Related papers: Reparameterizing Distributions on Lie Groups
We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors…
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the…
We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…
The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…
Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…
Optimization with noisy gradients has become ubiquitous in statistics and machine learning. Reparameterization gradients, or gradient estimates computed via the "reparameterization trick," represent a class of noisy gradients often used in…
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…
Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
The reparameterization trick is widely used in variational inference as it yields more accurate estimates of the gradient of the variational objective than alternative approaches such as the score function method. Although there is…
In recent years, skeleton-based action recognition has become a popular 3D classification problem. State-of-the-art methods typically first represent each motion sequence as a high-dimensional trajectory on a Lie group with an additional…
Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…
Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…
Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation,…
We study the Riemannian geometry of the Deep Linear Network (DLN) as a foundation for a thermodynamic description of the learning process. The main tools are the use of group actions to analyze overparametrization and the use of Riemannian…
Training neural network models with discrete (categorical or structured) latent variables can be computationally challenging, due to the need for marginalization over large or combinatorial sets. To circumvent this issue, one typically…
Learning distributions over permutations is a fundamental problem in machine learning, with applications in ranking, combinatorial optimization, structured prediction, and data association. Existing methods rely on mixtures of parametric…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…