arXiv research

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

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

Efficiently trains large GMMs with millions to billions of parameters.

Develops geometric foundations for sublinear Morse boundaries in mapping class groups and Teichmüller spaces.

Two new algorithms reduce online kernel regression's computational cost while maintaining optimal regret bounds.

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

NanoFlow reduces parameter complexity in normalizing flows.

New algorithms reduce rejection sampling complexity for shape-constrained distributions.

Paper presents a faster classical algorithm for principal component regression.

LaPSRL achieves optimal regret for isoperimetric RL distributions.

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…

Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top performance in this context, these approaches suffer from a high inference complexity…

Sketch-GNN reduces GNN training time and memory usage to sublinear scales.

New model for Knightian uncertainty with jumps.

Coresets are one of the central methods to facilitate the analysis of large data sets. We continue a recent line of research applying the theory of coresets to logistic regression. First, we show a negative result, namely, that no strongly sublinear sized coresets exist for logistic regression. To deal with intractable…

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…

This paper represents a preliminary (pre-reviewing) version of a sublinear variational algorithm for isotropic Gaussian mixture models (GMMs). Further developments of the algorithm for GMMs with diagonal covariance matrices (instead of isotropic clusters) and their corresponding benchmarking results have been published…

For a finite function class we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a $G$-heat equation. In the language of Peng's sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional $…

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.

Suppose X is any finite complex with vanishing L^2 Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The bounds are sensitive to the Novikov-Shubin invariants of X, and are improved in the presence of a spectral gap.

Dividing local Gaussian processes improve real-time prediction efficiency.

A well-known problem in data science and machine learning is {\em linear regression}, which is recently extended to dynamic graphs. Existing exact algorithms for updating the solution of dynamic graph regression require at least a linear time (in terms of $n$: the size of the graph). However, this time complexity might…

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

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. …

The paper provides an almost optimal learning and testing algorithm for sparse polynomials.

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

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…

Study online RL with mismatched dynamics, achieving sublinear regret.

New algorithms for constrained online optimization with memory and predictions.

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

GP-PSRL achieves sublinear regret for continuous control with unbounded state space.

Study online learning in unknown Markov games with sublinear regret.

We revisit the problem of learning from untrusted batches introduced by Qiao and Valiant [QV17]. Recently, Jain and Orlitsky [JO19] gave a simple semidefinite programming approach based on the cut-norm that achieves essentially information-theoretically optimal error in polynomial time. Concurrently, Chen et al. [CLM19…

A new algorithm reduces memory usage for long token attention in streaming applications.

Open problem seeks an online learning algorithm for binary classification.

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…

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

Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function cha…

New method reduces linear regret in high-dimensional bandit problems.

New method reduces GP bandit complexity while maintaining good performance.

New algorithm achieves sublinear regret in CMDPs without error cancellations.

New algorithm reduces regret in noisy context bandits.

Quantum algorithms reduce clustering input size, achieving near-linear approximation.

Extends tracking guarantees for time-varying variational inequalities.

Geodesic loops escape from balls at a sublinear rate imply virtually abelian fundamental group.

New approach for distributed online optimization of non-convex losses with sublinear regret.

Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending randomized CD to nonsmooth nonconvex settings, we develop a coordinate subgradi…