Related papers: Compressive Estimation of a Stochastic Process wit…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
Assuming that a stochastic process $X=(X_t)_{t\geq 0}$ is a sum of a compound Poisson process $Y=(Y_t)_{t\geq 0}$ with known intensity $\lambda$ and unknown jump size density $f,$ and an independent Brownian motion $Z=(Z_t)_{t\geq 0},$ we…
We analyze the problem of estimating a signal from multiple measurements on a $\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel…
Minimum mean square error (MMSE) estimation is widely used in signal processing and related fields. While it is known to be non-continuous with respect to all standard notions of stochastic convergence, it remains robust in practical…
We propose a stochastic model predictive control (MPC) framework for linear systems subject to joint-in-time chance constraints under unknown disturbance distributions. Unlike existing approaches that rely on parametric or Gaussian…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…
We discuss a class of difference-based estimators for the autocovariance in nonparametric regression when the signal is discontinuous (change-point regression), possibly highly fluctuating, and the errors form a stationary $m$-dependent…
We present new fundamental results for the mean square error (MSE)-optimal conditional mean estimator (CME) in one-bit quantized systems for a Gaussian mixture model (GMM) distributed signal of interest, possibly corrupted by additive white…
The predictability of a certain effect or phenomenon is often equated with the knowledge of relevant physical laws, typically understood as a functional or numerically derived relationship between the observations and known states of the…
This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the…
We consider the problem of recovering random graph signals from nonlinear measurements. For this case, closed-form Bayesian estimators are usually intractable and even numerical evaluation of these estimators may be hard to compute for…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
We propose a new framework for 2-D interpreting (features and samples) black-box machine learning models via a metamodeling technique, by which we study the output and input relationships of the underlying machine learning model. The…
We propose to utilize a variational autoencoder (VAE) for data-driven channel estimation. The underlying true and unknown channel distribution is modeled by the VAE as a conditional Gaussian distribution in a novel way, parameterized by the…
This paper studies the problem of jointly estimating multiple network processes driven by a common unknown input, thus effectively generalizing the classical blind multi-channel identification problem to graphs. More precisely, we model…