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Successive Halving is a popular algorithm for hyperparameter optimization which allocates exponentially more resources to promising candidates. However, the algorithm typically relies on intermediate performance values to make resource…

This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…

Reversibility is a key concept in Markov models and Master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model relies heavily on the reversibility…

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…

Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Generalized linear models play an essential role in a wide variety of statistical applications. This paper discusses an approximation of the likelihood in these models that can greatly facilitate computation. The basic idea is to replace a…

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…

The state-of-the-art linked Gaussian process offers a way to build analytical emulators for systems of computer models. We generalize the closed form expressions for the linked Gaussian process under the squared exponential kernel to a…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…

Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…

Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat\'ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based…

Gaussian process regression generally does not scale to beyond a few thousands data points without applying some sort of kernel approximation method. Most approximations focus on the high eigenvalue part of the spectrum of the kernel…

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…

Generative models which use explicit density modeling (e.g., variational autoencoders, flow-based generative models) involve finding a mapping from a known distribution, e.g. Gaussian, to the unknown input distribution. This often requires…

We introduce a novel unsupervised learning method for time series data with latent dynamical structure: the recognition-parametrized Gaussian state space model (RP-GSSM). The RP-GSSM is a probabilistic model that learns Markovian Gaussian…

Scalable Bayesian sampling is playing an important role in modern machine learning, especially in the fast-developed unsupervised-(deep)-learning models. While tremendous progresses have been achieved via scalable Bayesian sampling such as…