arXiv research

New method estimates nested expectations with biased and antithetic sampling.

This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one population corresponding to distribution P1 with as few samples as possible. The main…

Efficient sampling reduces memory usage for Minimax distance analysis.

O3 optimizes samples from generative models without extra training.

The paper addresses hypothesis selection with local differential privacy, requiring more samples than non-private methods.

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting …

The paper explains how importance sampling can be used for optimization of rare events.

BayesSum improves Bayesian quadrature for discrete domains, requiring fewer samples.

Paper introduces a new sampling method combining Consistency Models with importance sampling.

This paper presents a Bayesian optimization method with exponential convergence without the need of auxiliary optimization and without the delta-cover sampling. Most Bayesian optimization methods require auxiliary optimization: an additional non-convex global optimization problem, which can be time-consuming and hard t…

New MCMC algorithm reduces subset selection passes to 2 for optimal $k$-dimensional subspace approximation.

We consider two multi-armed bandit problems with $n$ arms: (i) given an $ε> 0$, identify an arm with mean that is within $ε$ of the largest mean and (ii) given a threshold $μ_0$ and integer $k$, identify $k$ arms with means larger than $μ_0$. Existing lower bounds and algorithms for the PAC framework suggest that both …

The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these hyperparameters considers different possible explanations for the data when maki…

A new method reduces sample complexity for meta-learning.

Bayes Error Rate estimators are evaluated for accuracy and sample requirements.

Thompson sampling has impressive empirical performance for many multi-armed bandit problems. But current algorithms for Thompson sampling only work for the case of conjugate priors since these algorithms require to infer the posterior, which is often computationally intractable when the prior is not conjugate. In this …

Several approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a supervised learning problem, have been proposed recently. Finding good policies with such methods requires not only an appropriate classifier, but also reliable e…

We derive and analyze learning algorithms for apprenticeship learning, policy evaluation, and policy gradient for average reward criteria. Existing algorithms explicitly require an upper bound on the mixing time. In contrast, we build on ideas from Markov chain theory and derive sampling algorithms that do not require …

A new method uses MCMC-assisted normalizing flows for efficient Bayesian sampling.

New method uses higher-order Langevin dynamics for efficient parallel sampling.

New method reduces diffusion model function evaluations for discrete data.

Simplifies BO by directly sampling from posterior, achieving 35x efficiency.

Though deep reinforcement learning has led to breakthroughs in many difficult domains, these successes have required an ever-increasing number of samples. As state-of-the-art reinforcement learning (RL) systems require an exponentially increasing number of samples, their development is restricted to a continually shrin…

Parallelized Bayesian quadrature improves sample efficiency and inference.

In this paper, we investigate a new form of automated curriculum learning based on adaptive selection of accuracy requirements, called accuracy-based curriculum learning. Using a reinforcement learning agent based on the Deep Deterministic Policy Gradient algorithm and addressing the Reacher environment, we first show …

Study shows efficient algorithms for noiseless linear regression require quadratic sample complexity in contamination rate.

Paper presents unsupervised calibration for split conformal classification.

Given a loss function $F:\mathcal{X} \rightarrow \R^+$ that can be written as the sum of losses over a large set of inputs $a_1,\ldots, a_n$, it is often desirable to approximate $F$ by subsampling the input points. Strong theoretical guarantees require taking into account the importance of each point, measured by how …

Several popular graph embedding techniques for representation learning and dimensionality reduction rely on performing computationally expensive eigendecompositions to derive a nonlinear transformation of the input data space. The resulting eigenvectors encode the embedding coordinates for the training samples only, an…

Zigzag sampling algorithm efficiently samples from strongly log-concave distributions with low computational cost.

Study shows membership inference requires many more samples than training data.

Single-step samplers generate high-quality samples efficiently.

New sampling algorithm for non-log-concave distributions requires many queries.

In the Best-$k$-Arm problem, we are given $n$ stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the $k$ arms with the largest means by taking as few samples as possible. In this paper, we make progress towards a complete characterization of the instance-wise sample…

Paper improves tensor completion by reducing sample entries needed.

Proposes generating virtual data points to overcome the curse of dimensionality.

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze the performance of the $\ell_1$-regularized least squares as well as a greedy esti…

Bayesian Networks (BNs) are useful tools giving a natural and compact representation of joint probability distributions. In many applications one needs to learn a Bayesian Network (BN) from data. In this context, it is important to understand the number of samples needed in order to guarantee a successful learning. Pre…

Generative AutoEncoders require a chosen probability distribution in latent space, usually multivariate Gaussian. The original Variational AutoEncoder (VAE) uses randomness in encoder - causing problematic distortion, and overlaps in latent space for distinct inputs. It turned out unnecessary: we can instead use determ…

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and …

Neural networks can learn from higher-order cumulants efficiently, requiring quadratic samples.

Tensor completion requires fewer samples with weak side information.

The paper designs tests for comparing ranked preference data and finds significant differences.

Study learning and refutation in non-interactive LDP, showing sample complexity equivalence.

New algorithm speeds up diffusion model sampling 4-14 times.

A new sampling strategy improves reliability and robustness optimization for complex designs.

This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require t…

Accelerates data generation in score-based models.