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We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov…

Statistics Theory · Mathematics 2024-04-04 J. S. Rosenthal , A. Dote , K. Dabiri , H. Tamura , S. Chen , A. Sheikholeslami

This work presents a fast and scalable algorithm for incremental learning of Gaussian mixture models. By performing rank-one updates on its precision matrices and determinants, its asymptotic time complexity is of \BigO{NKD^2} for $N$ data…

Machine Learning · Computer Science 2017-01-17 Rafael Pinto , Paulo Engel

We address the inverse problem for the mean-field Ising model with two- and three-body interactions using a Bayesian framework. Parameter recovery in this setting is notoriously difficult, particularly near phase transitions, at…

Methodology · Statistics 2025-11-03 Godwin Osabutey , Robert Richardson , Garritt L. Page

Since Hamming distances can be calculated by bitwise computations, they can be calculated with less computational load than L2 distances. Similarity searches can therefore be performed faster in Hamming distance space. The elements of…

Machine Learning · Computer Science 2013-03-19 Yui Noma , Makiko Konoshima

In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…

Numerical Analysis · Mathematics 2021-03-17 Yating Wang , Wei Deng , Lin Guang

Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…

Computation · Statistics 2018-03-28 Khoa T. Tran

We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by…

Machine Learning · Statistics 2019-12-12 Raaz Dwivedi , Yuansi Chen , Martin J. Wainwright , Bin Yu

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and…

Successful machine learning methods require a trade-off between memorization and generalization. Too much memorization and the model cannot generalize to unobserved examples. Too much over-generalization and we risk under-fitting the data.…

Artificial Intelligence · Computer Science 2023-03-09 Chase Yakaboski , Eugene Santos

Markov Chain Monte Carlo (MCMC) methods have revolutionised Bayesian data analysis over the years by making the direct computation of posterior probability densities feasible on modern workstations. However, the calculation of the prior…

Instrumentation and Methods for Astrophysics · Physics 2009-11-13 Rutger van Haasteren

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly…

Computation · Statistics 2016-03-11 Johan Dahlin , Fredrik Lindsten , Thomas B. Schön

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…

Machine Learning · Computer Science 2024-06-13 Fan Chen , Constantinos Daskalakis , Noah Golowich , Alexander Rakhlin

We present a framework for approximate Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained due to computational constraints, which is becoming increasingly common for applications of complex…

Methodology · Statistics 2023-09-01 Marko Järvenpää , Jukka Corander

Learning the structure of Bayesian networks from data is known to be a computationally challenging, NP-hard problem. The literature has long investigated how to perform structure learning from data containing large numbers of variables,…

Computation · Statistics 2019-10-25 Marco Scutari , Claudia Vitolo , Allan Tucker

Bayesian neural networks (BNNs) demonstrate promising success in improving the robustness and uncertainty quantification of modern deep learning. However, they generally struggle with underfitting at scale and parameter efficiency. On the…

Bayesian inference via standard Markov Chain Monte Carlo (MCMC) methods is too computationally intensive to handle large datasets, since the cost per step usually scales like $\Theta(n)$ in the number of data points $n$. We propose the…

Machine Learning · Statistics 2019-06-12 Robert Cornish , Paul Vanetti , Alexandre Bouchard-Côté , George Deligiannidis , Arnaud Doucet

Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning…

Machine Learning · Statistics 2017-07-27 Trevor Campbell , Brian Kulis , Jonathan How

In recent times empirical likelihood has been widely applied under Bayesian framework. Markov chain Monte Carlo (MCMC) methods are frequently employed to sample from the posterior distribution of the parameters of interest. However,…

Methodology · Statistics 2022-09-07 Sanjay Chaudhuri , Teng Yin

The emergence of big data has led to a growing interest in so-called convergence complexity analysis, which is the study of how the convergence rate of a Monte Carlo Markov chain (for an intractable Bayesian posterior distribution) scales…

Statistics Theory · Mathematics 2021-08-12 Zhumengmeng Jin , James P. Hobert

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…

Computation · Statistics 2026-03-30 Yujie Chen , Antik Chakraborty , Anindya Bhadra