193 research outputs found
Updating beliefs with incomplete observations
Currently, there is renewed interest in the problem, raised by Shafer in
1985, of updating probabilities when observations are incomplete. This is a
fundamental problem in general, and of particular interest for Bayesian
networks. Recently, Grunwald and Halpern have shown that commonly used updating
strategies fail in this case, except under very special assumptions. In this
paper we propose a new method for updating probabilities with incomplete
observations. Our approach is deliberately conservative: we make no assumptions
about the so-called incompleteness mechanism that associates complete with
incomplete observations. We model our ignorance about this mechanism by a
vacuous lower prevision, a tool from the theory of imprecise probabilities, and
we use only coherence arguments to turn prior into posterior probabilities. In
general, this new approach to updating produces lower and upper posterior
probabilities and expectations, as well as partially determinate decisions.
This is a logical consequence of the existing ignorance about the
incompleteness mechanism. We apply the new approach to the problem of
classification of new evidence in probabilistic expert systems, where it leads
to a new, so-called conservative updating rule. In the special case of Bayesian
networks constructed using expert knowledge, we provide an exact algorithm for
classification based on our updating rule, which has linear-time complexity for
a class of networks wider than polytrees. This result is then extended to the
more general framework of credal networks, where computations are often much
harder than with Bayesian nets. Using an example, we show that our rule appears
to provide a solid basis for reliable updating with incomplete observations,
when no strong assumptions about the incompleteness mechanism are justified.Comment: Replaced with extended versio
Partition function zeros at first-order phase transitions: Pirogov-Sinai theory
This paper is a continuation of our previous analysis [BBCKK] of partition
functions zeros in models with first-order phase transitions and periodic
boundary conditions. Here it is shown that the assumptions under which the
results of [BBCKK] were established are satisfied by a large class of lattice
models. These models are characterized by two basic properties: The existence
of only a finite number of ground states and the availability of an appropriate
contour representation. This setting includes, for instance, the Ising, Potts
and Blume-Capel models at low temperatures. The combined results of [BBCKK] and
the present paper provide complete control of the zeros of the partition
function with periodic boundary conditions for all models in the above class.Comment: 46 pages, 2 figs; continuation of math-ph/0304007 and
math-ph/0004003, to appear in J. Statist. Phys. (special issue dedicated to
Elliott Lieb
Branching Processes, and Random-Cluster Measures on Trees
Random-cluster measures on infinite regular trees are studied in conjunction
with a general type of `boundary condition', namely an equivalence relation on
the set of infinite paths of the tree. The uniqueness and non-uniqueness of
random-cluster measures are explored for certain classes of equivalence
relations. In proving uniqueness, the following problem concerning branching
processes is encountered and answered. Consider bond percolation on the
family-tree of a branching process. What is the probability that every
infinite path of , beginning at its root, contains some vertex which is
itself the root of an infinite open sub-tree
Enumerating Graph Partitions Without Too Small Connected Components Using Zero-suppressed Binary and Ternary Decision Diagrams
Partitioning a graph into balanced components is important for several applications. For multi-objective problems, it is useful not only to find one solution but also to enumerate all the solutions with good values of objectives. However, there are a vast number of graph partitions in a graph, and thus it is difficult to enumerate desired graph partitions efficiently. In this paper, an algorithm to enumerate all the graph partitions such that all the weights of the connected components are at least a specified value is proposed. To deal with a large search space, we use zero-suppressed binary decision diagrams (ZDDs) to represent sets of graph partitions and we design a new algorithm based on frontier-based search, which is a framework to directly construct a ZDD. Our algorithm utilizes not only ZDDs but also ternary decision diagrams (TDDs) and realizes an operation which seems difficult to be designed only by ZDDs. Experimental results show that the proposed algorithm runs up to tens of times faster than an existing state-of-the-art algorithm
Energy management in communication networks: a journey through modelling and optimization glasses
The widespread proliferation of Internet and wireless applications has
produced a significant increase of ICT energy footprint. As a response, in the
last five years, significant efforts have been undertaken to include
energy-awareness into network management. Several green networking frameworks
have been proposed by carefully managing the network routing and the power
state of network devices.
Even though approaches proposed differ based on network technologies and
sleep modes of nodes and interfaces, they all aim at tailoring the active
network resources to the varying traffic needs in order to minimize energy
consumption. From a modeling point of view, this has several commonalities with
classical network design and routing problems, even if with different
objectives and in a dynamic context.
With most researchers focused on addressing the complex and crucial
technological aspects of green networking schemes, there has been so far little
attention on understanding the modeling similarities and differences of
proposed solutions. This paper fills the gap surveying the literature with
optimization modeling glasses, following a tutorial approach that guides
through the different components of the models with a unified symbolism. A
detailed classification of the previous work based on the modeling issues
included is also proposed
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