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Found 32 papers, 17 papers with code
A Mathematical Perspective On Contrastive Learning
The methodology is typically framed as the identification of a set of encoders, one for each modality, that align representations within a common latent space.
Proximal optimal transport divergences
Building on the Benamou-Brenier dynamic formulation of optimal transport cost, we also establish a dynamic formulation for proximal OT divergences.
Learning Enhanced Ensemble Filters
The ensemble approach uses empirical measures as input to the MNM and is implemented using the set transformer, which is invariant to ensemble permutation and allows for different ensemble sizes.
Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach
Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference.
Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forcing or source terms, which commonly arise as pathwise solutions to stochastic PDEs.
Memorization and Regularization in Generative Diffusion Models
Diffusion models have emerged as a powerful framework for generative modeling.
Expected Information Gain Estimation via Density Approximations: Sample Allocation and Dimension Reduction
We then address the estimation of EIG in high dimensions, by deriving gradient-based upper bounds on the mutual information lost by projecting the parameters and/or observations to lower-dimensional subspaces.
Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier maps
Conditional simulation is a fundamental task in statistical modeling: Generate samples from the conditionals given finitely many data points from a joint distribution.
Dimension reduction via score ratio matching
Yet these matrices require gradients or even Hessians of the log-likelihood, excluding the purely data-driven setting and many problems of simulation-based inference.
Inverse Problems and Data Assimilation: A Machine Learning Approach
The aim of these notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation.
Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems
This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications.
TrIM: Transformed Iterative Mondrian Forests for Gradient-based Dimension Reduction and High-Dimensional Regression
We propose a computationally efficient algorithm for gradient-based linear dimension reduction and high-dimensional regression.
Learning Optimal Filters Using Variational Inference
Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction.
Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis
We introduce a new method to jointly reduce the dimension of the input and output space of a function between high-dimensional spaces.
Neural Approximate Mirror Maps for Constrained Diffusion Models
We learn an approximate mirror map that transforms data into an unconstrained space and a corresponding approximate inverse that maps data back to the constraint set.
Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots
Type 1: Approximate an unknown function given input/output data.
Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference
Our static approach approximates the map as the gradient of a partially input-convex neural network.
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.
A generative flow for conditional sampling via optimal transport
Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation.
Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models
Moreover, our procedure correctly matches the statistics of physical quantities, even when the low-frequency content of the inputs and outputs do not match, a crucial but difficult-to-satisfy assumption needed by current state-of-the-art alternatives.
Score-based Diffusion Models in Function Space
They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by denoising.
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.
Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport
We tackle this challenging Bayesian inference problem using a likelihood-free approach based on measure transport together with the construction of summary statistics for the image data.
A low-rank ensemble Kalman filter for elliptic observations
We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators.
Diagonal Nonlinear Transformations Preserve Structure in Covariance and Precision Matrices
For a multivariate normal distribution, the sparsity of the covariance and precision matrices encodes complete information about independence and conditional independence properties.
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.
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.
Bayesian Optimization of Combinatorial Structures
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences.
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.
