Related papers: High-dimensional Asymptotics of Langevin Dynamics …
Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a…
The recently discovered supersymmetric generalizations of Langevin dynamics and Kramers equation can be utilized for the exploration of free energy landscapes of systems whose large time-scale separation hampers the usefulness of standard…
The classical (overdamped) Langevin dynamics provide a natural algorithm for sampling from its invariant measure, which uniquely minimizes an energy functional over the space of probability measures, and which concentrates around the…
Langevin dynamics (LD) has been proven to be a powerful technique for optimizing a non-convex objective as an efficient algorithm to find local minima while eventually visiting a global minimum on longer time-scales. LD is based on the…
Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…
We consider one-dimensional inverse scattering in attenuating media where both the reflectivity and loss distributions are unknown. Mathematically, this corresponds to recovering the coefficients of a damped wave operator, or equivalently,…
We study the properties of a refined weak coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system presents a rich and new non-Markovian…
This work extends quantum optical models of high harmonic generation by considering a quantum stochastic analysis of the field modes coupled to an environment. In particular, we study the open system dynamics by solving the quantum Langevin…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…
We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…
We adapted the SWAP molecular dynamics algorithm for use in lattice Ising spin models. We dressed the spins with a randomly distributed length and we alternated long-range spin exchanges with conventional single spin flip Monte Carlo…
We analyze the low temperature asymptotics of the quasi-stationary distribution associated with the overdamped Langevin dynamics (a.k.a. the Einstein-Smoluchowski diffusion equation) in a bounded domain. This analysis is useful to…
Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the…
High-dimensional planted problems, such as finding a hidden dense subgraph within a random graph, often exhibit a gap between statistical and computational feasibility. While recovering the hidden structure may be statistically possible, it…
Complex Langevin (CL) is a computational method to circumvent the numerical sign problem with applications in finite-density quantum chromodynamics and the real-time dynamics of quantum field theories. It has long been known that, depending…
We consider the problem of inferring the dynamics of unknown (i.e. hidden) nodes from a set of observed trajectories and study analytically the average prediction error and the typical relaxation time of correlations between errors. We…
To gain a comprehensive view of what the LHC tells us about physics beyond the Standard Model (BSM), it is crucial that different BSM-sensitive analyses can be combined. But in general, search analyses are not statistically orthogonal, so…
The critical step in a molecular process is often a rare-event and has to be simulated by an enhanced sampling protocol. Recovering accurate dynamical estimates from such biased simulation is challenging. Girsanov reweighting is a method to…
We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces…