6,704 research outputs found
A Time and Space Efficient Junction Tree Architecture
The junction tree algorithm is a way of computing marginals of boolean
multivariate probability distributions that factorise over sets of random
variables. The junction tree algorithm first constructs a tree called a
junction tree who's vertices are sets of random variables. The algorithm then
performs a generalised version of belief propagation on the junction tree. The
Shafer-Shenoy and Hugin architectures are two ways to perform this belief
propagation that tradeoff time and space complexities in different ways: Hugin
propagation is at least as fast as Shafer-Shenoy propagation and in the cases
that we have large vertices of high degree is significantly faster. However,
this speed increase comes at the cost of an increased space complexity. This
paper first introduces a simple novel architecture, ARCH-1, which has the best
of both worlds: the speed of Hugin propagation and the low space requirements
of Shafer-Shenoy propagation. A more complicated novel architecture, ARCH-2, is
then introduced which has, up to a factor only linear in the maximum
cardinality of any vertex, time and space complexities at least as good as
ARCH-1 and in the cases that we have large vertices of high degree is
significantly faster than ARCH-1
Model Checking Linear Logic Specifications
The overall goal of this paper is to investigate the theoretical foundations
of algorithmic verification techniques for first order linear logic
specifications. The fragment of linear logic we consider in this paper is based
on the linear logic programming language called LO enriched with universally
quantified goal formulas. Although LO was originally introduced as a
theoretical foundation for extensions of logic programming languages, it can
also be viewed as a very general language to specify a wide range of
infinite-state concurrent systems.
Our approach is based on the relation between backward reachability and
provability highlighted in our previous work on propositional LO programs.
Following this line of research, we define here a general framework for the
bottom-up evaluation of first order linear logic specifications. The evaluation
procedure is based on an effective fixpoint operator working on a symbolic
representation of infinite collections of first order linear logic formulas.
The theory of well quasi-orderings can be used to provide sufficient conditions
for the termination of the evaluation of non trivial fragments of first order
linear logic.Comment: 53 pages, 12 figures "Under consideration for publication in Theory
and Practice of Logic Programming
Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis
The safety of infinite state systems can be checked by a backward
reachability procedure. For certain classes of systems, it is possible to prove
the termination of the procedure and hence conclude the decidability of the
safety problem. Although backward reachability is property-directed, it can
unnecessarily explore (large) portions of the state space of a system which are
not required to verify the safety property under consideration. To avoid this,
invariants can be used to dramatically prune the search space. Indeed, the
problem is to guess such appropriate invariants. In this paper, we present a
fully declarative and symbolic approach to the mechanization of backward
reachability of infinite state systems manipulating arrays by Satisfiability
Modulo Theories solving. Theories are used to specify the topology and the data
manipulated by the system. We identify sufficient conditions on the theories to
ensure the termination of backward reachability and we show the completeness of
a method for invariant synthesis (obtained as the dual of backward
reachability), again, under suitable hypotheses on the theories. We also
present a pragmatic approach to interleave invariant synthesis and backward
reachability so that a fix-point for the set of backward reachable states is
more easily obtained. Finally, we discuss heuristics that allow us to derive an
implementation of the techniques in the model checker MCMT, showing remarkable
speed-ups on a significant set of safety problems extracted from a variety of
sources.Comment: Accepted for publication in Logical Methods in Computer Scienc
Marginal multi-Bernoulli filters: RFS derivation of MHT, JIPDA and association-based MeMBer
Recent developments in random finite sets (RFSs) have yielded a variety of
tracking methods that avoid data association. This paper derives a form of the
full Bayes RFS filter and observes that data association is implicitly present,
in a data structure similar to MHT. Subsequently, algorithms are obtained by
approximating the distribution of associations. Two algorithms result: one
nearly identical to JIPDA, and another related to the MeMBer filter. Both
improve performance in challenging environments.Comment: Journal version at http://ieeexplore.ieee.org/document/7272821.
Matlab code of simple implementation included with ancillary file
Universality for critical heavy-tailed network models: Metric structure of maximal components
We study limits of the largest connected components (viewed as metric spaces)
obtained by critical percolation on uniformly chosen graphs and configuration
models with heavy-tailed degrees. For rank-one inhomogeneous random graphs,
such results were derived by Bhamidi, van der Hofstad, Sen [Probab. Theory
Relat. Fields 2018]. We develop general principles under which the identical
scaling limits as the rank-one case can be obtained. Of independent interest,
we derive refined asymptotics for various susceptibility functions and the
maximal diameter in the barely subcritical regime.Comment: Final published version. 47 pages, 6 figure
Efficient Subgraph Similarity Search on Large Probabilistic Graph Databases
Many studies have been conducted on seeking the efficient solution for
subgraph similarity search over certain (deterministic) graphs due to its wide
application in many fields, including bioinformatics, social network analysis,
and Resource Description Framework (RDF) data management. All these works
assume that the underlying data are certain. However, in reality, graphs are
often noisy and uncertain due to various factors, such as errors in data
extraction, inconsistencies in data integration, and privacy preserving
purposes. Therefore, in this paper, we study subgraph similarity search on
large probabilistic graph databases. Different from previous works assuming
that edges in an uncertain graph are independent of each other, we study the
uncertain graphs where edges' occurrences are correlated. We formally prove
that subgraph similarity search over probabilistic graphs is #P-complete, thus,
we employ a filter-and-verify framework to speed up the search. In the
filtering phase,we develop tight lower and upper bounds of subgraph similarity
probability based on a probabilistic matrix index, PMI. PMI is composed of
discriminative subgraph features associated with tight lower and upper bounds
of subgraph isomorphism probability. Based on PMI, we can sort out a large
number of probabilistic graphs and maximize the pruning capability. During the
verification phase, we develop an efficient sampling algorithm to validate the
remaining candidates. The efficiency of our proposed solutions has been
verified through extensive experiments.Comment: VLDB201
Maximum Entropy Discrimination
We present a general framework for discriminative estimation based on the maximum entropy principle and its extensions. All calculations involve distributions over structures and/or parameters rather than specific settings and reduce to relative entropy projections. This holds even when the data is not separable within the chosen parametric class, in the context of anomaly detection rather than classification, or when the labels in the training set are uncertain or incomplete. Support vector machines are naturally subsumed under this class and we provide several extensions. We are also able to estimate exactly and efficiently discriminative distributions over tree structures of class-conditional models within this framework. Preliminary experimental results are indicative of the potential in these techniques
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