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Found 29 papers, 12 papers with code
Preserving linear invariants in ensemble filtering methods
Finally, we assess the benefits of preserving linear invariants for the ensemble Kalman filter and nonlinear ensemble filters.
Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities
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.
Multitask methods for predicting molecular properties from heterogeneous data
Data generation remains a bottleneck in training surrogate models to predict molecular properties.
Stable generative modeling using diffusion maps
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.
Sampling in Unit Time with Kernel Fisher-Rao Flow
We introduce a new mean-field ODE and corresponding interacting particle systems (IPS) for sampling from an unnormalized target density.
Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference
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.
An adaptive ensemble filter for heavy-tailed distributions: tuning-free inflation and localization
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.
Distribution learning via neural differential equations: a nonparametric statistical perspective
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.
A transport approach to sequential simulation-based inference
We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters.
Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices
We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices.
Score Operator Newton transport
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.
Diffusion map particle systems for generative modeling
We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD).
Infinite-Dimensional Diffusion Models
For image distributions, these guidelines are in line with the canonical choices currently made for diffusion models.
Multi-Fidelity Covariance Estimation in the Log-Euclidean Geometry
We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold.
Ensemble transport smoothing. Part I: Unified framework
A companion paper (Ramgraber et al., 2023) explores the implementation of nonlinear ensemble transport smoothers in greater depth.
Ensemble transport smoothing. Part II: Nonlinear updates
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.
On minimax density estimation via measure transport
We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport.
A low-rank ensemble Kalman filter for elliptic observations
We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators.
Sampling via Controlled Stochastic Dynamical Systems
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.
Learning non-Gaussian graphical models via Hessian scores and triangular transport
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables.
On the representation and learning of monotone triangular transport maps
Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond.
Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference
We present a novel framework for conditional sampling of probability measures, using block triangular transport maps.
Batch greedy maximization of non-submodular functions: Guarantees and applications to experimental design
Our theoretical guarantees are characterized by the combination of submodularity and supermodularity ratios.
Geodesically parameterized covariance estimation
We consider instead a differential geometric interpretation of this problem: minimizing the geodesic distance to a sample covariance matrix ("natural projection").
Computation Differential Geometry
Coupling techniques for nonlinear ensemble filtering
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.
Greedy inference with structure-exploiting lazy maps
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.
A Stein variational Newton method
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.
Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data.
Inference via low-dimensional couplings
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.
