Related papers: Optimal Gaussian concentration bounds for stochast…

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well-understood despite it being a…

We consider the scenario in which a continuous-time Gauss-Markov process is estimated by the Kalman-Bucy filter over a Gaussian channel (sensor) with a variable sensor gain. The problem of scheduling the sensor gain over a finite time…

This article constructs simultaneous confidence bands (SCBs) for functional parameters using the Gaussian Kinematic formula of $t$-processes (tGKF). Although the tGKF relies on Gaussianity, we show that a central limit theorem (CLT) for the…

We consider the problem of optimizing an unknown (typically non-convex) function with a bounded norm in some Reproducing Kernel Hilbert Space (RKHS), based on noisy bandit feedback. We consider a novel variant of this problem in which the…

We find and investigate the optimal scheme of quantum distributed Gaussian sensing for estimation of the average of independent phase shifts. We show that the ultimate sensitivity is achievable by using an entangled symmetric Gaussian…

We consider SGD-type optimization on infinite-dimensional quadratic problems with power law spectral conditions. It is well-known that on such problems deterministic GD has loss convergence rates $L_t=O(t^{-\zeta})$, which can be improved…

It is generally believed that submodular functions -- and the more general class of $\gamma$-weakly submodular functions -- may only be optimized under the non-negativity assumption $f(S) \geq 0$. In this paper, we show that once the…

We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and…

This paper presents a method for the robust selection of measurements in a simultaneous localization and mapping (SLAM) framework. Existing methods check consistency or compatibility on a pairwise basis, however many measurement types are…

Gaussian Boson Sampling (GBS), which can be realized with a photonic quantum computing model, perform some special kind of sampling tasks. In [4], we introduced algorithms that use GBS samples to approximate Gaussian expectation problems.…

Spectral properties of Gram matrices are central to high dimensional asymptotic analyses of statistical estimators in regression and covariance estimation. These properties, in turn, depend critically on the extreme singular values and…

Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a single curve through the physical domain. They can also be extended to some dispersive wave equations, such as…

We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM)…

The purpose of this note is to prove a lower bound for the estimation of the memory parameter of a stationary long memory process. The memory parameter is defined here as the index of regular variation of the spectral density at 0. The…

Stochastic gradient descent based algorithms are typically used as the general optimization tools for most deep learning models. A Restricted Boltzmann Machine (RBM) is a probabilistic generative model that can be stacked to construct deep…

Gaussian Boson Sampling (GBS) is a recently developed paradigm of quantum computing consisting of sending a Gaussian state through a linear interferometer and then counting the number of photons in each output mode. When the system encodes…

We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…

We prove that there is only one translation-invariant Gibbsian point process w.r.t. to a chosen interaction if any of them satisfies a certain bound related to concentration-of-measure. This concentration-of-measure bound is e.g. fulfilled…

Gaussian process upper confidence bound (GP-UCB) is widely used for sequential optimization of expensive black-box functions. Although many upper bounds on its cumulative regret have been established in the literature, whether GP-UCB is…

In this paper, we study the existence and uniqueness of solutions to a class of non-Lipschitz G-BSDEs and the corresponding stochastic recursive optimal control problem. More precisely, we suppose that the generator of G-BSDE is uniformly…