Results 1 
6 of
6
Bethe Bounds and Approximating the Global Optimum
"... Abstract—Inference in general Markov random fields (MRFs) is NPhard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We pr ..."
Abstract

Cited by 9 (8 self)
 Add to MetaCart
(Show Context)
Abstract—Inference in general Markov random fields (MRFs) is NPhard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We prove new formulations of derivatives of the Bethe free energy, provide bounds on the derivatives and bracket the locations of stationary points, introducing a new technique called Bethe bound propagation. Several results apply to pairwise models whether associative or not. Applying these to discretized pseudomarginals in the associative case we present a polynomial time approximation scheme for global optimization provided the maximum degree is O(log n), anddiscussseveralextensions. I.
Approximating marginals using discrete energy minimization
, 2012
"... classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specifi ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
(Show Context)
classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission.
Quantifying Political Polarity Based on Bipartite Opinion Networks
"... Political inclinations of individuals (liberal vs. conservative) largely shape their opinions on several issues such as abortion, gun control, nuclear power, etc. These opinions are openly exerted in online forums, news sites, the parliament, and so on. In this paper, we address the problem of quant ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Political inclinations of individuals (liberal vs. conservative) largely shape their opinions on several issues such as abortion, gun control, nuclear power, etc. These opinions are openly exerted in online forums, news sites, the parliament, and so on. In this paper, we address the problem of quantifying political polarity of individuals and of political issues for classification and ranking. We use signed bipartite networks to represent the opinions of individuals on issues, and formulate the problem as a node classification task. We propose a linear algorithm that exploits network effects to learn both the polarity labels as well as the rankings of people and issues in a completely unsupervised manner. Through extensive experiments we demonstrate that our proposed method provides an effective, fast, and easytoimplement solution, while outperforming three existing baseline algorithms adapted to signed networks, on real political forum and US Congress datasets. Experiments on a wide variety of synthetic graphs with varying polarity and degree distributions of the nodes further demonstrate the robustness of our approach.
Making Pairwise Binary Graphical Models Attractive
"... Computing the partition function (i.e., the normalizing constant) of a given pairwise binary graphical model is NPhard in general. As a result, the partition function is typically estimated by approximate inference algorithms such as belief propagation (BP) and treereweighted belief propagation ..."
Abstract
 Add to MetaCart
(Show Context)
Computing the partition function (i.e., the normalizing constant) of a given pairwise binary graphical model is NPhard in general. As a result, the partition function is typically estimated by approximate inference algorithms such as belief propagation (BP) and treereweighted belief propagation (TRBP). The former provides reasonable estimates in practice but has convergence issues. The later has better convergence properties but typically provides poorer estimates. In this work, we propose a novel scheme that has better convergence properties than BP and provably provides better partition function estimates in many instances than TRBP. In particular, given an arbitrary pairwise binary graphical model, we construct a specific “attractive ” 2cover. We explore the properties of this special cover and show that it can be used to construct an algorithm with the desired properties. 1
Approximating Marginals Using Discrete Energy Minimization
"... We consider the problem of inference in a graphical model with binary variables. While in theory it is arguably preferable to compute marginal probabilities, in practice researchers often use MAP inference due to the availability of efficient discrete optimization algorithms. We bridge the gap be ..."
Abstract
 Add to MetaCart
(Show Context)
We consider the problem of inference in a graphical model with binary variables. While in theory it is arguably preferable to compute marginal probabilities, in practice researchers often use MAP inference due to the availability of efficient discrete optimization algorithms. We bridge the gap between the two approaches by introducing the Discrete Marginals technique in which approximate marginals are obtained by minimizing an objective function with unary and pairwise terms over a discretized domain. This allows the use of techniques originally developed for MAPMRF inference and learning. We explore two ways to set up the objective function by discretizing the Bethe free energy and by learning it from training data. Experimental results show that for certain types of graphs a learned function can outperform the Bethe approximation. We also establish a link between the Bethe free energy and submodular functions. 1.
Methods for Inference in Graphical Models
, 2014
"... Graphical models provide a flexible, powerful and compact way to model relationships between random variables, and have been applied with great success in many domains. Combining prior beliefs with observed evidence to form a prediction is called inference. Problems of great interest include findin ..."
Abstract
 Add to MetaCart
Graphical models provide a flexible, powerful and compact way to model relationships between random variables, and have been applied with great success in many domains. Combining prior beliefs with observed evidence to form a prediction is called inference. Problems of great interest include finding a configuration with highest probability (MAP inference) or solving for the distribution over a subset of variables (marginal inference). Further, these methods are often critical subroutines for learning the relationships. However, inference is computationally intractable in general. Hence, much effort has focused on two themes: finding subdomains where exact inference is solvable efficiently, or identifying approximate methods that work well. We explore both these themes, restricting attention to undirected graphical models with discrete variables. First we address exact MAP inference by advancing the recent method of reducing the problem to finding a maximum weight stable set (MWSS) on a derived graph, which, if perfect, admits polynomial time inference. We derive new results for this approach, including a general decomposition theorem for models of any order and number of labels, extensions of results for binary pairwise models with submodular cost functions to higher order, and a characterization of which binary pairwise models can be efficiently solved with this method. This clarifies the power of the approach on