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Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…

Statistics Theory · Mathematics 2023-11-16 Philipp Dettling , Mathias Drton , Mladen Kolar

We propose a novel blocked version of the continuous-time bouncy particle sampler of [Bouchard-C\^ot\'e et al., 2018] which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked…

Computation · Statistics 2021-07-12 Jacob Vorstrup Goldman , Sumeetpal Sidhu Singh

Recently, Eldan, Koehler, and Zeitouni (2020) showed that Glauber dynamics mixes rapidly for general Ising models so long as the difference between the largest and smallest eigenvalues of the coupling matrix is at most $1 - \epsilon$ for…

Data Structures and Algorithms · Computer Science 2023-12-01 Dmitriy Kunisky

We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating…

Numerical Analysis · Mathematics 2021-06-08 Assyr Abdulle , Giacomo Garegnani , Grigorios A. Pavliotis , Andrew M. Stuart , Andrea Zanoni

We propose to approximate the conditional expectation of a spatial random variable given its nearest-neighbour observations by an additive function. The setting is meaningful in practice and requires no unilateral ordering. It is capable of…

Statistics Theory · Mathematics 2016-03-28 Zudi Lu , Arvid Lundervold , Dag Tjøstheim , Qiwei Yao

Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in…

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be…

Machine Learning · Computer Science 2024-07-22 Giovanni Piccioli , Emanuele Troiani , Lenka Zdeborová

Background properties in experimental particle physics are typically estimated using large data sets. However, different events can exhibit different features because of the quantum mechanical nature of the underlying physics processes.…

Data Analysis, Statistics and Probability · Physics 2014-12-22 Federico Colecchia

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are…

Methodology · Statistics 2019-07-02 Daniel R. Kowal , David S. Matteson , David Ruppert

In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space R^d are extended to the space of compact sets on R^d equipped by…

Probability · Mathematics 2018-01-26 Daniela Novotna , Viktor Benes

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

Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…

Optimization and Control · Mathematics 2026-04-21 Zhuo Ouyang , Jixian Liu , Enrique Mallada

This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random measures. We propose a truncation method for the mixing distribution by discarding…

Statistics Theory · Mathematics 2015-07-17 Raffaele Argiento , Ilaria Bianchini , Alessandra Guglielmi

We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem…

Optimization and Control · Mathematics 2024-05-02 Maxim Raginsky

Dynamic structural equation modeling (DSEM) is widely used for analyzing intensive longitudinal data (ILD). Although many ILD have categorical (Bernoulli or binomially distributed) responses, currently available Metropolis-within-Gibbs…

Computation · Statistics 2026-04-01 Øystein Sørensen , Ethan M. McCormick

In modern contexts, some types of data are observed in high-resolution, essentially continuously in time. Such data units are best described as taking values in a space of functions. Subject units carrying the observations may have…

Methodology · Statistics 2021-07-21 Arkaprava Roy , Shubhashis Ghosal

The emergence of big data has led to so-called convergence complexity analysis, which is the study of how Markov chain Monte Carlo (MCMC) algorithms behave as the sample size, $n$, and/or the number of parameters, $p$, in the underlying…

Statistics Theory · Mathematics 2020-06-24 Bryant Davis , James P. Hobert

Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…

Statistics Theory · Mathematics 2026-02-20 Florian Schäfer

We introduce a symmetric random scan Gibbs sampler for scalable Bayesian variable selection that eliminates storage of the full cross-product matrix by computing required quantities on-the-fly. Data-informed proposal weights, constructed…

Methodology · Statistics 2026-01-14 Mengta Chung

We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…

Computer Vision and Pattern Recognition · Computer Science 2020-04-03 Tolga Birdal , Michael Arbel , Umut Şimşekli , Leonidas Guibas
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