Related papers: Information-Theoretic Bounds for Integral Estimati…
We study approximate stochastic It\^o integration of processes belonging to a class of progressively measurable stochastic processes that are H\"older continuous in the $r$th mean. Inspired by increasingly popularity of computations with…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and…
We study a simple-harmonic-oscillator quantum computer solving oracle decision problems. We show that such computers can perform better by using nonorthogonal Gaussian wave functions rather than orthogonal top-hat wave functions as input to…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
A trust-region algorithm using inexact function and derivatives values is introduced for solving unconstrained smooth optimization problems. This algorithm uses high-order Taylor models and allows the search of strong approximate minimizers…
We present an information-theoretic lower bound for the problem of parameter estimation with time-uniform coverage guarantees. Via a new a reduction to sequential testing, we obtain stronger lower bounds that capture the hardness of the…
We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…
This letter presents an almost sure convergence of the zeroth-order mirror descent algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate…
Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms,…
What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly…
System identification is a fundamental problem in control and learning, particularly in high-stakes applications where data efficiency is critical. Classical approaches, such as the ordinary least squares estimator (OLS), achieve an…
In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated possesses the single-index structure where neither the link function nor the index…
Recently, the information-theoretical framework has been proven to be able to obtain non-vacuous generalization bounds for large models trained by Stochastic Gradient Langevin Dynamics (SGLD) with isotropic noise. In this paper, we optimize…
We study the problem of nonparametric estimation of the fractional derivative of unknown spectral function of Gaussian stationary sequence (time series) and show that these problems is well posed with the classical speed of convergence when…
In this work we consider unconstrained optimization problems. The objective function is known through a zeroth order stochastic oracle that gives an estimate of the true objective function. To solve these problems, we propose a…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…
Simulation studies are used to understand the properties of statistical methods. A key luxury in many simulation studies is knowledge of the true value (i.e. the estimand) being targeted. With this oracle knowledge in-hand, the researcher…