arXiv research

Improved sampling from Gaussian distributions with privacy constraints.

New inequalities for unbounded functions improve denoising score matching.

CRIMED optimizes regret in bandits with unbounded stochastic corruption.

Paper solves nonparametric contextual bandit with unbounded contexts.

Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and mathematical finance, concerning degenerate diffusion processes. We show that th…

New margin-based learning guarantees improve generalization bounds.

New PAC-Bayes bounds for unbounded losses using Cramér-Chernoff techniques.

Flow Matching improves Wasserstein 1 distance convergence in high dimensions.

Classical multi-armed bandit problems use the expected value of an arm as a metric to evaluate its goodness. However, the expected value is a risk-neutral metric. In many applications like finance, one is interested in balancing the expected return of an arm (or portfolio) with the risk associated with that return. In …

Paper tackles unbounded density ratio estimation for covariate shift adaptation.

The paper extends logistic regression for unbounded majority classes and derives asymptotic properties.

Note improves confidence bounds for random variables.

KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence rate of this estimator for random variables whose densities are bounded away fr…

In this paper we continue the study of spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold, initiated in a previous paper. Under assumption that the singular foliation generated by the distribution is smooth, we prove that the Laplacian associated with the distributi…

Study uses spectral risk for learning with heavy-tailed data.

New approach to concentration inequalities for unbounded state space dynamical systems.

Two new algorithms improve performance in adversarial bandits with unbounded losses.

Deep neural networks classify unbounded Gaussian mixture data without dimensionality issues.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

Theory for deep neural network approximation of score function and its derivatives.

The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.

In this paper, we discuss spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold. First, we give a survey of results on generalized smooth distributions on manifolds, Riemannian structures and associated Laplacians. Then, under the assumption that the singular foliation…

PITMonitor monitors model calibration over time with formal error guarantees.

Golden L surface has unbounded bunching of saddle connections

We construct an unbounded representative for the shriek class associated to the embeddings of spheres into Euclidean space. We equip this unbounded Kasparov cycle with a connection and compute the unbounded Kasparov product with the Dirac operator on $\mathbb R^{n+1}$. We find that the resulting spectral triple for the…

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…

New algorithm estimates Gaussian means and covariances efficiently and privately.

This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded framework, we extend our analysis to the more challenging unbounded case. Our methodolo…

It is shown that the compactly supported identity component of the diffeomorphism group of the 2-dimensional punctured torus $\mathbb T^2_p$ is an unbounded group. It follows that the fragmentation norm of $\mathbb T^2_p$ is unbounded.

Study focal surfaces of wave fronts with unbounded curvatures.

The paper proves a regret bound for a sub-Gaussian mixture on unbounded data.

Study shows unbounded Pontryagin numbers on curved manifolds.

Paper tackles online control of linear systems with unbounded noise.

Paper shows robust generative learning with minimal assumptions on target distributions.

We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.

New approach finds solutions to games with unbounded controls.

Efficient method for learning continuous exponential families beyond Gaussian.

The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

New aggregation strategy handles unbounded losses with regret bounds.

New PAC-Bayes bounds for unbounded loss functions.

Geometric model of unbounded sl3 laminations with tropical coordinates.

In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice.

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).

Paper develops estimators for unbounded density ratios with applications in error control.

In this paper, we propose a novel perturbation-based exploration method in bandit algorithms with bounded or unbounded rewards, called residual bootstrap exploration (\texttt{ReBoot}). The \texttt{ReBoot} enforces exploration by injecting data-driven randomness through a residual-based perturbation mechanism. This nove…

We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.

In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature-dimension inequality $CDE'(n,K)$, which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, hea…

Study unbounded $\mathfrak{sl}_3$-laminations around punctures.