5,144 research outputs found
Probabilistic thread algebra
We add probabilistic features to basic thread algebra and its extensions with
thread-service interaction and strategic interleaving. Here, threads represent
the behaviours produced by instruction sequences under execution and services
represent the behaviours exhibited by the components of execution environments
of instruction sequences. In a paper concerned with probabilistic instruction
sequences, we proposed several kinds of probabilistic instructions and gave an
informal explanation for each of them. The probabilistic features added to the
extension of basic thread algebra with thread-service interaction make it
possible to give a formal explanation in terms of non-probabilistic
instructions and probabilistic services. The probabilistic features added to
the extensions of basic thread algebra with strategic interleaving make it
possible to cover strategies corresponding to probabilistic scheduling
algorithms.Comment: 25 pages (arXiv admin note: text overlap with arXiv:1408.2955,
arXiv:1402.4950); some simplifications made; substantially revise
DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives
We present a new parallel algorithm for probabilistic graphical model
optimization. The algorithm relies on data-parallel primitives (DPPs), which
provide portable performance over hardware architecture. We evaluate results on
CPUs and GPUs for an image segmentation problem. Compared to a serial baseline,
we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare
our performance to a reference, OpenMP-based algorithm, and find speedups of up
to 7X (CPU).Comment: LDAV 2018, October 201
On the behaviours produced by instruction sequences under execution
We study several aspects of the behaviours produced by instruction sequences
under execution in the setting of the algebraic theory of processes known as
ACP. We use ACP to describe the behaviours produced by instruction sequences
under execution and to describe two protocols implementing these behaviours in
the case where the processing of instructions takes place remotely. We also
show that all finite-state behaviours considered in ACP can be produced by
instruction sequences under execution.Comment: 36 pages, consolidates material from arXiv:0811.0436 [cs.PL],
arXiv:0902.2859 [cs.PL], and arXiv:0905.2257 [cs.PL]; abstract and
introduction rewritten, examples and proofs adde
Probabilistic Rely-guarantee Calculus
Jones' rely-guarantee calculus for shared variable concurrency is extended to
include probabilistic behaviours. We use an algebraic approach which combines
and adapts probabilistic Kleene algebras with concurrent Kleene algebra.
Soundness of the algebra is shown relative to a general probabilistic event
structure semantics. The main contribution of this paper is a collection of
rely-guarantee rules built on top of that semantics. In particular, we show how
to obtain bounds on probabilities by deriving rely-guarantee rules within the
true-concurrent denotational semantics. The use of these rules is illustrated
by a detailed verification of a simple probabilistic concurrent program: a
faulty Eratosthenes sieve.Comment: Preprint submitted to TCS-QAP
Probabilities on Sentences in an Expressive Logic
Automated reasoning about uncertain knowledge has many applications. One
difficulty when developing such systems is the lack of a completely
satisfactory integration of logic and probability. We address this problem
directly. Expressive languages like higher-order logic are ideally suited for
representing and reasoning about structured knowledge. Uncertain knowledge can
be modeled by using graded probabilities rather than binary truth-values. The
main technical problem studied in this paper is the following: Given a set of
sentences, each having some probability of being true, what probability should
be ascribed to other (query) sentences? A natural wish-list, among others, is
that the probability distribution (i) is consistent with the knowledge base,
(ii) allows for a consistent inference procedure and in particular (iii)
reduces to deductive logic in the limit of probabilities being 0 and 1, (iv)
allows (Bayesian) inductive reasoning and (v) learning in the limit and in
particular (vi) allows confirmation of universally quantified
hypotheses/sentences. We translate this wish-list into technical requirements
for a prior probability and show that probabilities satisfying all our criteria
exist. We also give explicit constructions and several general
characterizations of probabilities that satisfy some or all of the criteria and
various (counter) examples. We also derive necessary and sufficient conditions
for extending beliefs about finitely many sentences to suitable probabilities
over all sentences, and in particular least dogmatic or least biased ones. We
conclude with a brief outlook on how the developed theory might be used and
approximated in autonomous reasoning agents. Our theory is a step towards a
globally consistent and empirically satisfactory unification of probability and
logic.Comment: 52 LaTeX pages, 64 definiton/theorems/etc, presented at conference
Progic 2011 in New Yor
An Open Source C++ Implementation of Multi-Threaded Gaussian Mixture Models, k-Means and Expectation Maximisation
Modelling of multivariate densities is a core component in many signal
processing, pattern recognition and machine learning applications. The
modelling is often done via Gaussian mixture models (GMMs), which use
computationally expensive and potentially unstable training algorithms. We
provide an overview of a fast and robust implementation of GMMs in the C++
language, employing multi-threaded versions of the Expectation Maximisation
(EM) and k-means training algorithms. Multi-threading is achieved through
reformulation of the EM and k-means algorithms into a MapReduce-like framework.
Furthermore, the implementation uses several techniques to improve numerical
stability and modelling accuracy. We demonstrate that the multi-threaded
implementation achieves a speedup of an order of magnitude on a recent 16 core
machine, and that it can achieve higher modelling accuracy than a previously
well-established publically accessible implementation. The multi-threaded
implementation is included as a user-friendly class in recent releases of the
open source Armadillo C++ linear algebra library. The library is provided under
the permissive Apache~2.0 license, allowing unencumbered use in commercial
products
Straight-line instruction sequence completeness for total calculation on cancellation meadows
A combination of program algebra with the theory of meadows is designed
leading to a theory of computation in algebraic structures which use in
addition to a zero test and copying instructions the instruction set . It is proven that total functions on cancellation
meadows can be computed by straight-line programs using at most 5 auxiliary
variables. A similar result is obtained for signed meadows.Comment: 24 page
Fast processing of grid maps using graphical multiprocessors
Grid mapping is a very common technique used in mobile robotics to build a continuous 2D representation of the environment useful for navigation purposes. Although its computation is quite simple and fast, this algorithm uses the hypothesis of a known robot pose. In practice, this can require the re-computation of the map when the estimated robot poses change, as when a loop closure is detected. This paper presents a parallelization of a reference implementation of the grid mapping algorithm, which is suitable to be fully run on a graphics card showing huge processing speedups (up to 50×) while fully releasing the main processor, which can be very useful for many Simultaneous Localization and Mapping algorithms
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