Related papers: A stochastic reconstruction theorem
Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…
We show local well-posedness of the g-PAM and the $\phi^{K+1}_2$-equation for $K\geq 1$ on the two-dimensional torus when the coefficient field is random and correlated to the driving noise. In the setting considered here, even when the…
We compare the quantitative microstructural properties of Berea Sandstone with stochastic reconstructions of the same sandstone. The comparison is based on local porosity theory. The reconstructions employ Fourier space filtering of…
The stochastic embedding procedure associates a stochastic Euler-Lagrange equation (SEL) to the standard Euler-Lagrange equation (EL). Can we derive (SEL) from a generalized least action principle? To address this question, we develop a…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We study an extended system that without noise shows a spatially homogeneous state, but when submitted to an adequate multiplicative noise, some "noise-induced patterns" arise. The stochastic resonance between these structures is…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
In a pioneer work, R\'ev\'esz (1973) introduces the stochastic approximation method to build up a recursive kernel estimator of the regression function $x\mapsto E(Y|X=x)$. However, according to R\'ev\'esz (1977), his estimator has two main…
We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…
Modern machine learning embeddings provide powerful compression of high-dimensional data, yet they typically destroy the geometric structure required for classical likelihood-based statistical inference. This paper develops a rigorous…
Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show…
Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications and has significantly impacted machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either…
Many efforts have been devoted to training generative latent variable models with autoregressive decoders, such as recurrent neural networks (RNN). Stochastic recurrent models have been successful in capturing the variability observed in…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
On semiconductor growth surfaces, surface reconstructions appear. Estimation of the reconstructed structures is essential for understanding and controlling growth phenomena. In this study, the stability of a mixture of two different surface…
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…
For the space of functions that can be approximated by linear chirps, we prove a reconstruction theorem by random sampling at arbitrary rates.
We indicate that the nonlinear Schr\"odinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods,…
We analyze the phenomenon of stochastic resonance in an Ising-like system on a small-world network. The system, which is subject to the combined action of noise and an external modulation, can be interpreted as a stylized model of opinion…
We discuss how the Gross-Siebert reconstruction theorem applies to the local mirror symmetry of Chiang, Klemm, Yau and Zaslow. The reconstruction theorem associates to certain combinatorial data a degeneration of (log) Calabi-Yau varieties.…