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Stein Variational Gradient Descent (SVGD) is a popular variational inference algorithm which simulates an interacting particle system to approximately sample from a target distribution, with impressive empirical performance across various…

Machine Learning · Statistics 2023-10-09 Aniket Das , Dheeraj Nagaraj

The total variation distance is a metric of central importance in statistics and probability theory. However, somewhat surprisingly, questions about computing it algorithmically appear not to have been systematically studied until very…

Data Structures and Algorithms · Computer Science 2025-03-17 Arnab Bhattacharyya , Weiming Feng , Piyush Srivastava

3D Gaussian Splatting (3DGS) enables fast, high-quality novel view synthesis but typically relies on densification followed by pruning to optimize the number of Gaussians. Existing mask-based pruning, such as MaskGS, regularizes the global…

Computer Vision and Pattern Recognition · Computer Science 2025-09-16 Ashkan Taghipour , Vahid Naghshin , Benjamin Southwell , Farid Boussaid , Hamid Laga , Mohammed Bennamoun

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…

Machine Learning · Statistics 2019-05-15 Hugh Salimbeni , Vincent Dutordoir , James Hensman , Marc Peter Deisenroth

Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGLD) serving as a key tool for scalable posterior sampling and decentralized variants enabling…

Optimization and Control · Mathematics 2025-11-18 Waheed U. Bajwa , Mert Gurbuzbalaban , Mustafa Ali Kutbay , Lingjiong Zhu , Muhammad Zulqarnain

In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias &…

Machine Learning · Statistics 2014-10-01 Yarin Gal , Mark van der Wilk

A key tool for building differentially private systems is adding Gaussian noise to the output of a function evaluated on a sensitive dataset. Unfortunately, using a continuous distribution presents several practical challenges. First and…

Data Structures and Algorithms · Computer Science 2024-11-19 Clément L. Canonne , Gautam Kamath , Thomas Steinke

This paper is concerned with the approximation of probability distributions known up to normalization constants, with a focus on Bayesian inference for large-scale inverse problems in scientific computing. In this context, key challenges…

Machine Learning · Computer Science 2025-06-10 Baojun Che , Yifan Chen , Zhenghao Huan , Daniel Zhengyu Huang , Weijie Wang

We study the problem of estimating mixtures of Gaussians under the constraint of differential privacy (DP). Our main result is that $\text{poly}(k,d,1/\alpha,1/\varepsilon,\log(1/\delta))$ samples are sufficient to estimate a mixture of $k$…

Machine Learning · Statistics 2024-04-24 Mohammad Afzali , Hassan Ashtiani , Christopher Liaw

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…

Artificial Intelligence · Computer Science 2013-01-30 Kevin Murphy

We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over…

Machine Learning · Statistics 2017-04-12 Yannis Papanikolaou , James R. Foulds , Timothy N. Rubin , Grigorios Tsoumakas

We revisit the approximate Voronoi cells approach for solving the closest vector problem with preprocessing (CVPP) on high-dimensional lattices, and settle the open problem of Doulgerakis-Laarhoven-De Weger [PQCrypto, 2019] of determining…

Data Structures and Algorithms · Computer Science 2019-07-11 Thijs Laarhoven

arXiv:2206.10812v1 [stat.ME] proposes a useful algorithm, named generalized Diversity Subsampling (g-DS) algorithm, to select a subsample following some target probability distribution from a finite data set and demonstrates its…

Methodology · Statistics 2023-09-06 Boyang Shang

Efficiently solving the Shortest Vector Problem (SVP) in two-dimensional lattices holds practical significance in cryptography and computational geometry. While simpler than its high-dimensional counterpart, two-dimensional SVP motivates…

Computational Geometry · Computer Science 2025-07-02 Lihao Zhao , Chengliang Tian , Jingguo Bi , Guangwu Xu , Jia Yu

Gaussian processes (GPs) are instrumental in modeling spatial processes, offering precise interpolation and prediction capabilities across fields such as environmental science and biology. Recently, there has been growing interest in…

Methodology · Statistics 2025-09-04 Jiawen Chen , Aritra Halder , Yun Li , Sudipto Banerjee , Didong Li

We investigate graph problems in the following setting: we are given a graph $G$ and we are required to solve a problem on $G^2$. While we focus mostly on exploring this theme in the distributed CONGEST model, we show new results and…

Data Structures and Algorithms · Computer Science 2020-06-09 Reuven Bar-Yehuda , Keren Censor-Hillel , Yannic Maus , Shreyas Pai , Sriram V. Pemmaraju

The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…

Signal Processing · Electrical Eng. & Systems 2025-06-04 Erik G. Larsson , Nicolo Michelusi

The Minimum Dominating Set (MDS) problem is one of the most fundamental and challenging problems in distributed computing. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-04-18 Saeed Akhoondian Amiri , Stefan Schmid , Sebastian Siebertz

We present a distributed (non-Bayesian) learning algorithm for the problem of parameter estimation with Gaussian noise. The algorithm is expressed as explicit updates on the parameters of the Gaussian beliefs (i.e. means and precision). We…

Optimization and Control · Mathematics 2016-12-08 Angelia Nedić , Alex Olshevsky , César A. Uribe

We give a novel algorithm for enumerating lattice points in any convex body, and give applications to several classic lattice problems, including the Shortest and Closest Vector Problems (SVP and CVP, respectively) and Integer Programming…

Data Structures and Algorithms · Computer Science 2011-06-14 Daniel Dadush , Chris Peikert , Santosh Vempala