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Speculative decoding (SD) accelerates language model inference by drafting tokens from a cheap proposal model and verifying them against an expensive target model via rejection sampling. Because rejection truncates the draft block at the…

We develop a scalable multi-step Monte Carlo algorithm for inference under a large class of nonparametric Bayesian models for clustering and classification. Each step is "embarrassingly parallel" and can be implemented using the same Markov…

When performing Bayesian inference using Sequential Monte Carlo (SMC) methods, two considerations arise: the accuracy of the posterior approximation and computational efficiency. To address computational demands, Sequential Monte Carlo…

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…

We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using…

Sampling from high-dimensional distributions has wide applications in data science and machine learning but poses significant computational challenges. We introduce Subspace Langevin Monte Carlo (SLMC), a novel and efficient sampling method…

Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has…

Sequential Monte Carlo (SMC) methods have recently been applied to gravitational-wave inference as a powerful alternative to standard sampling techniques, such as Nested Sampling. At the same time, gradient-based Markov Chain Monte Carlo…

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible…

Methods of approximate Bayesian computation (ABC) are increasingly used for analysis of complex models. A major challenge for ABC is over-coming the often inherent problem of high rejection rates in the accept/reject methods based on…

State-space models (SSMs) are commonly used to model time series data where the observations depend on an unobserved latent process. However, inference on the model parameters of an SSM can be challenging, especially when the likelihood of…

Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…

The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…

Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and…

Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…

Sequential Monte Carlo (SMC) methods, also known as particle filters, constitute a class of algorithms used to approximate expectations with respect to a sequence of probability distributions as well as the normalising constants of those…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for…