87 research outputs found
Cutset Sampling for Bayesian Networks
The paper presents a new sampling methodology for Bayesian networks that
samples only a subset of variables and applies exact inference to the rest.
Cutset sampling is a network structure-exploiting application of the
Rao-Blackwellisation principle to sampling in Bayesian networks. It improves
convergence by exploiting memory-based inference algorithms. It can also be
viewed as an anytime approximation of the exact cutset-conditioning algorithm
developed by Pearl. Cutset sampling can be implemented efficiently when the
sampled variables constitute a loop-cutset of the Bayesian network and, more
generally, when the induced width of the networks graph conditioned on the
observed sampled variables is bounded by a constant w. We demonstrate
empirically the benefit of this scheme on a range of benchmarks
mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data
We present the R-package mgm for the estimation of k-order Mixed Graphical
Models (MGMs) and mixed Vector Autoregressive (mVAR) models in high-dimensional
data. These are a useful extensions of graphical models for only one variable
type, since data sets consisting of mixed types of variables (continuous,
count, categorical) are ubiquitous. In addition, we allow to relax the
stationarity assumption of both models by introducing time-varying versions
MGMs and mVAR models based on a kernel weighting approach. Time-varying models
offer a rich description of temporally evolving systems and allow to identify
external influences on the model structure such as the impact of interventions.
We provide the background of all implemented methods and provide fully
reproducible examples that illustrate how to use the package
Manhattan Cutset Sampling and Sensor Networks.
Cutset sampling is a new approach to acquiring two-dimensional data, i.e., images, where values are recorded densely along straight lines. This type of sampling is motivated by physical scenarios where data must be taken along straight paths, such as a boat taking water samples. Additionally, it may be possible to better reconstruct image edges using the dense amount of data collected on lines. Finally, an advantage of cutset sampling is in the design of wireless sensor networks. If battery-powered sensors are placed densely along straight lines, then the transmission energy required for communication between sensors can be reduced, thereby extending the network lifetime.
A special case of cutset sampling is Manhattan sampling, where data is recorded along evenly-spaced rows and columns. This thesis examines Manhattan sampling in three contexts. First, we prove a sampling theorem demonstrating an image can be perfectly reconstructed from Manhattan samples when its spectrum is bandlimited to the union of two Nyquist regions corresponding to the two lattices forming the Manhattan grid. An efficient ``onion peeling'' reconstruction method is provided, and we show that the Landau bound is achieved. This theorem is generalized to dimensions higher than two, where again signals are reconstructable from a Manhattan set if they are bandlimited to a union of Nyquist regions. Second, for non-bandlimited images, we present several algorithms for reconstructing natural images from Manhattan samples. The Locally Orthogonal Orientation Penalization (LOOP) algorithm is the best of the proposed algorithms in both subjective quality and mean-squared error. The LOOP algorithm reconstructs images well in general, and outperforms competing algorithms for reconstruction from non-lattice samples. Finally, we study cutset networks, which are new placement topologies for wireless sensor networks. Assuming a power-law model for communication energy, we show that cutset networks offer reduced communication energy costs over lattice and random topologies. Additionally, when solving centralized and decentralized source localization problems, cutset networks offer reduced energy costs over other topologies for fixed sensor densities and localization accuracies. Finally, with the eventual goal of analyzing different cutset topologies, we analyze the energy per distance required for efficient long-distance communication in lattice networks.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120876/1/mprelee_1.pd
Variational Probabilistic Inference and the QMR-DT Network
We describe a variational approximation method for efficient inference in
large-scale probabilistic models. Variational methods are deterministic
procedures that provide approximations to marginal and conditional
probabilities of interest. They provide alternatives to approximate inference
methods based on stochastic sampling or search. We describe a variational
approach to the problem of diagnostic inference in the `Quick Medical
Reference' (QMR) network. The QMR network is a large-scale probabilistic
graphical model built on statistical and expert knowledge. Exact probabilistic
inference is infeasible in this model for all but a small set of cases. We
evaluate our variational inference algorithm on a large set of diagnostic test
cases, comparing the algorithm to a state-of-the-art stochastic sampling
method
Cutset Width and Spacing for Reduced Cutset Coding of Markov Random Fields
In this paper we explore tradeoffs, regarding coding performance, between the thickness and spacing of the cutset used in Reduced Cutset Coding (RCC) of a Markov random field image model \cite{reyes2010}. Considering MRF models on a square lattice of sites, we show that under a stationarity condition, increasing the thickness of the cutset reduces coding rate for the cutset, increasing the spacing between components of the cutset increases the coding rate of the non-cutset pixels, though the coding rate of the latter is always strictly less than that of the former. We show that the redundancy of RCC can be decomposed into two terms, a correlation redundancy due to coding the components of the cutset independently, and a distribution redundancy due to coding the cutset as a reduced MRF. We provide analysis of these two sources of redundancy. We present results from numerical simulations with a homogeneous Ising model that bear out the analytical results. We also present a consistent estimation algorithm for the moment-matching reduced MRF for the cutset.http://deepblue.lib.umich.edu/bitstream/2027.42/117382/1/mgreyes_dlneuhoff_ISIT_2016_fullpaper_deepblue.pdfDescription of mgreyes_dlneuhoff_ISIT_2016_fullpaper_deepblue.pdf : articl
Gaussian Mixture Reduction for Time-Constrained Approximate Inference in Hybrid Bayesian Networks
Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous
variables, arise naturally in many application areas (e.g., image
understanding, data fusion, medical diagnosis, fraud detection). This paper
concerns inference in an important subclass of HBNs, the conditional Gaussian
(CG) networks, in which all continuous random variables have Gaussian
distributions and all children of continuous random variables must be
continuous. Inference in CG networks can be NP-hard even for special-case
structures, such as poly-trees, where inference in discrete Bayesian networks
can be performed in polynomial time. Therefore, approximate inference is
required. In approximate inference, it is often necessary to trade off accuracy
against solution time. This paper presents an extension to the Hybrid Message
Passing inference algorithm for general CG networks and an algorithm for
optimizing its accuracy given a bound on computation time. The extended
algorithm uses Gaussian mixture reduction to prevent an exponential increase in
the number of Gaussian mixture components. The trade-off algorithm performs
pre-processing to find optimal run-time settings for the extended algorithm.
Experimental results for four CG networks compare performance of the extended
algorithm with existing algorithms and show the optimal settings for these CG
networks
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