167,136 research outputs found
Asymptotic Mutual Information for the Two-Groups Stochastic Block Model
We develop an information-theoretic view of the stochastic block model, a
popular statistical model for the large-scale structure of complex networks. A
graph from such a model is generated by first assigning vertex labels at
random from a finite alphabet, and then connecting vertices with edge
probabilities depending on the labels of the endpoints. In the case of the
symmetric two-group model, we establish an explicit `single-letter'
characterization of the per-vertex mutual information between the vertex labels
and the graph.
The explicit expression of the mutual information is intimately related to
estimation-theoretic quantities, and --in particular-- reveals a phase
transition at the critical point for community detection. Below the critical
point the per-vertex mutual information is asymptotically the same as if edges
were independent. Correspondingly, no algorithm can estimate the partition
better than random guessing. Conversely, above the threshold, the per-vertex
mutual information is strictly smaller than the independent-edges upper bound.
In this regime there exists a procedure that estimates the vertex labels better
than random guessing.Comment: 41 pages, 3 pdf figure
Inferring Rankings Using Constrained Sensing
We consider the problem of recovering a function over the space of
permutations (or, the symmetric group) over elements from given partial
information; the partial information we consider is related to the group
theoretic Fourier Transform of the function. This problem naturally arises in
several settings such as ranked elections, multi-object tracking, ranking
systems, and recommendation systems. Inspired by the work of Donoho and Stark
in the context of discrete-time functions, we focus on non-negative functions
with a sparse support (support size domain size). Our recovery method is
based on finding the sparsest solution (through optimization) that is
consistent with the available information. As the main result, we derive
sufficient conditions for functions that can be recovered exactly from partial
information through optimization. Under a natural random model for the
generation of functions, we quantify the recoverability conditions by deriving
bounds on the sparsity (support size) for which the function satisfies the
sufficient conditions with a high probability as .
optimization is computationally hard. Therefore, the popular compressive
sensing literature considers solving the convex relaxation,
optimization, to find the sparsest solution. However, we show that
optimization fails to recover a function (even with constant sparsity)
generated using the random model with a high probability as . In
order to overcome this problem, we propose a novel iterative algorithm for the
recovery of functions that satisfy the sufficient conditions. Finally, using an
Information Theoretic framework, we study necessary conditions for exact
recovery to be possible.Comment: 19 page
Boolean Compressed Sensing and Noisy Group Testing
The fundamental task of group testing is to recover a small distinguished
subset of items from a large population while efficiently reducing the total
number of tests (measurements). The key contribution of this paper is in
adopting a new information-theoretic perspective on group testing problems. We
formulate the group testing problem as a channel coding/decoding problem and
derive a single-letter characterization for the total number of tests used to
identify the defective set. Although the focus of this paper is primarily on
group testing, our main result is generally applicable to other compressive
sensing models.
The single letter characterization is shown to be order-wise tight for many
interesting noisy group testing scenarios. Specifically, we consider an
additive Bernoulli() noise model where we show that, for items and
defectives, the number of tests is for arbitrarily
small average error probability and for a worst case
error criterion. We also consider dilution effects whereby a defective item in
a positive pool might get diluted with probability and potentially missed.
