Related papers: Generalization of the Gibbs algorithm with high pr…

We study the generalization performance of online learning algorithms trained on samples coming from a dependent source of data. We show that the generalization error of any stable online algorithm concentrates around its regret--an easily…

Preparing thermal (Gibbs) states is a common task in physics and computer science. Recent algorithms mimic cooling via system-bath coupling, where the cost is determined by mixing time, akin to classical Metropolis-like algorithms. However,…

The paper proves generalization results for a class of stochastic learning algorithms. The method applies whenever the algorithm generates an absolutely continuous distribution relative to some a-priori measure and the Radon Nikodym…

This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…

Various theories of quantum gravity predict the existence of a minimum length scale, which implies the Planck-scale modifications of the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Previous…

One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law, which justifies the tensor network approximations to thermal…

A paradigm shift in quantum thermometry is proposed. To date, thermometry has relied on local estimation, which is useful to reduce statistical fluctuations once the temperature is very well known. In order to estimate temperatures in cases…

The Gibbs sampler (a.k.a. Glauber dynamics and heat-bath algorithm) is a popular Markov Chain Monte Carlo algorithm which iteratively samples from the conditional distributions of a probability measure $\pi$ of interest. Under the…

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…

We study the notion of a generalization bound being uniformly tight, meaning that the difference between the bound and the population loss is small for all learning algorithms and all population distributions. Numerous generalization bounds…

Hybrid Gibbs samplers represent a prominent class of approximated Gibbs algorithms that utilize Markov chains to approximate conditional distributions, with the Metropolis-within-Gibbs algorithm standing out as a well-known example. Despite…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample…

Real-world problems, often couched as machine learning applications, involve quantities of interest that have real-world meaning, independent of any statistical model. To avoid potential model misspecification bias or over-complicating the…

Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…

Let $A$ be a finite set and $\phi:A^Z\to R$ be a locally constant potential. For each $\beta>0$ ("inverse temperature"), there is a unique Gibbs measure $\mu_{\beta\phi}$. We prove that, as $\beta\to+\infty$, the family…

We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for…

This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with \emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as…