Related papers: The Sample Complexity of Uniform Approximation for…
Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected…
The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional…
We study the $L_1$-approximation of $d$-variate monotone functions based on information from $n$ function evaluations. It is known that this problem suffers from the curse of dimensionality in the deterministic setting, that is, the number…
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…
We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution $D$. The seller has "data"' about $D$ in the form of $m \ge 1$ i.i.d. samples, and the algorithmic challenge is to use these…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
Multi-distribution learning generalizes the classic PAC learning to handle data coming from multiple distributions. Given a set of $k$ data distributions and a hypothesis class of VC dimension $d$, the goal is to learn a hypothesis that…
Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an…
A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of…
This paper studies the cosine as basis function for the approximation of univariate and continuous functions without memory. This work studies a supervised learning to obtain the approximation coefficients, instead of using the Discrete…
We establish sample complexity guarantees for estimating the covariance matrix of a strongly log-concave smooth distribution using the unadjusted Langevin algorithm (ULA). We quantitatively compare our complexity estimates on single-chain…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…
We consider functions on the $d$-dimensional unit cube whose partial derivatives up to order $r$ are bounded by one. It is known that the minimal number of function values that is needed to approximate the integral of such functions up to…
We study nonparametric estimation of univariate cumulative distribution functions (CDFs) pertaining to data missing at random. The proposed estimators smooth the inverse probability weighted (IPW) empirical CDF with the Bernstein operator,…
We describe an MCMC method for sampling distributions with soft constraints, which are constraints that are almost but not exactly satisfied. We sample a total distribution that is a convex combination of the target soft distribution with…
Similarity and metric learning provides a principled approach to construct a task-specific similarity from weakly supervised data. However, these methods are subject to the curse of dimensionality: as the number of features grows large,…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The aim of distributional TD learning is to estimate the return distribution of a discounted…
Continuous response variables often need to be transformed to meet regression modeling assumptions; however, finding the optimal transformation is challenging and results may vary with the choice of transformation. When a continuous…