In this case, it is shown that is and
for the average and the worst case error
criteria, respectively. Furthermore, our bounds allow us to verify existing
known bounds for noiseless group testing including the deterministic noise-free
case and approximate reconstruction with bounded distortion. Our proof of
achievability is based on random coding and the analysis of a Maximum
Likelihood Detector, and our information theoretic lower bound is based on
Fano's inequality.Comment: In this revision: reorganized the paper, added citations to related
work, and fixed some bug
Quality-based Multimodal Classification Using Tree-Structured Sparsity
Recent studies have demonstrated advantages of information fusion based on
sparsity models for multimodal classification. Among several sparsity models,
tree-structured sparsity provides a flexible framework for extraction of
cross-correlated information from different sources and for enforcing group
sparsity at multiple granularities. However, the existing algorithm only solves
an approximated version of the cost functional and the resulting solution is
not necessarily sparse at group levels. This paper reformulates the
tree-structured sparse model for multimodal classification task. An accelerated
proximal algorithm is proposed to solve the optimization problem, which is an
efficient tool for feature-level fusion among either homogeneous or
heterogeneous sources of information. In addition, a (fuzzy-set-theoretic)
possibilistic scheme is proposed to weight the available modalities, based on
their respective reliability, in a joint optimization problem for finding the
sparsity codes. This approach provides a general framework for quality-based
fusion that offers added robustness to several sparsity-based multimodal
classification algorithms. To demonstrate their efficacy, the proposed methods
are evaluated on three different applications - multiview face recognition,
multimodal face recognition, and target classification.Comment: To Appear in 2014 IEEE Conference on Computer Vision and Pattern
Recognition (CVPR 2014
Access Fees in Politics
This paper develops a game-theoretic model of lobbying in which a politician sells access to interest groups. The politician sets an access fee, or the minimum contribution necessary to secure access, and an interest group that pays this fee can share verifiable evidence in favor of its preferred policy. The more the politician knows about interest group evidence, the better able he is to identify and implement the welfare-maximizing policy. In equilibrium, a wealthy interest group must pay more for access than an otherwise similar poor group; and a group involved with an important issue must pay less than an otherwise similar group involved with a less-important issue. The politician sets higher-than-optimal access fees in order to increase contributions. A contribution limit can improve constituent welfare by lowering the price of access, which tends to result in a more-informed politician. However, a limit can also decrease the range of issues for which the politician is willing to sell access, thereby reducing politician information and constituent welfare. Although the optimal limit is binding for some issues, it is never optimal to ban contributions.Lobbying, campaign contributions, contribution limits, political access, hard information, evidence disclosure
An information theoretic approach to ecological inference in presence of spatial heterogeneity and dependence
This paper introduces Information Theoretic – based methods for estimating a target variable in a set of small geographical areas, by exploring spatially heterogeneous relationships at the disaggregate level. Controlling for spatial effects means introducing models whereby the assumption is that values in adjacent geographic locations are linked to each other by means of some form of underlying spatial relationship. This method offers a flexible framework for modeling the underlying variation in sub-group indicators, by addressing the spatial dependency problem. A basic ecological inference problem, which allows for spatial heterogeneity and dependence, is presented with the aim of first estimating the model at the aggregate level, and then of employing the estimated coefficients to obtain the sub-group level indicators. The Information Theoretic-based formulations could be a useful means of including spatial and inter-temporal features in analyses of micro-level behavior, and of providing an effective, flexible way of reconciling micro and macro data. An unique optimum solution may be obtained even if there are more parameters to be estimated than available moment conditions and the problem is ill-posed. Additional non-sample information from theory and/or empirical evidence can be introduced in the form of known probabilities by means of the cross-entropy formalism. Consistent estimates in small samples can be computed in the presence of incomplete micro-level data as well as in the presence of problems of collinearity and endogeneity in the individual local models, without imposing strong distributional assumptions. Keywords: Generalized Cross Entropy Estimation, Ecological Inference, Spatial Heterogeneity
Group-theoretic models of the inversion process in bacterial genomes
The variation in genome arrangements among bacterial taxa is largely due to
the process of inversion. Recent studies indicate that not all inversions are
equally probable, suggesting, for instance, that shorter inversions are more
frequent than longer, and those that move the terminus of replication are less
probable than those that do not. Current methods for establishing the inversion
distance between two bacterial genomes are unable to incorporate such
information. In this paper we suggest a group-theoretic framework that in
principle can take these constraints into account. In particular, we show that
by lifting the problem from circular permutations to the affine symmetric
group, the inversion distance can be found in polynomial time for a model in
which inversions are restricted to acting on two regions. This requires the
proof of new results in group theory, and suggests a vein of new combinatorial
problems concerning permutation groups on which group theorists will be needed
to collaborate with biologists. We apply the new method to inferring distances
and phylogenies for published Yersinia pestis data.Comment: 19 pages, 7 figures, in Press, Journal of Mathematical Biolog
A Cognitive-Motivational Model of Group Member Decision Satisfaction
A theoretic model of group member decision satisfaction based on a cognitive-motivational view of information- processing in inferential contexts is presented. Unlike normative-rational theorists, we acknowledge that information-processing is biased by the decision-maker\u27s motivations which are assumed to derive from situation- specific goals. Information processing is assumed to be more extensive when judgmental accuracy is the salient goal and less extensive when other goals (e.g., self-esteem) are relatively more salient. The model analyzes the implications of this view for the relationship between confidence and satisfaction. Research propositions are advanced
- …