AI Giving Back to Statistics? Discovery of the Coordinate System of Univariate Distributions by Beta Variational Autoencoder
Distributions are fundamental statistical elements that play essential theoretical and practical roles. The article discusses experiences of training neural networks to classify univariate empirical distributions and to represent them on the two-dimensional latent space forcing disentanglement based on the inputs of cumulative distribution functions (CDF). The latent space representation has been performed using an unsupervised beta variational autoencoder (beta-VAE). It separates distributions of different shapes while overlapping similar ones and empirically realises relationships between distributions that are known theoretically. The synthetic experiment of generated univariate continuous and discrete (Bernoulli) distributions with varying sample sizes and parameters has been performed to support the study. The representation on the latent two-dimensional coordinate system can be seen as an additional metadata of the real-world data that disentangles important distribution characteristics, such as shape of the CDF, classification probabilities of underlying theoretical distributions and their parameters, information entropy, and skewness. Entropy changes, providing an "arrow of time", determine dynamic trajectories along representations of distributions on the latent space. In addition, post beta-VAE unsupervised segmentation of the latent space based on weight-of-evidence (WOE) of posterior versus standard isotopic two-dimensional normal densities has been applied detecting the presence of assignable causes that distinguish exceptional CDF inputs.
Code (0)
등록된 구현이 없습니다.
Tasks
DisentanglementMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Grounded Discovery of Coordinate Term Relationships between Software Entities
We present an approach for the detection of coordinate-term relationships between entities from the software domain, that refer to Java classes. Usually, relations are found by examining corpus statistics associated with…
Coordinated Spectral Efficiency Prediction for Real-World 5G CoMP Systems
Coordinated multipoint (CoMP) systems incur substantial resource consumption due to the management of backhaul links and the coordination among various base stations (BSs). Accurate prediction of coordinated spectral eff…
DiversityManagementPredictionData-driven model discovery with Kolmogorov-Arnold networks
Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a …
Kolmogorov-Arnold NetworksmodelModel DiscoveryA Primer on Private Statistics
Differentially private statistical estimation has seen a flurry of developments over the last several years. Study has been divided into two schools of thought, focusing on empirical statistics versus population statisti…
Tactile: Giving Computer-Using Agents Hands and Feet
Computer-use agents are becoming capable software operators, but their interface to desktop applications is still often a brittle motor layer: they look at screenshots, predict coordinates, click, and hope that the visib…