A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new algorithm reduces frequentist regret in multi-agent bandit problems with sparse hypergraphs.
problem Deriving a frequentist regret bound for Thompson sampling in multi-agent settings with sparse hypergraphs.
method Proposed ε-exploring Multi-Agent Thompson Sampling (ε-MATS) algorithm that combines exploration and exploitation strategies.
result Achieves a worst-case frequentist regret bound sublinear in time horizon and local arm size, optimal up to constants and logarithms for sparse hypergraphs.
Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and simultaneous Bayesian credible sets in GP regression. As an intermediate result, we develop…
We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a…
The paper addresses frequentist regret of Linear Thompson Sampling in stochastic linear bandits.
problem The frequentist regret of Linear Thompson Sampling (LinTS) is worse than its Bayesian counterpart.
method The paper proves the fundamental nature of the frequentist regret bound for LinTS and proposes a data-driven version of LinTS to achieve minimax optimal frequentist regret.
result The frequentist regret bound for LinTS is O(ddT), which is the best possible under certain conditions.
The paper proposes a method to calibrate evidential clustering using bootstrapped finite mixture models.
problem Representing uncertainty in cluster membership using Dempster-Shafer mass functions.
method Constructing Dempster-Shafer mass functions by bootstrapping finite mixture models, computing confidence intervals, and calibrating the evidential partition.
result The proposed method calibrates the evidential partition such that the belief and plausibility degrees approximate the true probabilities with high confidence.
In the stochastic bandit problem, the goal is to maximize an unknown function via a sequence of noisy evaluations. Typically, the observation noise is assumed to be independent of the evaluation point and to satisfy a tail bound uniformly on the domain; a restrictive assumption for many applications. In this work, we c…
The study compares Bayesian and frequentist approaches in deep learning.
problem Comparing Bayesian and frequentist inference in deep learning.
method Conducts a comparative analysis of point and posterior estimators across various settings.
result Amortized point estimators generally outperform posterior inference, though posterior inference remains competitive in some low-dimensional problems.
A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) methods. VB methods tend to be faster while achieving comparabl…
DBPA assesses LLM perturbations using frequentist hypothesis testing.
problem Quantifying input perturbation impacts on LLM outputs.
method DBPA reformulates perturbation analysis as frequentist hypothesis testing, using Monte Carlo sampling for empirical null and alternative distributions.
result DBPA provides interpretable p-values and scalar effect sizes for LLM perturbations.
This monograph aims at providing an introduction to key concepts, algorithms, and theoretical results in machine learning. The treatment concentrates on probabilistic models for supervised and unsupervised learning problems. It introduces fundamental concepts and algorithms by building on first principles, while also e…
The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a Bayes-frequentist consolidated data analysis workflow that is more effective than eith…
We have recently proposed a new information-based approach to model selection, the Frequentist Information Criterion (FIC), that reconciles information-based and frequentist inference. The purpose of this current paper is to provide a simple example of the application of this criterion and a demonstration of the natura…