Related papers: A Large-Deviation Analysis of the Maximum-Likeliho…
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on 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…
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 study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
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…
We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…
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 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…
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…
This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…
We provide finite sample guarantees for the classical Chow-Liu algorithm (IEEE Trans.~Inform.~Theory, 1968) to learn a tree-structured graphical model of a distribution. For a distribution $P$ on $\Sigma^n$ and a tree $T$ on $n$ nodes, we…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic…
Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…
Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of…
Ancestral maximum likelihood (AML) is a method that simultaneously reconstructs a phylogenetic tree and ancestral sequences from extant data (sequences at the leaves). The tree and ancestral sequences maximize the probability of observing…
The predictive normalized maximum likelihood (pNML) approach has recently been proposed as the min-max optimal solution to the batch learning problem where both the training set and the test data feature are individuals, known sequences.…
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…
Combining discrete probability distributions and combinatorial optimization problems with neural network components has numerous applications but poses several challenges. We propose Implicit Maximum Likelihood Estimation (I-MLE), a…
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…