相关论文: Equivalence of state equations from different meth…
We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an…
Decentralized generalized approximate message-passing (GAMP) is proposed for compressed sensing from distributed generalized linear measurements in a tree-structured network. Consensus propagation is used to realize average consensus…
In power system steady-state estimation (PSSE), one needs to consider (1) the need for robust statistics, (2) the nonconvex transmission constraints, (3) the fast-varying nature of the inputs, and the corresponding need to track optimal…
As an analogy of best separable approximation (BSA) in the framework of entanglement theory, here we concentrate on the notion of best incoherent approximation, with application to characterizing and quantifying quantum coherence. From both…
Path analysis is a model class of structural equation modeling (SEM), which it describes causal relations among measured variables in the form of a multiple linear regression. This paper presents two estimation formulations, one each for…
The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations…
Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee…
If a dynamic system has active constraints on the state vector and they are known, then taking them into account during modeling is often advantageous. Unfortunately, in the constrained discrete-time state-space estimation, the state…
Loss functions play a central role in supervised classification. Cross-entropy (CE) is widely used, whereas the mean absolute error (MAE) loss can offer robustness but is difficult to optimize. Interpolating between the CE and MAE losses,…
Dynamic structural equation models (DSEMs) combine time-series modeling of within-person processes with hierarchical modeling of between-person differences and differences between timepoints, and have become very popular for the analysis of…
Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation with the geometrically uniform…
The standard linear regression (SLR) problem is to recover a vector $\mathbf{x}^0$ from noisy linear observations $\mathbf{y}=\mathbf{Ax}^0+\mathbf{w}$. The approximate message passing (AMP) algorithm recently proposed by Donoho, Maleki,…
Vector approximate message passing (VAMP) is a computationally simple approach to the recovery of a signal $\mathbf{x}$ from noisy linear measurements $\mathbf{y}=\mathbf{Ax}+\mathbf{w}$. Like the AMP proposed by Donoho, Maleki, and…
Equation discovery is a fundamental learning task for uncovering the underlying dynamics of complex systems, with wide-ranging applications in areas such as brain connectivity analysis, climate modeling, gene regulation, and physical…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
Min-max optimization problems, also known as saddle point problems, have attracted significant attention due to their applications in various fields, such as fair beamforming, generative adversarial networks (GANs), and adversarial…
Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…
In this paper, we propose a method to predict the asymptotic performance of the alternating direction method of multipliers (ADMM) for compressed sensing, where we reconstruct an unknown structured signal from its underdetermined linear…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and…