Related papers: A Linear Systems Theory of Normalizing Flows

Normalizing flows are a class of machine learning models used to construct a complex distribution through a bijective mapping of a simple base distribution. We demonstrate that normalizing flows are particularly well suited as a Monte Carlo…

Normalizing flows are an established approach for modelling complex probability densities through invertible transformations from a base distribution. However, the accuracy with which the target distribution can be captured by the…

Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory,…

Time series analysis is a fundamental task in various application domains, and deep learning approaches have demonstrated remarkable performance in this area. However, many real-world time series data exhibit significant periodic or…

We propose a renormalisation group inspired normalising flow that combines benefits from traditional Markov chain Monte Carlo methods and standard normalising flows to sample lattice field theories. Specifically, we use samples from a…

Learning to integrate non-linear equations from highly resolved direct numerical simulations (DNSs) has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock…

We propose a unifying approach that starts from the perturbative construction of trivializing maps by L\"uscher and then improves on it by learning. The resulting continuous normalizing flow model can be implemented using common tools of…

Particle filtering is used to compute good nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average. Easy-to-sample distributions often lead to degenerate…

The future motion of traffic participants is inherently uncertain. To plan safely, therefore, an autonomous agent must take into account multiple possible trajectory outcomes and prioritize them. Recently, this problem has been addressed…

Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume…

Computing the marginal likelihood (also called the Bayesian model evidence) is an important task in Bayesian model selection, providing a principled quantitative way to compare models. The learned harmonic mean estimator solves the…

We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. More precisely, we construct a bijective transformation (a normalizing flow characterizing by neural networks) between a…

Normalizing Flows (NFs) are universal density estimators based on Neural Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to…

This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function. Similar to probabilistic filtering, the model maintains a Gaussian…

There is a vast literature on representation learning based on principles such as coding efficiency, statistical independence, causality, controllability, or symmetry. In this paper we propose to learn representations from sequence data by…

In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally…

Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete…

Unsupervised representation learning aims at describing raw data efficiently to solve various downstream tasks. It has been approached with many techniques, such as manifold learning, diffusion maps, or more recently self-supervised…

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as…

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…