38,652 research outputs found
Toward An Uncertainty Principle For Weighted Graphs
International audienceThe uncertainty principle states that a signal cannot be localized both in time and frequency. With the aim of extending this result to signals on graphs, Agaskar & Lu introduce notions of graph and spectral spreads. They show that a graph uncertainty principle holds for some families of unweighted graphs. This principle states that a signal cannot be simultaneously localized both in graph and spectral domains. In this paper, we aim to extend their work to weighted graphs. We show that a naive extension of their definitions leads to inconsistent results such as discontinuity of the graph spread when regarded as a function of the graph structure. To circumvent this problem, we propose another definition of graph spread that relies on an inverse similarity matrix. We also discuss the choice of the distance function that appears in this definition. Finally, we compute and plot uncertainty curves for families of weighted graphs
Learning Large-Scale Bayesian Networks with the sparsebn Package
Learning graphical models from data is an important problem with wide
applications, ranging from genomics to the social sciences. Nowadays datasets
often have upwards of thousands---sometimes tens or hundreds of thousands---of
variables and far fewer samples. To meet this challenge, we have developed a
new R package called sparsebn for learning the structure of large, sparse
graphical models with a focus on Bayesian networks. While there are many
existing software packages for this task, this package focuses on the unique
setting of learning large networks from high-dimensional data, possibly with
interventions. As such, the methods provided place a premium on scalability and
consistency in a high-dimensional setting. Furthermore, in the presence of
interventions, the methods implemented here achieve the goal of learning a
causal network from data. Additionally, the sparsebn package is fully
compatible with existing software packages for network analysis.Comment: To appear in the Journal of Statistical Software, 39 pages, 7 figure
Signals on Graphs: Uncertainty Principle and Sampling
In many applications, the observations can be represented as a signal defined
over the vertices of a graph. The analysis of such signals requires the
extension of standard signal processing tools. In this work, first, we provide
a class of graph signals that are maximally concentrated on the graph domain
and on its dual. Then, building on this framework, we derive an uncertainty
principle for graph signals and illustrate the conditions for the recovery of
band-limited signals from a subset of samples. We show an interesting link
between uncertainty principle and sampling and propose alternative signal
recovery algorithms, including a generalization to frame-based reconstruction
methods. After showing that the performance of signal recovery algorithms is
significantly affected by the location of samples, we suggest and compare a few
alternative sampling strategies. Finally, we provide the conditions for perfect
recovery of a useful signal corrupted by sparse noise, showing that this
problem is also intrinsically related to vertex-frequency localization
properties.Comment: This article is the revised version submitted to the IEEE
Transactions on Signal Processing on May, 2016; first revision was submitted
on January, 2016; original manuscript was submitted on July, 2015. The work
includes 16 pages, 8 figure
Interference and inequality in quantum decision theory
The quantum decision theory is examined in its simplest form of two-condition
two-choice setting. A set of inequalities to be satisfied by any quantum
conditional probability describing the decision process is derived.
Experimental data indicating the breakdown of classical explanations are
critically examined with quantum theory using the full set of quantum phases.Comment: LaTeX Elsevier format 10 pages, 6 figures, reference section
expanded, 2nd (and final) versio
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