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The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples.…
In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are…
In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…
Recently proposed generative models for discrete data, such as Masked Diffusion Models (MDMs), exploit conditional independence approximations to reduce the computational cost of popular Auto-Regressive Models (ARMs), at the price of some…
The presence of missing values within high-dimensional data is an ubiquitous problem for many applied sciences. A serious limitation of many available data mining and machine learning methods is their inability to handle partially missing…
Entropy production is a universal measure of irreversibility and energy dissipation in physical, chemical, and biological systems operating far from equilibrium. However, quantifying and spatiotemporally localising it in complex processes…
Algebraic statistics is a recently evolving field, where one would treat statistical models as algebraic objects and thereby use tools from computational commutative algebra and algebraic geometry in the analysis and computation of…
Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but…
In the analysis of any type of system, granting maximum information extraction from its data is non-trivial. Confidence in successful information extraction typically builds on prior knowledge of the studied system or on the user's…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and…
Good generative models should not only synthesize high quality data, but also utilize interpretable representations that aid human understanding of their behavior. However, it is difficult to measure objectively if and to what degree…
The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a $\sigma$-finite measure, and not necessarily a probability measure. Under this…
We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of…
Snapshot back-ended reduced basis methods for dynamical systems commonly rely on the singular value decomposition of a matrix whose columns are high-fidelity solution vectors. An alternative basis generation framework is developed here. The…
For linear systems, many data-driven control methods rely on the behavioral framework, using historical data of the system to predict the future trajectories. However, measurement noise introduces errors in predictions. When the noise is…
Max-value entropy search (MES) is one of the state-of-the-art approaches in Bayesian optimization (BO). In this paper, we propose a novel variant of MES for constrained problems, called Constrained MES via Information lower BOund…
The reconstruction of images from a small number of projections using the maximum-entropy method (MEM) with the Shannon entropy is considered. MEM provides higher-quality image reconstruction for sources with extended components than the…
In this paper, we propose a maximum entropy method for predicting disease risks. It is based on a patient's medical history with diseases coded in ICD-10 which can be used in various cases. The complete algorithm with strict mathematical…