Related papers: Principal Manifold Flows
Variational inference with normalizing flows (NFs) is an increasingly popular alternative to MCMC methods. In particular, NFs based on coupling layers (Real NVPs) are frequently used due to their good empirical performance. In theory,…
Normalizing Flows (NFs) are powerful and efficient models for density estimation. When modeling densities on manifolds, NFs can be generalized to injective flows but the Jacobian determinant becomes computationally prohibitive. Current…
Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…
The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to…
Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is…
Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). We propose to train CNFs on manifolds by minimizing…
Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their…
Normalizing flows define a probability distribution by an explicit invertible transformation $\boldsymbol{\mathbf{z}}=f(\boldsymbol{\mathbf{x}})$. In this work, we present implicit normalizing flows (ImpFlows), which generalize normalizing…
Neural networks-based learning of the distribution of non-dispatchable renewable electricity generation from sources such as photovoltaics (PV) and wind as well as load demands has recently gained attention. Normalizing flow density models…
Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations…
Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the…
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…
The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided…
Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…
Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…
By chaining a sequence of differentiable invertible transformations, normalizing flows (NF) provide an expressive method of posterior approximation, exact density evaluation, and sampling. The trend in normalizing flow literature has been…
We are interested in learning generative models for complex geometries described via manifolds, such as spheres, tori, and other implicit surfaces. Current extensions of existing (Euclidean) generative models are restricted to specific…
Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new…
The normalization constraint on probability density poses a significant challenge for solving the Fokker-Planck equation. Normalizing Flow, an invertible generative model leverages the change of variables formula to ensure probability…
We show that normalising flows become pathological when used to model targets whose supports have complicated topologies. In this scenario, we prove that a flow must become arbitrarily numerically noninvertible in order to approximate the…