Related papers: Perturbative Corrections for Approximate Inference…

As fine-tuning becomes impractical at scale, probing is emerging as the preferred evaluation protocol. However, standard linear probing can understate the capability of models whose pre-training optimizes local representations rather than…

We propose a nonparametric procedure to achieve fast inference in generative graphical models when the number of latent states is very large. The approach is based on iterative latent variable preselection, where we alternate between…

Gaussian Mixture Models (GMMs) commonly arise in communication systems, particularly in bilinear joint estimation and detection problems. Although the product of GMMs is still a GMM, as the number of factors increases, the number of…

We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…

Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

Stochastic inference on Lie groups plays a key role in state estimation problems such as; inertial navigation, visual inertial odometry, pose estimation in virtual reality, etc. A key problem is fusing independent concentrated Gaussian…

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…

Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the…

Solving large-scale capacity expansion problems (CEPs) is central to cost-effective decarbonization of regional-scale energy systems. To ensure the intended outcomes of CEPs, modeling uncertainty due to weather-dependent variable renewable…

The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is…

We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral…

The accuracy of Bayesian inference can be negatively affected by the use of inaccurate forward models. In the case of gravitational-wave inference, accurate but computationally expensive waveform models are sometimes substituted with faster…

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG…

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…

Laplace approximations are a standard tool for computationally efficient inference in latent Gaussian models, but they fail for quantile regression with the asymmetric Laplace likelihood because the observed Hessian vanishes almost…

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…

Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks. Equilibrium Propagation (EP) is an alternative with comparable efficiency and strong…