Event Generation and Statistical Sampling for Physics with Deep Generative Models and a Density Information Buffer

We present a study for the generation of events from a physical process with deep generative models. The simulation of physical processes requires not only the production of physical events, but also to ensure these events occur with the correct frequencies. We investigate the feasibility of learning the event generation and the frequency of occurrence with Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) to produce events like Monte Carlo generators. We study three processes: a simple two-body decay, the processes $e^+e^-\to Z \to l^+l^-$ and $p p \to t\bar{t}$ including the decay of the top quarks and a simulation of the detector response. We find that the tested GAN architectures and the standard VAE are not able to learn the distributions precisely. By buffering density information of encoded Monte Carlo events given the encoder of a VAE we are able to construct a prior for the sampling of new events from the decoder that yields distributions that are in very good agreement with real Monte Carlo events and are generated several orders of magnitude faster. Applications of this work include generic density estimation and sampling, targeted event generation via a principal component analysis of encoded ground truth data, anomaly detection and more efficient importance sampling, e.g. for the phase space integration of matrix elements in quantum field theories.Comment: 24 pages, 10 figure

Decorrelation of Neutral Vector Variables: Theory and Applications

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations

One-shot learning of object categories

Learning visual models of object categories notoriously requires hundreds or thousands of training examples. We show that it is possible to learn much information about a category from just one, or a handful, of images. The key insight is that, rather than learning from scratch, one can take advantage of knowledge coming from previously learned categories, no matter how different these categories might be. We explore a Bayesian implementation of this idea. Object categories are represented by probabilistic models. Prior knowledge is represented as a probability density function on the parameters of these models. The posterior model for an object category is obtained by updating the prior in the light of one or more observations. We test a simple implementation of our algorithm on a database of 101 diverse object categories. We compare category models learned by an implementation of our Bayesian approach to models learned from by maximum likelihood (ML) and maximum a posteriori (MAP) methods. We find that on a database of more than 100 categories, the Bayesian approach produces informative models when the number of training examples is too small for other methods to operate successfully

SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model densities whereas VAEs learn stochastic transformations that are non-invertible and thus typically do not provide tractable estimates of the marginal likelihood. In this paper, we introduce SurVAE Flows: A modular framework of composable transformations that encompasses VAEs and normalizing flows. SurVAE Flows bridge the gap between normalizing flows and VAEs with surjective transformations, wherein the transformations are deterministic in one direction -- thereby allowing exact likelihood computation, and stochastic in the reverse direction -- hence providing a lower bound on the corresponding likelihood. We show that several recently proposed methods, including dequantization and augmented normalizing flows, can be expressed as SurVAE Flows. Finally, we introduce common operations such as the max value, the absolute value, sorting and stochastic permutation as composable layers in SurVAE Flows

Learning Representations for Face Recognition: A Review from Holistic to Deep Learning

For decades, researchers have investigated how to recognize facial images. This study reviews the development of different face recognition (FR) methods, namely, holistic learning, handcrafted local feature learning, shallow learning, and deep learning (DL). With the development of methods, the accuracy of recognizing faces in the labeled faces in the wild (LFW) database has been increased. The accuracy of holistic learning is 60%, that of handcrafted local feature learning increases to 70%, and that of shallow learning is 86%. Finally, DL achieves human-level performance (97% accuracy). This enhanced accuracy is caused by large datasets and graphics processing units (GPUs) with massively parallel processing capabilities. Furthermore, FR challenges and current research studies are discussed to understand future research directions. The results of this study show that presently the database of labeled faces in the wild has reached 99.85% accuracy

An Unsupervised Approach to Modelling Visual Data

For very large visual datasets, producing expert ground-truth data for training supervised algorithms can represent a substantial human effort. In these situations there is scope for the use of unsupervised approaches that can model collections of images and automatically summarise their content. The primary motivation for this thesis comes from the problem of labelling large visual datasets of the seafloor obtained by an Autonomous Underwater Vehicle (AUV) for ecological analysis. It is expensive to label this data, as taxonomical experts for the specific region are required, whereas automatically generated summaries can be used to focus the efforts of experts, and inform decisions on additional sampling. The contributions in this thesis arise from modelling this visual data in entirely unsupervised ways to obtain comprehensive visual summaries. Firstly, popular unsupervised image feature learning approaches are adapted to work with large datasets and unsupervised clustering algorithms. Next, using Bayesian models the performance of rudimentary scene clustering is boosted by sharing clusters between multiple related datasets, such as regular photo albums or AUV surveys. These Bayesian scene clustering models are extended to simultaneously cluster sub-image segments to form unsupervised notions of “objects” within scenes. The frequency distribution of these objects within scenes is used as the scene descriptor for simultaneous scene clustering. Finally, this simultaneous clustering model is extended to make use of whole image descriptors, which encode rudimentary spatial information, as well as object frequency distributions to describe scenes. This is achieved by unifying the previously presented Bayesian clustering models, and in so doing rectifies some of their weaknesses and limitations. Hence, the final contribution of this thesis is a practical unsupervised algorithm for modelling images from the super-pixel to album levels, and is applicable to large datasets