arXiv research

New concentration inequality for U-statistics of Markov chains.

New inequality for ternary variables improves on existing measures.

Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time versi…

Proves new concentration inequalities for sub-gaussian and sub-exponential variables.

New method improves RL in continuous spaces with kernel smoothing.

The paper develops concentration inequalities for structured random data, extending beyond independent terms.

We improve bounds for stochastic processes, especially those with heavy tails.

We prove semi-empirical concentration inequalities for random variables which are given as possibly nonlinear functions of independent random variables. These inequalities describe concentration of random variable in terms of the data/distribution-dependent Efron-Stein (ES) estimate of its variance and they do not requ…

We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like deviation bounds with sublinear exponents in deviation size for missing mass, but …

We present a new PAC-Bayesian generalization bound. Standard bounds contain a $\sqrt{L_n \cdot \KL/n}$ complexity term which dominates unless $L_n$, the empirical error of the learning algorithm's randomized predictions, vanishes. We manage to replace $L_n$ by a term which vanishes in many more situations, essentially …

We give tight concentration bounds for mixtures of martingales that are simultaneously uniform over (a) mixture distributions, in a PAC-Bayes sense; and (b) all finite times. These bounds are proved in terms of the martingale variance, extending classical Bernstein inequalities, and sharpening and simplifying prior wor…

Estimates barycenter in geodesic spaces with finite sample bounds.

This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to the class of continuous time processes. Our analysis relies on a new supermarti…

A new method improves uncertainty quantification in Bayesian inference.

CascadeBAI identifies best arms in cascading bandits with fixed confidence.

Deep Bayesian neural networks effectively select variables with rigorous uncertainty quantification.

A new method for streaming PCA provides confidence intervals for eigenvector entries.

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization can cover Euclidean spaces with large dimensionality, with the optimal dependence…

Machine learning selects the best prediction rules from noisy data.

We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad …

When I first encountered PAC-Bayesian concentration inequalities they seemed to me to be rather disconnected from good old-fashioned results like Hoeffding's and Bernstein's inequalities. But, at least for one flavour of the PAC-Bayesian bounds, there is actually a very close relation, and the main innovation is a cont…

In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the outcomes that have not been seen in a given sample which is an important quantity…

Near-optimal confidence intervals for bounded data.

The betting CI outperforms classical methods in constructing confidence intervals for bounded means.

Adaptive Bernstein copulas improve risk management by preventing overfitting and reducing simulation effort.

Survey Bernstein-type theorems for graphical surfaces in Euclidean and Lorentz-Minkowski spaces.

In this paper we study nonconvex penalization using Bernstein functions. Since the Bernstein function is concave and nonsmooth at the origin, it can induce a class of nonconvex functions for high-dimensional sparse estimation problems. We derive a threshold function based on the Bernstein penalty and give its mathemati…

In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation problems. We derive a thresholding function based on the Bernstein penalty and di…

Ancient solutions to mean curvature flow have unique shapes.

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-…

The study models insurance dependence using Bernstein copulas.

Bayesian nonparametric models get better posterior estimates via SPDE methods.

Improved understanding of translating solitons using new techniques.

We summarize results concerning the Bernstein property of differential equations.

Explains Bernstein theorems for various geometric PDEs.

Improved analysis of UCRL2 with empirical Bernstein inequality reduces exploration-exploitation regret.

Ancient symplectic solutions to mean curvature flow are flat.

In this paper, we prove some Bernstein type results for $n$-dimensional minimal Lagrangian graphs in quaternion Euclidean space $H^n\cong R^{4n}$. In particular, we also get a new Bernstein Theorem for special Lagrangian graphs in $C^n$

New algorithms reduce regret in neural logistic bandits.

We present Bernstein-Sato identities for scalar-, spinor- and differential form-valued distribution kernels on Euclidean space associated to conformal symmetry breaking operators. The associated Bernstein-Sato operators lead to partially new formulae for conformal symmetry breaking differential operators on functions, …

New algorithms avoid non-monotonic risk curves in statistical learning.

The paper proves Calabi-Bernstein type results for minimal and maximal surfaces in 3D and 3D-L spacetime.

We study the regret minimization problem in the novel setting of generalized kernelized bandits (GKBs), where we optimize an unknown function $f^*$ belonging to a reproducing kernel Hilbert space (RKHS) having access to samples generated by an exponential family (EF) reward model whose mean is a non-linear function $μ(…

Article provides Bernstein gradient estimates for heat equations with potential terms.

The paper solves Bernstein problems for specific submanifolds in high-dimensional spaces.

New algorithm learns policies without uniform overlap assumption.

Sharp inequalities for matrix means with unknown variance.