Related papers: Large Deviation Strategy for Inverse Problem
Generative inference in Large Language Models (LLMs) is impeded by the growing memory demands of Key-Value (KV) cache, especially for longer sequences. Traditional KV cache eviction strategies, which discard less critical KV pairs based on…
The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the 'classical' approach…
A discrete-time linear dynamical system (LDS) is given by an update matrix $M \in \mathbb{R}^{d\times d}$, and has the trajectories $\langle s, Ms, M^2s, \ldots \rangle$ for $s \in \mathbb{R}^d$. Reachability-type decision problems of…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse…
The boom of DL technology leads to massive DL models built and shared, which facilitates the acquisition and reuse of DL models. For a given task, we encounter multiple DL models available with the same functionality, which are considered…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…
Large Language Models (LLMs) are large-scale pretrained models that have achieved remarkable success across diverse domains. These successes have been driven by unprecedented complexity and scale in both data and computations. However, due…
We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…
Based on the tensor-based large margin distribution and the nonparallel support tensor machine, we establish a novel classifier for binary classification problem in this paper, termed the Large Margin Distribution based NonParallel Support…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
Feature selection is a crucial step in machine learning, especially for high-dimensional datasets, where irrelevant and redundant features can degrade model performance and increase computational costs. This paper proposes a novel…
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional…
This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL…
Sliced inverse regression (SIR) is a popular sufficient dimension reduction method that identifies a few linear transformations of the covariates without losing regression information with the response. In high-dimensional settings, SIR can…
Large Language Models (LLMs) increasingly rely on inference-time reasoning algorithms such as chain-of-thought and multi-branch reasoning to improve accuracy on complex tasks. These methods, however, substantially increase token usage and…
A randomized misfit approach is presented for the efficient solution of large-scale PDE-constrained inverse problems with high-dimensional data. The purpose of this paper is to offer a theory-based framework for random projections in this…
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
Data selection for fine-tuning large language models (LLMs) aims to choose a high-quality subset from existing datasets, allowing the trained model to outperform baselines trained on the full dataset. However, the expanding body of research…