1,721,036 research outputs found
Conditioning and Dilation with Coherent Nearly-Linear Models
Full text linkIn previous work [1] we introduced Nearly-Linear (NL) models, a class of neighbourhood models obtaining upper/lower probabilities by means of a linear affine transformation (with barriers) of a given probability. NL models are partitioned into more subfamilies, some of which are coherent. One, that of the Vertical Barrier Models (VBM), includes known models, such as the Pari-Mutuel, the ε-contamination or the Total Variation model as special instances. In this paper we study conditioning of coherent NL models, obtaining formulae for their natural extension. We show that VBMs are stable after conditioning, i.e. return a conditional model that is still a VBM, and that this is true also for the special instances mentioned above but not in general for NL models. We then analyse dilation for coherent NL models, a phenomenon that makes our ex-post opinion on an event A, after conditioning it on any event in a partition of hypotheses, vaguer than our ex-ante opinion on A
New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations
Full text linkWe present new results in the calculus for fuzzy-valued functions of a single real variable. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in fuzzy calculus. Concepts related to convergence and limits, continuity, level-wise gH-differentiability of first and second orders have nice and useful midpoint expressions. Using mid-point representation of fuzzy-valued functions, partial orders and properties of monotonicity and convexity are discussed and analysed in detail. Periodicity is easy to represent and identify. Graphical examples and pictures accompany the presentation
Probabilistic Coarsening for Knowledge Graph Embeddings
No full textKnowledge graphs have risen in popularity in recent years, demonstrating their utility in applications across the spectrum of computer science. Finding their embedded representations is thus highly desirable as it makes them easily operated on and reasoned with by machines. With this in mind, we propose a simple meta-strategy for embedding knowledge graphs using probabilistic coarsening. In this approach, a knowledge graph is first coarsened before being embedded by an arbitrary embedding method. The resulting coarse embeddings are then extended down as those of the initial knowledge graph. Although straightforward, this allows for faster training by reducing knowledge graph complexity while revealing its higher-order structures. We demonstrate this empirically on four real-world datasets, which show that coarse embeddings are learned faster and are often of higher quality. We conclude that coarsening is a recommended prepossessing step regardless of the underlying embedding method used
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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