13,537 research outputs found
Constructing (Bi)Similar Finite State Abstractions using Asynchronous -Complete Approximations
This paper constructs a finite state abstraction of a possibly
continuous-time and infinite state model in two steps. First, a finite external
signal space is added, generating a so called -dynamical system.
Secondly, the strongest asynchronous -complete approximation of the external
dynamics is constructed. As our main results, we show that (i) the abstraction
simulates the original system, and (ii) bisimilarity between the original
system and its abstraction holds, if and only if the original system is
-complete and its state space satisfies an additional property
Comparing Asynchronous -Complete Approximations and Quotient Based Abstractions
This paper is concerned with a detailed comparison of two different
abstraction techniques for the construction of finite state symbolic models for
controller synthesis of hybrid systems. Namely, we compare quotient based
abstractions (QBA), with different realizations of strongest (asynchronous)
-complete approximations (SAlCA) Even though the idea behind their
construction is very similar, we show that they are generally incomparable both
in terms of behavioral inclusion and similarity relations. We therefore derive
necessary and sufficient conditions for QBA to coincide with particular
realizations of SAlCA. Depending on the original system, either QBA or SAlCA
can be a tighter abstraction
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
Streaming, Distributed Variational Inference for Bayesian Nonparametrics
This paper presents a methodology for creating streaming, distributed
inference algorithms for Bayesian nonparametric (BNP) models. In the proposed
framework, processing nodes receive a sequence of data minibatches, compute a
variational posterior for each, and make asynchronous streaming updates to a
central model. In contrast to previous algorithms, the proposed framework is
truly streaming, distributed, asynchronous, learning-rate-free, and
truncation-free. The key challenge in developing the framework, arising from
the fact that BNP models do not impose an inherent ordering on their
components, is finding the correspondence between minibatch and central BNP
posterior components before performing each update. To address this, the paper
develops a combinatorial optimization problem over component correspondences,
and provides an efficient solution technique. The paper concludes with an
application of the methodology to the DP mixture model, with experimental
results demonstrating its practical scalability and performance.Comment: This paper was presented at NIPS 2015. Please use the following
BibTeX citation: @inproceedings{Campbell15_NIPS, Author = {Trevor Campbell
and Julian Straub and John W. {Fisher III} and Jonathan P. How}, Title =
{Streaming, Distributed Variational Inference for Bayesian Nonparametrics},
Booktitle = {Advances in Neural Information Processing Systems (NIPS)}, Year
= {2015}
Towards Practical Graph-Based Verification for an Object-Oriented Concurrency Model
To harness the power of multi-core and distributed platforms, and to make the
development of concurrent software more accessible to software engineers,
different object-oriented concurrency models such as SCOOP have been proposed.
Despite the practical importance of analysing SCOOP programs, there are
currently no general verification approaches that operate directly on program
code without additional annotations. One reason for this is the multitude of
partially conflicting semantic formalisations for SCOOP (either in theory or
by-implementation). Here, we propose a simple graph transformation system (GTS)
based run-time semantics for SCOOP that grasps the most common features of all
known semantics of the language. This run-time model is implemented in the
state-of-the-art GTS tool GROOVE, which allows us to simulate, analyse, and
verify a subset of SCOOP programs with respect to deadlocks and other
behavioural properties. Besides proposing the first approach to verify SCOOP
programs by automatic translation to GTS, we also highlight our experiences of
applying GTS (and especially GROOVE) for specifying semantics in the form of a
run-time model, which should be transferable to GTS models for other concurrent
languages and libraries.Comment: In Proceedings GaM 2015, arXiv:1504.0244
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
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