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Selecting powerful predictors for an outcome is a cornerstone task for machine learning. However, some types of questions can only be answered by identifying the predictors that causally affect the outcome. A recent approach to this causal…

One of the main modeling in many data science applications is the Gaussian Mixture Model (GMM), and Mean Field Variational Bayesian Inference (MFVBI) is classically used for approximate fast computation. In this paper, we provide a…

We propose a novel computationally low-cost method for estimating a general predictive measure of generalised Bayesian inference. The proposed method utilises posterior covariance and provides estimators of the Gibbs and the plugin…

The Bayesian Synthetic Likelihood (BSL) method is a widely-used tool for likelihood-free Bayesian inference. This method assumes that some summary statistics are normally distributed, which can be incorrect in many applications. We propose…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Motivated by big data and the vast parameter spaces in modern machine learning models, optimisation approaches to Bayesian inference have seen a surge in popularity in recent years. In this paper, we address the connection between the…

In recent years, Full-Waveform Inversion (FWI) has been extensively used to derive high-resolution subsurface velocity models from seismic data. However, due to the nonlinearity and ill-posed nature of the problem, FWI requires a good…

Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…

We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant improvement over the recent introspective neural networks (INN) method by enhancing…

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…

In recent years, uncertainty-aware full waveform inversion (FWI) has received increasing attention, with a growing emphasis on producing informative uncertainty estimates alongside inversion results. Bayesian inference methods--particularly…

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

We establish novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters (weights and biases) and Lipschitz activation functions, in the wide limit. Our bounds apply for the joint output of a network…

Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non-linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic…

Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…

Full Waveform Inversion (FWI) is a technique widely used in geophysics to obtain high-resolution subsurface velocity models from waveform seismic data. Due to its large computation cost, most flavors of FWI rely only on the computation of…

Full-Waveform Inversion (FWI) is a nonlinear iterative seismic imaging technique that, by reducing the misfit between recorded and predicted seismic waveforms, can produce detailed estimates of subsurface geophysical properties.…