Related papers: A Sample Complexity Measure with Applications to L…
We study multi-item profit maximization when there is an underlying distribution over buyers' values. In practice, a full description of the distribution is typically unavailable, so we study the setting where the mechanism designer only…
We study the tradeoff between sample complexity and round complexity in on-demand sampling, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of…
Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
This paper studies sample average approximation (SAA) in solving convex or strongly convex stochastic programming (SP) problems. In estimating SAA's sample efficiency, the state-of-the-art sample complexity bounds entail metric entropy…
Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that…
This paper considers the sample-efficiency of preference learning, which models and predicts human choices based on comparative judgments. The minimax optimal estimation error rate $\Theta(d/n)$ in classical estimation theory requires that…
We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative…
Slice sampling is a well-established Markov chain Monte Carlo method for (approximate) sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a…
Statistical inference is often simplified by sample-splitting. This simplification comes at the cost of the introduction of randomness not native to the data. We propose a simple procedure for sequentially aggregating statistics constructed…
Despite empirical risk minimization (ERM) is widely applied in the machine learning community, its performance is limited on data with spurious correlation or subpopulation that is introduced by hidden attributes. Existing literature…
A new generalized Statistical Complexity Measure (SCM) was proposed by Rosso et al in 2010. It is a functional that captures the notions of order/disorder and of distance to an equilibrium distribution. The former is computed by a measure…
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…
We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of $n$ additive bidders whose values for $m$ heterogeneous items are drawn…
The Empirical Revenue Maximization (ERM) is one of the most important price learning algorithms in auction design: as the literature shows it can learn approximately optimal reserve prices for revenue-maximizing auctioneers in both repeated…
The effective sample size (ESS) is widely used in sample-based simulation methods for assessing the quality of a Monte Carlo approximation of a given distribution and of related integrals. In this paper, we revisit the approximation of the…
This paper concerns a high-dimensional stochastic programming problem of minimizing a function of expected cost with a matrix argument. To this problem, one of the most widely applied solution paradigms is the sample average approximation…
Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration…
The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…
Traditionally, the Bayesian optimal auction design problem has been considered either when the bidder values are i.i.d., or when each bidder is individually identifiable via her value distribution. The latter is a reasonable approach when…