2,030 research outputs found
Monotonic Properties of the Least Squares Mean
We settle an open problem of several years standing by showing that the
least-squares mean for positive definite matrices is monotone for the usual
(Loewner) order. Indeed we show this is a special case of its appropriate
generalization to partially ordered complete metric spaces of nonpositive
curvature. Our techniques extend to establish other basic properties of the
least squares mean such as continuity and joint concavity. Moreover, we
introduce a weighted least squares means and extend our results to this
setting.Comment: 21 page
A Boxology of Design Patterns for Hybrid Learning and Reasoning Systems
We propose a set of compositional design patterns to describe a large variety
of systems that combine statistical techniques from machine learning with
symbolic techniques from knowledge representation. As in other areas of
computer science (knowledge engineering, software engineering, ontology
engineering, process mining and others), such design patterns help to
systematize the literature, clarify which combinations of techniques serve
which purposes, and encourage re-use of software components. We have validated
our set of compositional design patterns against a large body of recent
literature.Comment: 12 pages,55 reference
Logic Negation with Spiking Neural P Systems
Nowadays, the success of neural networks as reasoning systems is doubtless.
Nonetheless, one of the drawbacks of such reasoning systems is that they work
as black-boxes and the acquired knowledge is not human readable. In this paper,
we present a new step in order to close the gap between connectionist and logic
based reasoning systems. We show that two of the most used inference rules for
obtaining negative information in rule based reasoning systems, the so-called
Closed World Assumption and Negation as Finite Failure can be characterized by
means of spiking neural P systems, a formal model of the third generation of
neural networks born in the framework of membrane computing.Comment: 25 pages, 1 figur
Feature selection algorithms: a survey and experimental evaluation
In view of the substantial number of existing feature selection
algorithms, the need arises to count on criteria that
enables to adequately decide which algorithm to use in certain
situations. This work reviews several fundamental algorithms found in the
literature and assesses their performance in a controlled
scenario. A scoring measure ranks the algorithms by
taking into account the amount of relevance, irrelevance
and redundance on sample data sets. This measure computes the
degree of matching between the output given by the algorithm and the known
optimal solution. Sample size effects are also studied.Postprint (published version
Interactive Learning-Based Realizability for Heyting Arithmetic with EM1
We apply to the semantics of Arithmetic the idea of ``finite approximation''
used to provide computational interpretations of Herbrand's Theorem, and we
interpret classical proofs as constructive proofs (with constructive rules for
) over a suitable structure \StructureN for the language of
natural numbers and maps of G\"odel's system \SystemT. We introduce a new
Realizability semantics we call ``Interactive learning-based Realizability'',
for Heyting Arithmetic plus \EM_1 (Excluded middle axiom restricted to
formulas). Individuals of \StructureN evolve with time, and
realizers may ``interact'' with them, by influencing their evolution. We build
our semantics over Avigad's fixed point result, but the same semantics may be
defined over different constructive interpretations of classical arithmetic
(Berardi and de' Liguoro use continuations). Our notion of realizability
extends intuitionistic realizability and differs from it only in the atomic
case: we interpret atomic realizers as ``learning agents''
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