Related papers: Testable Likelihoods for Beyond-the-Standard Model…
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…
Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
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…
The recent introduction of machine learning techniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional HMC algorithm. Naive use of…
Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new…
Simulated events are key ingredients in almost all high-energy physics analyses. However, imperfections in the simulation can lead to sizeable differences between the observed data and simulated events. The effects of such mismodelling on…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…
Eliciting a high-dimensional probability distribution from an expert via noisy judgments is notoriously challenging, yet useful for many applications, such as prior elicitation and reward modeling. We introduce a method for eliciting the…
We propose two new evaluation metrics to assess realness of generated images based on normalizing flows: a simpler and efficient flow-based likelihood distance (FLD) and a more exact dual-flow based likelihood distance (D-FLD). Because…
Assessing model adequacy is a crucial step in regression analysis, ensuring the validity of statistical inferences. For Generalized Functional Linear Models (GFLMs), which are widely used for modeling relationships between scalar responses…
Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…
Through examples of coordinate and probability transformation between different distributions, the basic principle of normalizing flow is introduced in a simple and concise manner. From the perspective of the distribution of random variable…
An invertible function is bi-Lipschitz if both the function and its inverse have bounded Lipschitz constants. Nowadays, most Normalizing Flows are bi-Lipschitz by design or by training to limit numerical errors (among other things). In this…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…
Many modern applications of Bayesian inference, such as in cosmology, are based on complicated forward models with high-dimensional parameter spaces. This considerably limits the sampling of posterior distributions conditioned on observed…
Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…