199 citations · 1.1k across the 75 of their papers we have counts for
82 papers
Upper and Lower Bounds on Expected Soft Maxima of Gaussian Processes
Yifeng Chu, Maxim Raginsky
We obtain upper and lower bounds for "smoothed" versions of the expected supremum of centered Gaussian processes with finite or countable index sets. These so-called soft maxima ar…
A Behavioral Framework for Data-Driven Modeling of Nonlinear Systems in Vector-Valued Reproducing Kernel Hilbert Spaces
Boya Hou, Maxim Raginsky
We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-inva…
Information-theoretic Limits of Learning and Estimation
Abbas El Gamal, Maxim Raginsky
Information theory plays a central role in establishing fundamental limits on what any learning or estimation algorithm can -- and cannot -- achieve, regardless of computational po…
Expressivity of Quadratic Neural ODEs
Joshua Hanson, Maxim Raginsky
This work focuses on deriving quantitative approximation error bounds for neural ordinary differential equations having at most quadratic nonlinearities in the dynamics. The simple…
Talagrand Meets Talagrand: Upper and Lower Bounds on Expected Soft Maxima of Gaussian Processes with Finite Index Sets
Yifeng Chu, Maxim Raginsky
Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer scienc…
Rademacher Complexity of Neural ODEs via Chen-Fliess Series
Joshua Hanson, Maxim Raginsky
We show how continuous-depth neural ODE models can be framed as single-layer, infinite-width nets using the Chen--Fliess series expansion for nonlinear ODEs. In this net, the outpu…