Related papers: Learning and Concentration for High Dimensional Li…

This paper is concerned with the long-time dynamics of the nonlinear wave equation in one-space dimension, $$ u_{tt} - \delta^2 u_{xx} +V'(u) =0 \qquad x\in [0,1] $$ where $\delta>0$ is a parameter and $V(u)$ is a potential bounded from…

This note describes the concentration phenomenon for a high dimensional sub-gaussian vector \( X \). In the Gaussian case, for any linear operator \( Q \), it holds \( P\bigl( \| Q X \|^{2} - tr (B) > 2 \sqrt{x\, tr(B^{2})} + 2 \| B \| x…

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal…

Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…

We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…

We propose a method that allows for a rigorous statistical analysis of neural responses to natural stimuli which are non-Gaussian and exhibit strong correlations. We have in mind a model in which neurons are selective for a small number of…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…

This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…

We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…

We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a…

We propose a new approach to inverse reinforcement learning (IRL) based on the deep Gaussian process (deep GP) model, which is capable of learning complicated reward structures with few demonstrations. Our model stacks multiple latent GP…

The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems…

In Gaussian Process (GP) dynamical model learning for robot control, particularly for systems constrained by computational resources like small quadrotors equipped with low-end processors, analyzing stability and designing a stable…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…

The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…

Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…

In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols,…