2,355 research outputs found
Facets of Distribution Identities in Probabilistic Team Semantics
We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences. We also relate the framework to the first-order theory of the reals and apply our methods to the open question on the complexity of the implication problem of conditional independence.Peer reviewe
Unified Foundations of Team Semantics via Semirings
Semiring semantics for first-order logic provides a way to trace how facts
represented by a model are used to deduce satisfaction of a formula. Team
semantics is a framework for studying logics of dependence and independence in
diverse contexts such as databases, quantum mechanics, and statistics by
extending first-order logic with atoms that describe dependencies between
variables. Combining these two, we propose a unifying approach for analysing
the concepts of dependence and independence via a novel semiring team
semantics, which subsumes all the previously considered variants for
first-order team semantics. In particular, we study the preservation of
satisfaction of dependencies and formulae between different semirings. In
addition we create links to reasoning tasks such as provenance, counting, and
repairs
Crossing Generative Adversarial Networks for Cross-View Person Re-identification
Person re-identification (\textit{re-id}) refers to matching pedestrians
across disjoint yet non-overlapping camera views. The most effective way to
match these pedestrians undertaking significant visual variations is to seek
reliably invariant features that can describe the person of interest
faithfully. Most of existing methods are presented in a supervised manner to
produce discriminative features by relying on labeled paired images in
correspondence. However, annotating pair-wise images is prohibitively expensive
in labors, and thus not practical in large-scale networked cameras. Moreover,
seeking comparable representations across camera views demands a flexible model
to address the complex distributions of images. In this work, we study the
co-occurrence statistic patterns between pairs of images, and propose to
crossing Generative Adversarial Network (Cross-GAN) for learning a joint
distribution for cross-image representations in a unsupervised manner. Given a
pair of person images, the proposed model consists of the variational
auto-encoder to encode the pair into respective latent variables, a proposed
cross-view alignment to reduce the view disparity, and an adversarial layer to
seek the joint distribution of latent representations. The learned latent
representations are well-aligned to reflect the co-occurrence patterns of
paired images. We empirically evaluate the proposed model against challenging
datasets, and our results show the importance of joint invariant features in
improving matching rates of person re-id with comparison to semi/unsupervised
state-of-the-arts.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1702.03431 by
other author
Logics with probabilistic team semantics and the Boolean negation
We study the expressivity and the complexity of various logics in
probabilistic team semantics with the Boolean negation. In particular, we study
the extension of probabilistic independence logic with the Boolean negation,
and a recently introduced logic FOPT. We give a comprehensive picture of the
relative expressivity of these logics together with the most studied logics in
probabilistic team semantics setting, as well as relating their expressivity to
a numerical variant of second-order logic. In addition, we introduce novel
entropy atoms and show that the extension of first-order logic by entropy atoms
subsumes probabilistic independence logic. Finally, we obtain some results on
the complexity of model checking, validity, and satisfiability of our logics
On elementary logics for quantitative dependencies
We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under the Boolean negation. Our logics employ new probabilistic atoms that resemble so-called extended atoms from the team semantics literature. We also define counterparts of our logics over metafinite structures and show that all of our logics can be translated into functional fixed point logic implying a polynomial time upper bound for data complexity with respect to BSS-computations.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe
Descriptive complexity of real computation and probabilistic independence logic
We introduce a novel variant of BSS machines called Separate Branching BSS machines (S-BSS in short) and develop a Fagin-type logical characterisation for languages decidable in non-deterministic polynomial time by S-BSS machines. We show that NP on S-BSS machines is strictly included in NP on BSS machines and that every NP language on S-BSS machines is a countable union of closed sets in the usual topology of R^n. Moreover, we establish that on Boolean inputs NP on S-BSS machines without real constants characterises a natural fragment of the complexity class existsR (a class of problems polynomial time reducible to the true existential theory of the reals) and hence lies between NP and PSPACE. Finally we apply our results to determine the data complexity of probabilistic independence logic.Peer reviewe
Tractability Frontiers in Probabilistic Team Semantics and Existential Second-Order Logic over the Reals
Peer reviewe
Diversity, dependence and independence
We propose a very general, unifying framework for the concepts of dependence and independence. For this purpose, we introduce the notion of diversity rank. By means of this diversity rank we identify total determination with the inability to create more diversity, and independence with the presence of maximum diversity. We show that our theory of dependence and independence covers a variety of dependence concepts, for example the seemingly unrelated concepts of linear dependence in algebra and dependence of variables in logic.Peer reviewe
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