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Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…
Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as…
A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…
This paper introduces a differentiable representation for the optimization of boustrophedon path plans in convex polygons, explores an additional parameter of these path plans that can be optimized, discusses the properties of this…
We consider invariant covariant derivatives on reductive homogeneous spaces corresponding to the well-known invariant affine connections. These invariant covariant derivatives are expressed in terms of horizontally lifted vector fields on…
A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output…
Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while…
The main computational challenge in Bayesian inference is to compute integrals against a high-dimensional posterior distribution. In the past decades, variational inference (VI) has emerged as a tractable approximation to these integrals,…
The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural…
We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and…