Related papers: Uniform mean estimation via generic chaining
Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…
Generative models aim to learn the distribution of datasets, such as images, so as to be able to generate samples that statistically resemble real data. However, learning the underlying probability distribution can be very challenging and…
This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…
We examine Fourier frames and, more generally, frame measures for different probability measures. We prove that if a measure has an associated frame measure, then it must have a certain uniformity in the sense that the weight is distributed…
Random feature model with a nonlinear activation function has been shown to perform asymptotically equivalent to a Gaussian model in terms of training and generalization errors. Analysis of the equivalent model reveals an important yet not…
We propose a method to conduct uniform inference for the (optimal) value function, that is, the function that results from optimizing an objective function marginally over one of its arguments. Marginal optimization is not Hadamard…
We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a…
We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
As a powerful tool for longitudinal data analysis, the generalized estimating equations have been widely studied in the academic community. However, in large-scale settings, this approach faces pronounced computational and storage…
Let ${\mathcal P}$ be a family of probability measures on a measurable space $(S,{\mathcal A}).$ Given a Banach space $E,$ a functional $f:E\mapsto {\mathbb R}$ and a mapping $\theta: {\mathcal P}\mapsto E,$ our goal is to estimate…
We will show that the sequence appearing in the double recurrence theorem is a good universal weight for the Furstenberg averages. That is, given a system $(X, \mathcal{F}, \mu, T)$ and bounded functions $f_1, f_2 \in L^\infty(\mu)$, there…
Let $f:\mathbb{R}^k\to \mathbb{R}$ be a measurable function, and let $\{U_i\}_{i\in\mathbb{N}}$ be a sequence of i.i.d. random variables. Consider the random process $Z_i=f(U_{i},...,U_{i+k-1})$. We show that for all $\ell$, there is a…
We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian…
A Gelfand-Tsetlin function is a real-valued function $\phi:C \to \mathbb{R}$ defined on a finite subset $C$ of the lattice $\mathbb{Z}^2$ with the property that $\phi(x) \leq \phi(y)$ for every edge $\langle x,y \rangle$ directed north or…
We study stochastic optimization problems with objective function given by the expectation of the maximum of two linear functions defined on the component random variables of a multivariate Gaussian distribution. We consider random…