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The ratio of two densities provides a direct characterization of their differences. We consider the two-sample comparison problem by estimating this ratio given i.i.d. observations from two distributions. To this end, we propose additive…

Methodology · Statistics 2026-04-23 Naoki Awaya , Yuliang Xu , Li Ma

Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…

Machine Learning · Computer Science 2016-10-04 Nevin L. Zhang , Leonard K. M. Poon

We present a Bayesian model for area-level count data that uses Gaussian random effects with a novel type of G-Wishart prior on the inverse variance--covariance matrix. Specifically, we introduce a new distribution called the truncated…

Methodology · Statistics 2015-12-04 Theresa R. Smith , Jon Wakefield , Adrian Dobra

It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…

Numerical Analysis · Mathematics 2025-02-11 Daniela Calvetti , Erkki Somersalo

We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…

Methodology · Statistics 2023-03-20 Zachary M. Pisano

Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…

Cosmology and Nongalactic Astrophysics · Physics 2018-12-13 Alex Hall , Andy Taylor

Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…

Cosmology and Nongalactic Astrophysics · Physics 2018-12-26 Theodor Bjorkmo , M. C. David Marsh

Correlation analysis is a fundamental step in uncovering meaningful insights from complex datasets. In this paper, we study the problem of detecting correlations between two random graphs following the Gaussian Wigner model with unlabeled…

Statistics Theory · Mathematics 2025-05-21 Dong Huang , Pengkun Yang

The selection of the most suitable evolutionary model to analyze the given molecular data is usually left to biologist's choice. In his famous book, J Felsenstein suggested that certain linear equations satisfied by the expected…

Populations and Evolution · Quantitative Biology 2012-11-20 Marta Casanellas , Jesus Fernandez-Sanchez , Anna Kedzierska

Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we…

Methodology · Statistics 2015-12-24 Mathias Drton , Shaowei Lin , Luca Weihs , Piotr Zwiernik

In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central…

Machine Learning · Computer Science 2018-12-05 Mostafa Tavassolipour , Seyed Abolfazl Motahari , Mohammad-Taghi Manzuri Shalmani

Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support…

Machine Learning · Statistics 2019-01-28 Ashish Katiyar , Jessica Hoffmann , Constantine Caramanis

This paper studies the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. We propose a two-step Gaussian approximation procedure that does not impose structural assumptions on…

Statistics Theory · Mathematics 2016-10-04 Xiaohui Chen

We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges…

Machine Learning · Computer Science 2019-12-19 Furong Huang , Niranjan U. N. , Ioakeim Perros , Robert Chen , Jimeng Sun , Anima Anandkumar

We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…

Methodology · Statistics 2015-11-17 Xiao Li , Jinzhu Jia , Yuan Yao

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…

Statistics Theory · Mathematics 2018-01-17 Stanislav Minsker , Xiaohan Wei

Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…

Astrophysics · Physics 2009-11-07 Patrick Valageas , Andrew J. Barber , Dipak Munshi

Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior…

Statistics Theory · Mathematics 2021-07-19 Reza Mohammadi , Helene Massam , Gerard Letac

The analysis of high dimensional survival data is challenging, primarily due to the problem of overfitting which occurs when spurious relationships are inferred from data that subsequently fail to exist in test data. Here we propose a novel…

Statistics Theory · Mathematics 2016-01-28 James E. Barrett , Anthony C. C. Coolen

In this work, we provide a refinement of the selective CLT result of Tian and Taylor (2015), which allows for selective inference in non-parametric settings by adjusting for the asymptotic Gaussian limit for selection. Under some regularity…

Methodology · Statistics 2017-09-29 Jelena Markovic , Jonathan Taylor