arXiv research

Sharp Liouville theorem for minimal graphs on manifolds with nonnegative Ricci curvature.

New sublinear sketches improve ANN and KDE for massive data streams.

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

New data structure identifies close match from multiple distributions.

For $α\in (1,2)$, we present a generalized central limit theorem for $α$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, p…

The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is problematic as real-world problem sets continue to grow in categorical types, such as …

We study the problem of estimating the expected reward of the optimal policy in the stochastic disjoint linear bandit setting. We prove that for certain settings it is possible to obtain an accurate estimate of the optimal policy value even with a number of samples that is sublinear in the number that would be required…

GP-UCB resolves sublinear regret for kernelized bandits.

Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and state-space models still scales poorly; each MCMC transition takes linear time i…

New algorithms reduce communication for sparse mean estimation in noisy distributed systems.

Quantum algorithm speeds up Gibbs partition function estimation.

The paper tackles estimating optimal policy value in linear bandits with general context distributions.

The paper shows how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.

Algorithm maximizes revenue-risk by estimating price impact kernel and optimizing control problems.

This work addresses dynamic KDE data structures with robustness to adversarial queries.

Minimal graphs grow slowly on curved spaces, proving constant solutions.

NanoFlow reduces parameter complexity in normalizing flows.

LIBO optimizes repeated bandit tasks without prior knowledge or regret.

Paper proposes OPF policy for fair resource allocation with sublinear regret.

The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric space. For example, the sublinear Higson corona of n-dimensional E…

New model for Knightian uncertainty with jumps.

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too small to reliably learn any accurate model. Our first result applies to the settin…

We study the growth of harmonic functions on complete Riemann-ian manifolds where the extrinsic diameter of geodesic spheres is sublinear. It is an generalization of a result of A. Kazue. We also get a Cheng and Yau estimates for the gradient of harmonic functions.

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…

Method completes mixed matrix from complex surveys with heterogeneous missingness.

Paper recovers uncertainty from dynamic valuation rules.

Study on optimal rates for sequential probability assignment using smoothed analysis.

New algorithms improve efficiency in learning from personalized rewards.

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …

Estimates population profile from small random samples.

The paper develops methods for time-varying constrained online convex optimization.

This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in $L^2$ is defined as the best $L^2$-estimate, given a $σ$-subalgebra and a degree of model uncertainty. When the random vector represents the payoff…

New algorithms for constrained online optimization with memory and predictions.

Simplifies and optimizes learning from untrusted batches with structure.

We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$ time, where $b < 1$. This sketch can correctly report the nearest neighbors of any …

Memory-limited learning tackles adversarial bandits with reduced storage.

New algorithm for reinforcement learning in uncertain environments with unknown thresholds.

New method connects CAT(0) spaces to hyperbolic spaces.

Study online learning in unknown Markov games with sublinear regret.

SmoothFBO tackles non-stationary functional bilevel optimization.

Open problem seeks an online learning algorithm for binary classification.

We tackle linear bandits with partially observable features, achieving sublinear regret.

Efficiently trains large GMMs with millions to billions of parameters.

Average signature of 2-bridge knots approximates sqrt(2c/π).

Dividing local Gaussian processes improve real-time prediction efficiency.

Efficient algorithm for learning from indirect feedback in complex decision-making scenarios.

Algorithm recovers graph from Glauber dynamics trajectory without mixing.