Related papers: Representing and Combining Partially Specified CPT…

Researchers are actively trying to gain better insights into the representational properties of convolutional neural networks for guiding better network designs and for interpreting a network's computational nature. Gaining such insights…

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…

Imagery is frequently used to model, represent and communicate knowledge. In particular, graphs are one of the most powerful tools, being able to represent relations between objects. Causal relations are frequently represented by directed…

In this paper we define a new product-like binary operation on directed graphs, and we discuss some of its properties. We also briefly discuss its application in constructing the subtyping relation in generic nominally-typed object-oriented…

A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision…

There has been an ever-increasing interest in multidisciplinary research on representing and reasoning with imperfect data. Possibilistic networks present one of the powerful frameworks of interest for representing uncertain and imprecise…

This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…

An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The…

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…

In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential…

We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi-isometry with uniform parameters for a large enough family…

We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…

Contemporary undertakings provide limitless opportunities for widespread application of machine reasoning and artificial intelligence in situations characterised by uncertainty, hostility and sheer volume of data. The paper develops a…

A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…

A partially ordered set P is representable if there is a bounded distributive lattice such that its ordered set of prime ideals is order-isomorphic to P. We show that if the order components of a poset P are representable, then so is P.…

Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…

We define a map from the unipotent representations of a split semisimple group over a finite field to (essentially) the set of pairs of left cells representations of the Weyl group in the same two-sided cell. We use this map to parametrize…

Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…

Representing domain knowledge is crucial for any task. There has been a wide range of techniques developed to represent this knowledge, from older logic based approaches to the more recent deep learning based techniques (i.e. embeddings).…

In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…