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Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
This paper introduces a new proximal stochastic gradient method with variance reduction and stabilization for minimizing the sum of a convex stochastic function and a group sparsity-inducing regularization function. Since the method may be…
Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…
Singular values of a data in a matrix form provide insights on the structure of the data, the effective dimensionality, and the choice of hyper-parameters on higher-level data analysis tools. However, in many practical applications such as…
We study the problem of estimating the diagonal of an implicitly given matrix $A$. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product $Av$. For random variable $v$ drawn from an appropriate…
Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main contribution of this manuscript is a proposed algorithmic…
Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements $f(H)_{ij}$ decay rapidly…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…
The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning problems. In practice, to ensure high quality…
Approximating a function $f(x)$ on $[-1,1]$ based on $N+1$ samples is a classical problem in numerical analysis. If the samples come with heteroskedastic noise depending on $x$ of variance $\sigma(x)^2$, an $O(N\log N)$ algorithm for this…
The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…
Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
High computational costs of manifold learning prohibit its application for large point sets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire…
This article is concerned with Monte-Carlo methods for the estimation of the trace of an implicitly given matrix $A$ whose information is only available through matrix-vector products. Such a method approximates the trace by an average of…
In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
We show how to transform a non-differentiable rasterizer into a differentiable one with minimal engineering efforts and no external dependencies (no Pytorch/Tensorflow). We rely on Stochastic Gradient Estimation, a technique that consists…
According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation,…