84,431 research outputs found
On the Inability of Markov Models to Capture Criticality in Human Mobility
We examine the non-Markovian nature of human mobility by exposing the
inability of Markov models to capture criticality in human mobility. In
particular, the assumed Markovian nature of mobility was used to establish a
theoretical upper bound on the predictability of human mobility (expressed as a
minimum error probability limit), based on temporally correlated entropy. Since
its inception, this bound has been widely used and empirically validated using
Markov chains. We show that recurrent-neural architectures can achieve
significantly higher predictability, surpassing this widely used upper bound.
In order to explain this anomaly, we shed light on several underlying
assumptions in previous research works that has resulted in this bias. By
evaluating the mobility predictability on real-world datasets, we show that
human mobility exhibits scale-invariant long-range correlations, bearing
similarity to a power-law decay. This is in contrast to the initial assumption
that human mobility follows an exponential decay. This assumption of
exponential decay coupled with Lempel-Ziv compression in computing Fano's
inequality has led to an inaccurate estimation of the predictability upper
bound. We show that this approach inflates the entropy, consequently lowering
the upper bound on human mobility predictability. We finally highlight that
this approach tends to overlook long-range correlations in human mobility. This
explains why recurrent-neural architectures that are designed to handle
long-range structural correlations surpass the previously computed upper bound
on mobility predictability
Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems
Handwritten digit recognition by bio-inspired hierarchical networks
The human brain processes information showing learning and prediction
abilities but the underlying neuronal mechanisms still remain unknown.
Recently, many studies prove that neuronal networks are able of both
generalizations and associations of sensory inputs. In this paper, following a
set of neurophysiological evidences, we propose a learning framework with a
strong biological plausibility that mimics prominent functions of cortical
circuitries. We developed the Inductive Conceptual Network (ICN), that is a
hierarchical bio-inspired network, able to learn invariant patterns by
Variable-order Markov Models implemented in its nodes. The outputs of the
top-most node of ICN hierarchy, representing the highest input generalization,
allow for automatic classification of inputs. We found that the ICN clusterized
MNIST images with an error of 5.73% and USPS images with an error of 12.56%
Tandem: A Context-Aware Method for Spontaneous Clustering of Dynamic Wireless Sensor Nodes
Wireless sensor nodes attached to everyday objects and worn by people are able to collaborate and actively assist users in their activities. We propose a method through which wireless sensor nodes organize spontaneously into clusters based on a common context. Provided that the confidence of sharing a common context varies in time, the algorithm takes into account a window-based history of believes. We approximate the behaviour of the algorithm using a Markov chain model and we analyse theoretically the cluster stability. We compare the theoretical approximation with simulations, by making use of experimental results reported from field tests. We show the tradeoff between the time history necessary to achieve a certain stability and the responsiveness of the clustering algorithm
Spectral Estimation of Conditional Random Graph Models for Large-Scale Network Data
Generative models for graphs have been typically committed to strong prior
assumptions concerning the form of the modeled distributions. Moreover, the
vast majority of currently available models are either only suitable for
characterizing some particular network properties (such as degree distribution
or clustering coefficient), or they are aimed at estimating joint probability
distributions, which is often intractable in large-scale networks. In this
paper, we first propose a novel network statistic, based on the Laplacian
spectrum of graphs, which allows to dispense with any parametric assumption
concerning the modeled network properties. Second, we use the defined statistic
to develop the Fiedler random graph model, switching the focus from the
estimation of joint probability distributions to a more tractable conditional
estimation setting. After analyzing the dependence structure characterizing
Fiedler random graphs, we evaluate them experimentally in edge prediction over
several real-world networks, showing that they allow to reach a much higher
prediction accuracy than various alternative statistical models.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
A two-level Markov model for packet loss in UDP/IP-based real-time video applications targeting residential users
The packet loss characteristics of Internet paths that include residential broadband links are not well understood, and there are no good models for their behaviour. This compli- cates the design of real-time video applications targeting home users, since it is difficult to choose appropriate error correction and concealment algorithms without a good model for the types of loss observed. Using measurements of residential broadband networks in the UK and Finland, we show that existing models for packet loss, such as the Gilbert model and simple hidden Markov models, do not effectively model the loss patterns seen in this environment. We present a new two-level Markov model for packet loss that can more accurately describe the characteristics of these links, and quantify the effectiveness of this model. We demonstrate that our new packet loss model allows for improved application design, by using it to model the performance of forward error correction on such links
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