Related papers: Weighted least-squares approximation with determin…
Invariable step size based least-mean-square error (ISS-LMS) was considered as a very simple adaptive filtering algorithm and hence it has been widely utilized in many applications, such as adaptive channel estimation. It is well known that…
The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When…
The stochastic proximal point (SPP) methods have gained recent attention for stochastic optimization, with strong convergence guarantees and superior robustness to the classic stochastic gradient descent (SGD) methods showcased at little to…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least…
We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal…
We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…
This paper gives poly-logarithmic-round, distributed D-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio D is the maximum number of…
Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…
We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any…
Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
We consider the problem of approximating a function in general nonlinear subsets of $L^2$ when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…
Processes (MDPs) often require frequent decision making, that is, taking an action every microsecond, second, or minute. Infinite horizon discount reward formulation is still relevant for a large portion of these applications, because…
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when…
Low-rank approximations of large kernel matrices are ubiquitous in machine learning, particularly for scaling Gaussian Processes to massive datasets. The Pivoted Cholesky decomposition is a standard tool for this task, offering a…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
In this work we introduce a novel weighted message-passing algorithm based on the cavity method to estimate volume-related properties of random polytopes, properties which are relevant in various research fields ranging from metabolic…
We review how to simulate continuous determinantal point processes (DPPs) and improve the current simulation algorithms in several important special cases as well as detail how certain types of conditional simulation can be carried out.…
The local pivotal method (LPM) is a successful sampling method for taking well-spread samples from discrete populations. We show how the LPM can be utilized to sample from arbitrary continuous distributions and thereby give powerful…