arXiv research

New guarantees for adaptive combinatorial maximization with various objectives.

Unified approach to experimental design using interlacing polynomials.

MPNN improves on UniFL approximation with provable guarantees.

Improved Nyström approximation for kernel quadrature with theoretical guarantees.

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank estimation and combinatorial optimization, so much so that our bounds are reminisce…

One-pass algorithm finds small subset for $\ell_p$ subspace approximation with additive error.

Cross-validation (CV) is a popular approach for assessing and selecting predictive models. However, when the number of folds is large, CV suffers from a need to repeatedly refit a learning procedure on a large number of training datasets. Recent work in empirical risk minimization (ERM) approximates the expensive refit…

The paper provides approximation guarantees for neural networks trained with gradient flow.

NODEs can approximate a wide range of diffeomorphisms with strong guarantees.

Express improves causal attention guarantees for language models.

New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.

New algorithm for weighted low rank approximation with provable guarantees.

Extends neural network approximations to guarantee continuity of real-world learning tasks.

Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of dimensionality by minimizing a pessimistic bound on the policy loss. This approach tur…

Diminishing-returns (DR) submodular optimization is an important field with many real-world applications in machine learning, economics and communication systems. It captures a subclass of non-convex optimization that provides both practical and theoretical guarantees. In this paper, we study the fundamental problem of…

Improves bandits with knapsacks guarantees for partially stochastic workloads.

Uniform approximations for RHTs improve kernel approximation and distance estimation.

We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-no…

Theoretical analysis of entropy approximation for Gaussian mixtures.

Study on approximability and generalization in machine learning.

Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an approach to scalable approximate GP regression with finite-data guarantees on th…

Paper introduces deterministic EM approximations for non-convex likelihood functions.

Four algorithms improve sparse tensor BR1Approx with theoretical guarantees.

New algorithm for computing Wasserstein barycenters with guarantees.

New guarantees for VI in symmetric cases, extending previous results.

Data-independent pruning method reduces neural network size with accuracy guarantees.

Approximate dynamic programming algorithms, such as approximate value iteration, have been successfully applied to many complex reinforcement learning tasks, and a better approximate dynamic programming algorithm is expected to further extend the applicability of reinforcement learning to various tasks. In this paper w…

New convergence guarantees for learning with unknown nuisance parameters.

In this paper, we study fundamental problems of maximizing DR-submodular continuous functions that have real-world applications in the domain of machine learning, economics, operations research and communication systems. It captures a subclass of non-convex optimization that provides both theoretical and practical guar…

New methods stabilize Q-learning with linear approximations.

Random feature method approximates operators with theoretical guarantees and reduced computation.

Black-box variational inference tries to approximate a complex target distribution though a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural properties of the objective. This paper shows that for location-scale family approximations, if the targ…

This paper analyzes momentum Q-learning with finite-sample guarantees.

This paper tackles discontinuous neural networks for better approximation of piecewise continuous functions.

New algorithms achieve uniform-PAC guarantees for RL with bounded eluder dimension.

New method for optimistic planning in MDPs using regularization.

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifica…

DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others. DR-submodularity captures a subclass of non-convex functions that enables both exact…

Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides approximation and statistical guarantees of GANs for the estimation of data distri…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling from a given distribution is impossible or computationally expensive and, there…

New offline RL method works with limited data and function approximators.

The paper develops time-uniform inference methods for stochastic approximation parameters.

The paper provides tight bounds for improving multi-armed bandits problem.

New method reduces summary points for datasets while maintaining quality.

Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity measure used for graph sparsification. This choice is motivated by the observation…

Efficiently certifies global robustness of large neural networks with probabilistic guarantees.

Improved theoretical guarantees for SBEED algorithm.

We study the problem of approximating a surface $F$ in $R^3$ by a high quality mesh, a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The MidNormal algorithm generates a triangular mesh that is guaranteed to have angles in the interval $[49.1^o, 81.8^o]$. As the mesh size $…