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The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…

Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of…

Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…

This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression…

Deep generative models have been demonstrated as problematic in the unsupervised out-of-distribution (OOD) detection task, where they tend to assign higher likelihoods to OOD samples. Previous studies on this issue are usually not…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to…

We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; both for i.i.d. and ergodic sampling under non-restrictive…

We propose an optimization algorithm to compute the optimal sensor locations in experimental design in the formulation of Bayesian inverse problems, where the parameter-to-observable mapping is described through an integral equation and its…

We develop the theory of Energy Conserving Descent (ECD) and introduce ECDSep, a gradient-based optimization algorithm able to tackle convex and non-convex optimization problems. The method is based on the novel ECD framework of…

This paper investigates guesswork over ordered statistics and formulates the achievable guesswork complexity of ordered statistics decoding (OSD) in binary additive white Gaussian noise (AWGN) channels. The achievable guesswork complexity…

Graphical user interface (GUI) agents have recently emerged as an intriguing paradigm for human-computer interaction, capable of automatically executing user instructions to operate intelligent terminal devices. However, when encountering…

We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…

The Design of Experiments (DOEs) is a fundamental scientific methodology that provides researchers with systematic principles and techniques to enhance the validity, reliability, and efficiency of experimental outcomes. In this study, we…

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…

Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…

We propose a novel exponentially-modified Gaussian (EMG) mixture residual model. The EMG mixture is well suited to model residuals that are contaminated by a distribution with positive support. This is in contrast to commonly used robust…

The challenge of optimal design of experiments (DOE) pervades materials science, physics, chemistry, and biology. Bayesian optimization has been used to address this challenge in vast sample spaces, although it requires framing experimental…

We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…

Learning enabled components (LECs), while critical for decision making in autonomous vehicles (AVs), are likely to make incorrect decisions when presented with samples outside of their training distributions. Out-of-distribution (OOD)…