相关论文: Likelihood-free MCMC with Amortized Approximate Ra…

The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…

Scientific analyses often rely on slow, but accurate forward models for observable data conditioned on known model parameters. While various emulation schemes exist to approximate these slow calculations, these approaches are only safe if…

We study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by Monte Carlo methods (and in particular Markov Chain Monte Carlo). We derive conditions on the step size and the Monte Carlo…

The reliability assessment of a machine learning model's prediction is an important quantity for the deployment in safety critical applications. Not only can it be used to detect novel sceneries, either as out-of-distribution or anomaly…

Generalized linear mixed models are useful in studying hierarchical data with possibly non-Gaussian responses. However, the intractability of likelihood functions poses challenges for estimation. We develop a new method suitable for this…

Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step…

Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased…

While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing…

We present a new version of the truncated harmonic mean estimator (THAMES) for univariate or multivariate mixture models. The estimator computes the marginal likelihood from Markov chain Monte Carlo (MCMC) samples, is consistent,…

We develop a Monte Carlo-free approach to inference post output from randomized algorithms with a convex loss and a convex penalty. The pivotal statistic based on a truncated law, called the selective pivot, usually lacks closed form…

In this work we establish the posterior consistency for a parametrized family of partially observed, fully dominated Markov models. As a main assumption, we suppose that the prior distribution assigns positive probability to all…

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model…

Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice.…

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…

Bayesian inference is a powerful tool for parameter estimation and uncertainty quantification in dynamical systems. However, for nonlinear oscillator networks such as Kuramoto models, widely used to study synchronization phenomena in…

Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for…

We propose a novel a posteriori error estimator for the N\'ed\'elec finite element discretization of time-harmonic Maxwell's equations. After the approximation of the electric field is computed, we propose a fully localized algorithm to…

Statistical inference of analytically non-tractable posteriors is a difficult problem because of marginalization of correlated variables and stochastic methods such as MCMC and VI are commonly used. We argue that stochastic KL divergence…

In the thesis we take the split chain approach to analyzing Markov chains and use it to establish fixed-width results for estimators obtained via Markov chain Monte Carlo procedures (MCMC). Theoretical results include necessary and…