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We calculate smoothed correlators for a large random matrix model with a potential containing products of two traces $\tr W_1(M) \cdot \tr W_2(M)$ in addition to a single trace $\tr V(M)$. Connected correlation function of density…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
We construct a very general family of characteristic functions describing Random Matrix Ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure which we characterize by a `spread…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
Geometrical model of structure of the universe is examined to obtain analytical expression for the two points nonlinear correlation function. According to the model the objects (galaxies) are concentrated into two types of structure…
By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…
Clustered and longitudinal data are pervasive in scientific studies, from prenatal health programs to clinical trials and public health surveillance. Such data often involve non-Gaussian responses--including binary, categorical, and count…
This article presents a novel method for causal discovery with generalized structural equation models suited for analyzing diverse types of outcomes, including discrete, continuous, and mixed data. Causal discovery often faces challenges…
Flatness of the loss curve is conjectured to be connected to the generalization ability of machine learning models, in particular neural networks. While it has been empirically observed that flatness measures consistently correlate strongly…
The increasing application of deep-learning is accompanied by a shift towards highly non-linear statistical models. In terms of their geometry it is natural to identify these models with Riemannian manifolds. The further analysis of the…
We develop the formalism to include substructure in the halo model of clustering. Real halos are not likely to be perfectly smooth, but have substructure which has so far been neglected in the halo model -- our formalism allows one to…
We explore in depth how categorical data can be processed with embeddings in the context of claim severity modeling. We develop several models that range in complexity from simple neural networks to state-of-the-art attention based…
Due to advancements in digital cameras, it is easy to gather multiple images (or videos) from an object under different conditions. Therefore, image-set classification has attracted more attention, and different solutions were proposed to…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex…
The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.
As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…
Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…
Trend filtering is a modern approach to nonparametric regression that is more adaptive to local smoothness than splines or similar basis procedures. Existing analyses of trend filtering focus on estimating a function corrupted by…
Distributed lag models (DLMs) express the cumulative and delayed dependence between pairs of time-indexed response and explanatory variables. In practical application, users of DLMs examine the estimated influence of a series of lagged…