7 research outputs found
Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models
Graphical models use graphs to compactly capture stochastic dependencies
amongst a collection of random variables. Inference over graphical models
corresponds to finding marginal probability distributions given joint
probability distributions. In general, this is computationally intractable,
which has led to a quest for finding efficient approximate inference
algorithms. We propose a framework for generalized inference over graphical
models that can be used as a wrapper for improving the estimates of approximate
inference algorithms. Instead of applying an inference algorithm to the
original graph, we apply the inference algorithm to a block-graph, defined as a
graph in which the nodes are non-overlapping clusters of nodes from the
original graph. This results in marginal estimates of a cluster of nodes, which
we further marginalize to get the marginal estimates of each node. Our proposed
block-graph construction algorithm is simple, efficient, and motivated by the
observation that approximate inference is more accurate on graphs with longer
cycles. We present extensive numerical simulations that illustrate our
block-graph framework with a variety of inference algorithms (e.g., those in
the libDAI software package). These simulations show the improvements provided
by our framework.Comment: Extended the previous version to include extensive numerical
simulations. See http://www.ima.umn.edu/~dvats/GeneralizedInference.html for
code and dat
IRIS: a method for reverse engineering of regulatory relations in gene networks
<p>Abstract</p> <p>Background</p> <p>The ultimate aim of systems biology is to understand and describe how molecular components interact to manifest collective behaviour that is the sum of the single parts. Building a network of molecular interactions is the basic step in modelling a complex entity such as the cell. Even if gene-gene interactions only partially describe real networks because of post-transcriptional modifications and protein regulation, using microarray technology it is possible to combine measurements for thousands of genes into a single analysis step that provides a picture of the cell's gene expression. Several databases provide information about known molecular interactions and various methods have been developed to infer gene networks from expression data. However, network topology alone is not enough to perform simulations and predictions of how a molecular system will respond to perturbations. Rules for interactions among the single parts are needed for a complete definition of the network behaviour. Another interesting question is how to integrate information carried by the network topology, which can be derived from the literature, with large-scale experimental data.</p> <p>Results</p> <p>Here we propose an algorithm, called inference of regulatory interaction schema (IRIS), that uses an iterative approach to map gene expression profile values (both steady-state and time-course) into discrete states and a simple probabilistic method to infer the regulatory functions of the network. These interaction rules are integrated into a factor graph model. We test IRIS on two synthetic networks to determine its accuracy and compare it to other methods. We also apply IRIS to gene expression microarray data for the <it>Saccharomyces cerevisiae </it>cell cycle and for human B-cells and compare the results to literature findings.</p> <p>Conclusions</p> <p>IRIS is a rapid and efficient tool for the inference of regulatory relations in gene networks. A topological description of the network and a matrix of gene expression profiles are required as input to the algorithm. IRIS maps gene expression data onto discrete values and then computes regulatory functions as conditional probability tables. The suitability of the method is demonstrated for synthetic data and microarray data. The resulting network can also be embedded in a factor graph model.</p
Cycle-based Cluster Variational Method for Direct and Inverse Inference
We elaborate on the idea that loop corrections to belief propagation could be
dealt with in a systematic way on pairwise Markov random fields, by using the
elements of a cycle basis to define region in a generalized belief propagation
setting. The region graph is specified in such a way as to avoid dual loops as
much as possible, by discarding redundant Lagrange multipliers, in order to
facilitate the convergence, while avoiding instabilities associated to minimal
factor graph construction. We end up with a two-level algorithm, where a belief
propagation algorithm is run alternatively at the level of each cycle and at
the inter-region level. The inverse problem of finding the couplings of a
Markov random field from empirical covariances can be addressed region wise. It
turns out that this can be done efficiently in particular in the Ising context,
where fixed point equations can be derived along with a one-parameter log
likelihood function to minimize. Numerical experiments confirm the
effectiveness of these considerations both for the direct and inverse MRF
inference.Comment: 47 pages, 16 figure
IBIA: An Incremental Build-Infer-Approximate Framework for Approximate Inference of Partition Function
Exact computation of the partition function is known to be intractable,
necessitating approximate inference techniques. Existing methods for
approximate inference are slow to converge for many benchmarks. The control of
accuracy-complexity trade-off is also non-trivial in many of these methods. We
propose a novel incremental build-infer-approximate (IBIA) framework for
approximate inference that addresses these issues. In this framework, the
probabilistic graphical model is converted into a sequence of clique tree
forests (SCTF) with bounded clique sizes. We show that the SCTF can be used to
efficiently compute the partition function. We propose two new algorithms which
are used to construct the SCTF and prove the correctness of both. The first is
an algorithm for incremental construction of CTFs that is guaranteed to give a
valid CTF with bounded clique sizes and the second is an approximation
algorithm that takes a calibrated CTF as input and yields a valid and
calibrated CTF with reduced clique sizes as the output. We have evaluated our
method using several benchmark sets from recent UAI competitions and our
results show good accuracies with competitive runtimes
Loop Corrections for Approximate Inference on Factor Graphs
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Loop corrections for approximate inference on factor graphs
We propose a method to improve approximate inference methods by correcting for the influence of loops in the graphical model. The method is a generalization and alternative implementation of a recent idea from Montanari and Rizzo (2005). It is applicable to arbitrary factor graphs, provided that the size of the Markov blankets is not too large. It consists of two steps: (i) an approximate inference method, for example, belief propagation, is used to approximate cavity distributions for each variable (i.e., probability distributions on the Markov blanket of a variable for a modified graphical model in which the factors involving that variable have been removed); (ii) all cavity distributions are improved by a message-passing algorithm that cancels out approximation errors by imposing certain consistency constraints. This loop correction (LC) method usually gives significantly better results than the original, uncorrected, approximate inference algorithm that is used to estimate the effect of loops. Indeed, we often observe that the loop-corrected error is approximately the square of the error of the uncorrected approximate inference method. In this article, we compare different variants of the loop correction method with other approximate inference methods on a variety of graphical models, including “real world ” networks, and conclude that the LC method generally obtains the most accurate results