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Found 16 papers, 3 papers with code
Wasserstein proximal operators describe score-based generative models and resolve memorization
Via a Cole-Hopf transformation and taking advantage of the fact that the cross-entropy can be related to a linear functional of the density, we show that the HJB equation is an uncontrolled FP equation.
Statistical Guarantees of Group-Invariant GANs
Group-invariant generative adversarial networks (GANs) are a type of GANs in which the generators and discriminators are hardwired with group symmetries.
A mean-field games laboratory for generative modeling
The mathematical structure described by the MFG optimality conditions identifies the inductive biases of generative flows.
Sample Complexity of Probability Divergences under Group Symmetry
We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions.
Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data
We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples.
Function-space regularized Rényi divergences
We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space.
Structure-preserving GANs
Generative adversarial networks (GANs), a class of distribution-learning methods based on a two-player game between a generator and a discriminator, can generally be formulated as a minmax problem based on the variational representation of a divergence between the unknown and the generated distributions.
A Variance Reduction Method for Neural-based Divergence Estimation
Unfortunately, the approximation of expectations that are inherent in variational formulas by statistical averages can be problematic due to high statistical variance, e. g., exponential for the Kullback-Leibler divergence and certain estimators.
Model Uncertainty and Correctability for Directed Graphical Models
Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence.
$(f,Γ)$-Divergences: Interpolating between $f$-Divergences and Integral Probability Metrics
We develop a rigorous and general framework for constructing information-theoretic divergences that subsume both $f$-divergences and integral probability metrics (IPMs), such as the $1$-Wasserstein distance.
Mutual Information for Explainable Deep Learning of Multiscale Systems
Timely completion of design cycles for complex systems ranging from consumer electronics to hypersonic vehicles relies on rapid simulation-based prototyping.
Uncertainty quantification for Markov Random Fields
In the latter, we develop uncertainty quantification bounds for finite size effects and phase diagrams, which constitute two of the typical predictions goals of statistical mechanics modeling.
Variational Representations and Neural Network Estimation of Rényi Divergences
We further show that this R\'enyi variational formula holds over a range of function spaces; this leads to a formula for the optimizer under very weak assumptions and is also key in our development of a consistency theory for R\'enyi divergence estimators.
GINNs: Graph-Informed Neural Networks for Multiscale Physics
We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and multiphysics systems.
Optimizing Variational Representations of Divergences and Accelerating their Statistical Estimation
Recently, they have gained popularity in machine learning as a tractable and scalable approach for training probabilistic models and for statistically differentiating between data distributions.
Causality and Bayesian network PDEs for multiscale representations of porous media
The global sensitivity indices are used to rank the effect of uncertainty in microscopic parameters on macroscopic QoIs, to quantify the impact of causality on the multiscale model's predictions, and to provide physical interpretations of these results for hierarchical nanoporous materials.
