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The Generalized Linear Model (GLM) for the Gamma distribution (glmGamma) is widely used in modeling continuous, non-negative and positive-skewed data, such as insurance claims and survival data. However, model selection for GLM depends on…
Meta-analysis, because of both logistical convenience and statistical efficiency, is widely popular for synthesizing information on common parameters of interest across multiple studies. We propose developing a generalized meta-analysis…
Generalized Linear Models (GLM) form a wide class of regression and classification models, where prediction is a function of a linear combination of the input variables. For statistical inference in high dimension, sparsity inducing…
In this paper, we first present a unified framework for the modelling of generalized lattice Boltzmann method (GLBM). We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct…
Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that…
We present a new Lagrangian approach for the dynamical structure of the generalized Proca theory (GP). This approach includes the A-Z constraint structure of the model in the Lagrangian formalism and ends up with an accurate count of the…
A key problem in statistics and machine learning is the determination of network structure from data. We consider the case where the structure of the graph to be reconstructed is known to be scale-free. We show that in such cases it is…
High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
We introduce the spatial disorder-generalized Langevin equation (SD-GLE), a data-driven method for constructing coarse-grained (CG) dynamics in heterogeneous systems. Unlike conventional CG approaches that rely on a mean-field potential,…
The generalized Langevin equation is used as a model for various coarse-grained physical processes, e.g., the time evolution of the velocity of a given larger particle in an implicitly represented solvent, when the relevant time scales of…
General log-linear models specified by non-negative integer design matrices have a potentially wide range of applications, although using models without the genuine overall effect, that is, ones which cannot be reparameterized to include a…
Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…
In this Letter, we use a general renormalization-group algorithm to implement Propp and Wilson's "coupling from the past" approach to complex physical systems. Our algorithm follows the evolution of the entire configuration space under the…
Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…
This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It additionally implements a Monte Carlo algorithm specifically tailored for sampling…
Generative models have recently achieved remarkable success and widespread adoption in society, yet they often struggle to generate realistic and accurate outputs. This challenge extends beyond language and vision into fields like…