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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…

Machine Learning · Computer Science 2024-11-19 Sutanu Gayen , Sanket Kale , Sayantan Sen

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in…

Machine Learning · Computer Science 2012-06-18 Tony S. Jebara

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

Methodology · Statistics 2021-12-14 Eunice Okome Obiang , Pascal Jézéquel , Frédéric Proïa

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…

Machine Learning · Statistics 2021-04-01 Konstantinos E. Nikolakakis , Dionysios S. Kalogerias , Anand D. Sarwate

We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a…

Machine Learning · Statistics 2021-02-18 Konstantinos E. Nikolakakis , Dionysios S. Kalogerias , Anand D. Sarwate

Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…

Machine Learning · Computer Science 2020-03-10 Jonathan Kelner , Frederic Koehler , Raghu Meka , Ankur Moitra

A new synthesis scheme is proposed to generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is shown by vanishing total variation distance between the synthesized…

Information Theory · Computer Science 2017-05-09 Ali Moharrer , Shuangqing Wei , George T. Amariucai , Jing Deng

Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…

Methodology · Statistics 2012-02-20 Inma Tur , Robert Castelo

Gaussian Bayesian networks (a.k.a. linear Gaussian structural equation models) are widely used to model causal interactions among continuous variables. In this work, we study the problem of learning a fixed-structure Gaussian Bayesian…

Data Structures and Algorithms · Computer Science 2022-10-19 Arnab Bhattacharyya , Davin Choo , Rishikesh Gajjala , Sutanu Gayen , Yuhao Wang

We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any…

Statistics Theory · Mathematics 2018-10-30 Dennis Leung , Mathias Drton

In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or…

Machine Learning · Computer Science 2024-08-13 Kun Zhang , Shaoan Xie , Ignavier Ng , Yujia Zheng

We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical…

Machine Learning · Computer Science 2023-02-10 Dmitrii Avdiukhin , Grigory Yaroslavtsev , Danny Vainstein , Orr Fischer , Sauman Das , Faraz Mirza

Latent tree graphical models are widely used in computational biology, signal and image processing, and network tomography. Here we design a new efficient, estimation procedure for latent tree models, including Gaussian and discrete,…

Probability · Mathematics 2011-09-23 Elchanan Mossel , Sebastien Roch , Allan Sly

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

Methodology · Statistics 2008-07-13 Robert B. Gramacy , Herbert K. H. Lee

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

Machine Learning · Computer Science 2019-11-01 Akshay Krishnamurthy , Arya Mazumdar , Andrew McGregor , Soumyabrata Pal

In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…

Machine Learning · Computer Science 2014-08-12 Ricardo Silva , Robert B. Gramacy

In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…

Machine Learning · Computer Science 2010-03-15 Ricardo Silva , Robert B. Gramacy

In this paper, we study the problem of structure learning for Bayesian networks in which nodes take discrete values. The problem is NP-hard in general but we show that under certain conditions we can recover the true structure of a Bayesian…

Machine Learning · Computer Science 2021-02-19 Adarsh Barik , Jean Honorio

Causal learning has long concerned itself with the accurate recovery of underlying causal mechanisms. Such causal modelling enables better explanations of out-of-distribution data. Prior works on causal learning assume that the high-level…

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

Machine Learning · Statistics 2018-05-23 Steven Atkinson , Nicholas Zabaras