Related papers: Large Deviation Strategy for Inverse Problem
We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…
Researchers in the biological sciences nowadays often encounter the curse of high-dimensionality, which many previously developed statistical models fail to overcome. To tackle this problem, sufficient dimension reduction aims to estimate…
Distribution system state estimation (DSSE) plays a crucial role in the real-time monitoring, control, and operation of distribution networks. Besides intensive computational requirements, conventional DSSE methods need high-quality…
We prove the the large deviation principle(LDP) for the law of the one-dimensional semilinear stochastic partial differential equations driven by nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation…
This article presents the formulation and steady-state analysis of the distributed estimation algorithms based on the diffusion cooperation scheme in the presence of errors due to the unreliable data transfer among nodes. In particular, we…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
Recent advancements have significantly augmented the reasoning capabilities of Large Language Models (LLMs) through various methodologies, especially chain-of-thought (CoT) reasoning. However, previous methods fail to address reasoning…
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical…
Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…
Large Language Models (LLMs) demonstrate strong generalization and reasoning abilities, making them well-suited for complex decision-making tasks such as medical consultation (MC). However, existing LLM-based methods often fail to capture…
The quality of inverse problem solutions obtained through deep learning [Barbastathis et al, 2019] is limited by the nature of the priors learned from examples presented during the training phase. In the case of quantitative phase retrieval…
We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
Large language models (LLMs) have recently achieved significant success across various application domains, garnering substantial attention from different communities. Unfortunately, even for the best LLM, many \textit{faults} still exist…
While Large Reasoning Models (LRMs) have achieved remarkable performance by scaling test-time compute, they frequently suffer from Cognitive Inertia, a failure pattern manifesting as either overthinking (inertia of motion) or reasoning…
Inference scaling helps LLMs solve complex reasoning problems through extended runtime computation. On top of long chain-of-thought (long-CoT) models, purely inference-time techniques such as best-of-N (BoN) sampling, majority voting, or…
Large Vision-Language Models (LVLMs) have achieved impressive performance across a wide range of multimodal tasks. However, they still face critical challenges in modeling long-range dependencies under the usage of Rotary Positional…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…