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The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…

We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior distribution, and the increase of the…

Equilibrium propagation (EP) is a compelling alternative to the backpropagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight…

We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This can be formulated as parametric expensive multi-objective optimization problems…

Gaussian process (GP) is arguably one of the most widely used machine learning algorithms in practice. One of its prominent applications is Bayesian optimization (BO). Although the vanilla GP itself is already a powerful tool for BO, it is…

Design optimization under uncertainty is notoriously difficult when the objective function is expensive to evaluate. State-of-the-art techniques, e.g, stochastic optimization or sampling average approximation, fail to learn exploitable…

Additive parameter updates, as used in gradient descent and its adaptive extensions, underpin most modern machine-learning optimization. Yet, such additive schemes often demand numerous iterations and intricate learning-rate schedules to…

Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard assessment tools for such outcomes (e.g. deviance residuals) often show a large discrepancy from the…

Diffusion models learn a time-indexed score field $\mathbf{s}_\theta(\mathbf{x}_t,t)$ that often inherits approximate equivariances (flips, rotations, circular shifts) from in-distribution (ID) data and convolutional backbones. Most…

Uncertainty estimation (UE) techniques -- such as the Gaussian process (GP), Bayesian neural networks (BNN), Monte Carlo dropout (MCDropout) -- aim to improve the interpretability of machine learning models by assigning an estimated…

Gaussian process regression (GPR) model has been widely used to fit data when the regression function is unknown and its nice properties have been well established. In this article, we introduce an extended t-process regression (eTPR)…

Deeply-learned planning methods are often based on learning representations that are optimized for unrelated tasks. For example, they might be trained on reconstructing the environment. These representations are then combined with predictor…

Expectation propagation (EP) is a family of algorithms for performing approximate inference in probabilistic models. The updates of EP involve the evaluation of moments -- expectations of certain functions -- which can be estimated from…

Capital allocation is a procedure for quantifying the contribution of each source of risk to aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation under which the…

The quantification of uncertainty is important for the adoption of machine learning, especially to reject out-of-distribution (OOD) data back to human experts for review. Yet progress has been slow, as a balance must be struck between…

Eigenoptions (EOs) have been recently introduced as a promising idea for generating a diverse set of options through the graph Laplacian, having been shown to allow efficient exploration. Despite its initial promising results, a couple of…

We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a…

We present a general framework for deriving entropy production rates (EPRs) in active matter systems driven by non-Gaussian active fluctuations. Employing the probability-flow equivalence technique, we rigorously obtain an entropy…