Related papers: Sequential sampling for optimal weighted least squ…
Geographical data are generally autocorrelated. In this case, it is preferable to select spread units. In this paper, we propose a new method for selecting well-spread samples from a finite spatial population with equal or unequal inclusion…
In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…
$D^2$-sampling is a fundamental component of sampling-based clustering algorithms such as $k$-means++. Given a dataset $V \subset \mathbb{R}^d$ with $N$ points and a center set $C \subset \mathbb{R}^d$, $D^2$-sampling refers to picking a…
We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary…
The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…
A new unequal probability sampling method is proposed. This method is sequential. The decision to select or not each unit is made based on the order in which the units appear. A variant of this method allows selecting a sample from a…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We…
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
In this paper, for $\mu$ and $\nu$ two probability measures on $\mathbb{R}^d$ with finite moments of order $\rho\ge 1$, we define the respective projections for the $W_\rho$-Wasserstein distance of $\mu$ and $\nu$ on the sets of probability…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
We consider the problem of approximating an analytic function on a compact interval from its values at $M+1$ distinct points. When the points are equispaced, a recent result (the so-called impossibility theorem) has shown that the best…