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This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a…

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

Often in real-world datasets, especially in high dimensional data, some feature values are missing. Since most data analysis and statistical methods do not handle gracefully missing values, the first step in the analysis requires the…

Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…

This article considers a linear model in a high dimensional data scenario. We propose a process which uses multiple loss functions both to select relevant predictors and to estimate parameters, and study its asymptotic properties. Variable…

Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying…

We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective…

A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…

In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…

Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the…

We study modeling and identification of processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly…

Most accurate predictions are typically obtained by learning machines with complex feature spaces (as e.g. induced by kernels). Unfortunately, such decision rules are hardly accessible to humans and cannot easily be used to gain insights…

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The…

This paper argues that the method of least squares has significant unfulfilled potential in modern machine learning, far beyond merely being a tool for fitting linear models. To release its potential, we derive custom gradients that…

Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we…

Many datasets suffer from missing values due to various reasons,which not only increases the processing difficulty of related tasks but also reduces the accuracy of classification. To address this problem, the mainstream approach is to use…

This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…

We propose a new, generic and flexible methodology for nonparametric function estimation, in which we first estimate the number and locations of any features that may be present in the function, and then estimate the function parametrically…

We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making…