A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Langevin MCMC samples efficiently from Riemannian manifolds with geometric Euler-Murayama analysis.
It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel conce…
A new method de-randomizes MCMC dynamics using the Stein operator.
New geometric SDEs and discretizations on Riemannian manifolds with error bounds.
We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and achieves both faster speed and higher accuracy at every iteration than the current sta…
It is challenging to develop stochastic gradient based scalable inference for deep discrete latent variable models (LVMs), due to the difficulties in not only computing the gradients, but also adapting the step sizes to different latent factors and hidden layers. For the Poisson gamma belief network (PGBN), a recently …
We extend Gaussian Differential Privacy to curved Riemannian manifolds.
Optimal preconditioning improves Langevin sampling efficiency.
Geometric Variational Inference improves efficiency in complex probability distributions.
Unified framework for MCMC algorithms simplifies their design and application.
The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets…
New algorithms improve MCMC efficiency for complex distributions.
Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC might suffer from poor mixing rates when random variables exhibit strong couplings …
Unified framework for MCMC and machine learning problems.
JaxSGMC simplifies SG-MCMC for Bayesian deep learning.
Paper proposes first unlearning algorithm for MCMC models.
TensorFlow Probability MCMC toolkit improves MCMC efficiency for modern hardware.
Stochastic EM with biased MCMC improves inference stability.
Develops a flexible deep autoencoding topic model with scalable hybrid Bayesian inference.
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, s…
Cyclical MCMC tackles high-dimensional multimodal distributions, showing convergence under certain conditions.
Paper compares MCMC-based copula methods for exchange option pricing.
This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform no…
Nonlinear MCMC improves Bayesian machine learning sampling.
Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with limitations in practice: MCMC methods can be computationally demanding; VI methods …
Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic process, and MCMC moves to propose new values for the parameters. We show how p…
Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models (HMMs) for time-dependent data. There are two challenges to applying SG-MCMC in this…
New analysis of SGD with MCMC gradient estimator shows convergence rate and saddle point escape.
Proposes MIVI for efficient posterior estimation and design of MCMC transitions.
This study evaluates different normalizing flow architectures for MCMC.
AutoStep MCMC adapts step size locally for better sampling efficiency.
Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at every iteration. Here we present Firefly Monte Carlo (FlyMC) an auxiliary variabl…
Stochastic gradient MCMC (SG-MCMC) has played an important role in large-scale Bayesian learning, with well-developed theoretical convergence properties. In such applications of SG-MCMC, it is becoming increasingly popular to employ distributed systems, where stochastic gradients are computed based on some outdated par…
The book covers scalable MCMC methods for Bayesian learning.
We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for observations is estimated from a random subset of observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smal…
Study improves Bayesian calibration of mechanical properties using active learning and MCMC.
The modern scale of data has brought new challenges to Bayesian inference. In particular, conventional MCMC algorithms are computationally very expensive for large data sets. A promising approach to solve this problem is embarrassingly parallel MCMC (EP-MCMC), which first partitions the data into multiple subsets and r…
New method reduces computational cost for Bayesian inference.
Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC…
Bayesian neural networks tutorial via MCMC in Python.
New model improves MCMC efficiency and multi-modal distribution exploration.
MetFlow combines MCMC and VI efficiently for better inference.
Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has been increasingly popular in Bayesian learning due to its ability to deal with large data. A standard SG-MCMC algorithm simulates samples from a discretized-time Markov chain to approximate a target distribution. However, the samples are typically highly correl…
Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typicall…
This work optimizes MCMC algorithms for modern accelerators without synchronization overheads.
Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of th…
Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators,…
With the rapidly growing scales of statistical problems, subset based communication-free parallel MCMC methods are a promising future for large scale Bayesian analysis. In this article, we propose a new Weierstrass sampler for parallel MCMC based on independent subsets. The new sampler approximates the full data poster…