1 code implementation • 22 Apr 2024 • Mathieu Le Provost, Jan Glaubitz, Youssef Marzouk
Finally, we assess the benefits of preserving linear invariants for the ensemble Kalman filter and nonlinear ensemble filters.
no code implementations • 23 Feb 2024 • Fengyi Li, Ayoub Belhadji, Youssef Marzouk
We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters.
no code implementations • 31 Jan 2024 • Katharine Fisher, Michael Herbst, Youssef Marzouk
Data generation remains a bottleneck in training surrogate models to predict molecular properties.
no code implementations • 9 Jan 2024 • Georg Gottwald, Fengyi Li, Youssef Marzouk, Sebastian Reich
Diffusion maps are used to approximate the drift term from the available training samples, which is then implemented in a discrete-time Langevin sampler to generate new samples.
1 code implementation • 8 Jan 2024 • Aimee Maurais, Youssef Marzouk
We introduce a new mean-field ODE and corresponding interacting particle systems (IPS) for sampling from an unnormalized target density.
2 code implementations • 25 Oct 2023 • Zheyu Oliver Wang, Ricardo Baptista, Youssef Marzouk, Lars Ruthotto, Deepanshu Verma
PCP-Map models conditional transport maps as the gradient of a partially input convex neural network (PICNN) and uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives.
1 code implementation • 12 Oct 2023 • Mathieu Le Provost, Ricardo Baptista, Jeff D. Eldredge, Youssef Marzouk
In these settings, the Kalman filter and its ensemble version - the ensemble Kalman filter (EnKF) - that have been designed under Gaussian assumptions result in degraded performance.
no code implementations • 3 Sep 2023 • Youssef Marzouk, Zhi Ren, Sven Wang, Jakob Zech
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions.
no code implementations • 26 Aug 2023 • Paul-Baptiste Rubio, Youssef Marzouk, Matthew Parno
We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters.
no code implementations • 23 Jul 2023 • Aimee Maurais, Terrence Alsup, Benjamin Peherstorfer, Youssef Marzouk
We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices.
no code implementations • 16 May 2023 • Nisha Chandramoorthy, Florian Schaefer, Youssef Marzouk
We propose a new approach for sampling and Bayesian computation that uses the score of the target distribution to construct a transport from a given reference distribution to the target.
no code implementations • 1 Apr 2023 • Fengyi Li, Youssef Marzouk
We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD).
no code implementations • 20 Feb 2023 • Jakiw Pidstrigach, Youssef Marzouk, Sebastian Reich, Sven Wang
For image distributions, these guidelines are in line with the canonical choices currently made for diffusion models.
1 code implementation • 31 Jan 2023 • Aimee Maurais, Terrence Alsup, Benjamin Peherstorfer, Youssef Marzouk
We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold.
1 code implementation • 31 Oct 2022 • Maximilian Ramgraber, Ricardo Baptista, Dennis McLaughlin, Youssef Marzouk
A companion paper (Ramgraber et al., 2023) explores the implementation of nonlinear ensemble transport smoothers in greater depth.
1 code implementation • 31 Oct 2022 • Maximilian Ramgraber, Ricardo Baptista, Dennis McLaughlin, Youssef Marzouk
Smoothing is a specialized form of Bayesian inference for state-space models that characterizes the posterior distribution of a collection of states given an associated sequence of observations.
no code implementations • 20 Jul 2022 • Sven Wang, Youssef Marzouk
We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport.
2 code implementations • 10 Mar 2022 • Mathieu Le Provost, Ricardo Baptista, Youssef Marzouk, Jeff D. Eldredge
We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators.
no code implementations • NeurIPS Workshop ICBINB 2021 • Benjamin Zhang, Tuhin Sahai, Youssef Marzouk
Given a target distribution and a reference stochastic differential equation (SDE), the Doob $h$-transform produces a controlled stochastic process whose marginal at a finite time $T$ will be equal to the target distribution.
no code implementations • 8 Jan 2021 • Ricardo Baptista, Youssef Marzouk, Rebecca E. Morrison, Olivier Zahm
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables.
1 code implementation • 22 Sep 2020 • Ricardo Baptista, Youssef Marzouk, Olivier Zahm
Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond.
1 code implementation • 11 Jun 2020 • Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki, Youssef Marzouk
We present a novel framework for conditional sampling of probability measures, using block triangular transport maps.
no code implementations • 3 Jun 2020 • Jayanth Jagalur-Mohan, Youssef Marzouk
Our theoretical guarantees are characterized by the combination of submodularity and supermodularity ratios.
no code implementations • 6 Jan 2020 • Antoni Musolas, Steven T. Smith, Youssef Marzouk
We consider instead a differential geometric interpretation of this problem: minimizing the geodesic distance to a sample covariance matrix ("natural projection").
Computation Differential Geometry
no code implementations • 30 Jun 2019 • Alessio Spantini, Ricardo Baptista, Youssef Marzouk
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time.
1 code implementation • NeurIPS 2020 • Michael C. Brennan, Daniele Bigoni, Olivier Zahm, Alessio Spantini, Youssef Marzouk
We prove weak convergence of the generated sequence of distributions to the posterior, and we demonstrate the benefits of the framework on challenging inference problems in machine learning and differential equations, using inverse autoregressive flows and polynomial maps as examples of the underlying density estimators.
1 code implementation • NeurIPS 2018 • Gianluca Detommaso, Tiangang Cui, Alessio Spantini, Youssef Marzouk, Robert Scheichl
Stein variational gradient descent (SVGD) was recently proposed as a general purpose nonparametric variational inference algorithm [Liu & Wang, NIPS 2016]: it minimizes the Kullback-Leibler divergence between the target distribution and its approximation by implementing a form of functional gradient descent on a reproducing kernel Hilbert space.
no code implementations • NeurIPS 2017 • Rebecca E. Morrison, Ricardo Baptista, Youssef Marzouk
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data.
no code implementations • 17 Mar 2017 • Alessio Spantini, Daniele Bigoni, Youssef Marzouk
In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e. g., a standard Gaussian) with a target measure of interest.