2,824 research outputs found
The Minimum Wiener Connector
The Wiener index of a graph is the sum of all pairwise shortest-path
distances between its vertices. In this paper we study the novel problem of
finding a minimum Wiener connector: given a connected graph and a set
of query vertices, find a subgraph of that connects all
query vertices and has minimum Wiener index.
We show that The Minimum Wiener Connector admits a polynomial-time (albeit
impractical) exact algorithm for the special case where the number of query
vertices is bounded. We show that in general the problem is NP-hard, and has no
PTAS unless . Our main contribution is a
constant-factor approximation algorithm running in time
.
A thorough experimentation on a large variety of real-world graphs confirms
that our method returns smaller and denser solutions than other methods, and
does so by adding to the query set a small number of important vertices
(i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International
Conference on Management of Dat
Rank-normalization, folding, and localization: An improved for assessing convergence of MCMC
Markov chain Monte Carlo is a key computational tool in Bayesian statistics,
but it can be challenging to monitor the convergence of an iterative stochastic
algorithm. In this paper we show that the convergence diagnostic
of Gelman and Rubin (1992) has serious flaws. Traditional will
fail to correctly diagnose convergence failures when the chain has a heavy tail
or when the variance varies across the chains. In this paper we propose an
alternative rank-based diagnostic that fixes these problems. We also introduce
a collection of quantile-based local efficiency measures, along with a
practical approach for computing Monte Carlo error estimates for quantiles. We
suggest that common trace plots should be replaced with rank plots from
multiple chains. Finally, we give recommendations for how these methods should
be used in practice.Comment: Minor revision for improved clarit
Rank-normalization, folding, and localization: An improved for assessing convergence of MCMC
Markov chain Monte Carlo is a key computational tool in Bayesian statistics,
but it can be challenging to monitor the convergence of an iterative stochastic
algorithm. In this paper we show that the convergence diagnostic
of Gelman and Rubin (1992) has serious flaws. Traditional will
fail to correctly diagnose convergence failures when the chain has a heavy tail
or when the variance varies across the chains. In this paper we propose an
alternative rank-based diagnostic that fixes these problems. We also introduce
a collection of quantile-based local efficiency measures, along with a
practical approach for computing Monte Carlo error estimates for quantiles. We
suggest that common trace plots should be replaced with rank plots from
multiple chains. Finally, we give recommendations for how these methods should
be used in practice.Comment: Minor revision for improved clarit
Inference in Hybrid Bayesian Networks with Nonlinear Deterministic Conditionals.
This is the peer reviewed version of the following article: Cobb, B. R. and Shenoy, P. P. (2017), Inference in Hybrid Bayesian Networks with Nonlinear Deterministic Conditionals. Int. J. Intell. Syst., 32: 1217–1246. doi:10.1002/int.21897, which has been published in final form at https://doi.org/10.1002/int.21897. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.To enable inference in hybrid Bayesian networks (BNs) containing nonlinear deterministic conditional distributions, Cobb and Shenoy in 2005 propose approximating nonlinear deterministic functions by piecewise linear (PL) ones. In this paper, we describe a method for finding PL approximations of nonlinear functions based on a penalized mean square error (MSE) heuristic, which consists of minimizing a penalized MSE function subject to two principles, domain and symmetry. We illustrate our method for some commonly used one-dimensional and two-dimensional nonlinear deterministic functions such as math formula, math formula, math formula, and math formula. Finally, we solve two small examples of hybrid BNs containing nonlinear deterministic conditionals that arise in practice
Novel Split-Based Approaches to Computing Phylogenetic Diversity and Planar Split Networks
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