132,462 research outputs found
Phase transition and hysteresis in scale-free network traffic
We model information traffic on scale-free networks by introducing the node
queue length L proportional to the node degree and its delivering ability C
proportional to L. The simulation gives the overall capacity of the traffic
system, which is quantified by a phase transition from free flow to congestion.
It is found that the maximal capacity of the system results from the case of
the local routing coefficient \phi slightly larger than zero, and we provide an
analysis for the optimal value of \phi. In addition, we report for the first
time the fundamental diagram of flow against density, in which hysteresis is
found, and thus we can classify the traffic flow with four states: free flow,
saturated flow, bistable, and jammed.Comment: 5 pages, 4 figure
Equitability, mutual information, and the maximal information coefficient
Reshef et al. recently proposed a new statistical measure, the "maximal
information coefficient" (MIC), for quantifying arbitrary dependencies between
pairs of stochastic quantities. MIC is based on mutual information, a
fundamental quantity in information theory that is widely understood to serve
this need. MIC, however, is not an estimate of mutual information. Indeed, it
was claimed that MIC possesses a desirable mathematical property called
"equitability" that mutual information lacks. This was not proven; instead it
was argued solely through the analysis of simulated data. Here we show that
this claim, in fact, is incorrect. First we offer mathematical proof that no
(non-trivial) dependence measure satisfies the definition of equitability
proposed by Reshef et al.. We then propose a self-consistent and more general
definition of equitability that follows naturally from the Data Processing
Inequality. Mutual information satisfies this new definition of equitability
while MIC does not. Finally, we show that the simulation evidence offered by
Reshef et al. was artifactual. We conclude that estimating mutual information
is not only practical for many real-world applications, but also provides a
natural solution to the problem of quantifying associations in large data sets
A Framework to Adjust Dependency Measure Estimates for Chance
Estimating the strength of dependency between two variables is fundamental
for exploratory analysis and many other applications in data mining. For
example: non-linear dependencies between two continuous variables can be
explored with the Maximal Information Coefficient (MIC); and categorical
variables that are dependent to the target class are selected using Gini gain
in random forests. Nonetheless, because dependency measures are estimated on
finite samples, the interpretability of their quantification and the accuracy
when ranking dependencies become challenging. Dependency estimates are not
equal to 0 when variables are independent, cannot be compared if computed on
different sample size, and they are inflated by chance on variables with more
categories. In this paper, we propose a framework to adjust dependency measure
estimates on finite samples. Our adjustments, which are simple and applicable
to any dependency measure, are helpful in improving interpretability when
quantifying dependency and in improving accuracy on the task of ranking
dependencies. In particular, we demonstrate that our approach enhances the
interpretability of MIC when used as a proxy for the amount of noise between
variables, and to gain accuracy when ranking variables during the splitting
procedure in random forests.Comment: In Proceedings of the 2016 SIAM International Conference on Data
Minin
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