Related papers: On the decomposition of Generalized Additive Indep…
Dual discriminator generative adversarial networks (D2 GANs) were introduced to mitigate the problem of mode collapse in generative adversarial networks. In D2 GANs, two discriminators are employed alongside a generator: one discriminator…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
The rapid advancement of machine learning techniques has re-energized research into general artificial intelligence. While the idea of domain-agnostic meta-learning is appealing, this emerging field must come to terms with its relationship…
Prevailing methods for assessing and comparing generative AIs incentivize responses that serve a hypothetical representative individual. Evaluating models in these terms presumes homogeneous preferences across the population and engenders…
In this note we discuss (Gaussian) intrinsic conditional autoregressive (CAR) models for disconnected graphs, with the aim of providing practical guidelines for how these models should be defined, scaled and implemented. We show how these…
Generalized additive models (GAMs) are a commonly used, flexible framework applied to many problems in statistical ecology. GAMs are often considered to be a purely frequentist framework (`generalized linear models with wiggly bits'),…
In this perspective paper, we introduce the concept of Specialized Generalist Artificial Intelligence (SGAI or simply SGI) as a crucial milestone toward Artificial General Intelligence (AGI). Compared to directly scaling general abilities,…
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a…
We study generalized and degenerate Whittaker models for reductive groups over local fields of characteristic zero (archimedean or non-archimedean). Our main result is the construction of epimorphisms from the generalized Whittaker model…
Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence…
We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet…
Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic…
In this study, we develop nonparametric analysis of deviance tools for generalized partially linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance,…
Generalized additive mixed models are introduced as an extension of the generalized linear mixed model which makes it possible to deal with temporal autocorrelational structure in experimental data. This autocorrelational structure is…
The widespread deployment of general-purpose AI (GPAI) systems introduces significant new risks. Yet the infrastructure, practices, and norms for reporting flaws in GPAI systems remain seriously underdeveloped, lagging far behind more…
Decomposition algebras and axial decomposition algebras are classes of commutative nonassociative algebras which are generalizations of axial algebras. The classes decomposition algebras, axial decomposition al;gebras and non-primitive…