to approximately sample…

We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a…