2,053 research outputs found
Smart random walkers: the cost of knowing the path
In this work we study the problem of targeting signals in networks using
entropy information measurements to quantify the cost of targeting. We
introduce a penalization rule that imposes a restriction to the long paths and
therefore focus the signal to the target. By this scheme we go continuously
from fully random walkers to walkers biased to the target. We found that the
optimal degree of penalization is mainly determined by the topology of the
network. By analyzing several examples, we have found that a small amount of
penalization reduces considerably the typical walk length, and from this we
conclude that a network can be efficiently navigated with restricted
information.Comment: 9 pages, 11 figure
A note on the evaluation of generative models
Probabilistic generative models can be used for compression, denoising,
inpainting, texture synthesis, semi-supervised learning, unsupervised feature
learning, and other tasks. Given this wide range of applications, it is not
surprising that a lot of heterogeneity exists in the way these models are
formulated, trained, and evaluated. As a consequence, direct comparison between
models is often difficult. This article reviews mostly known but often
underappreciated properties relating to the evaluation and interpretation of
generative models with a focus on image models. In particular, we show that
three of the currently most commonly used criteria---average log-likelihood,
Parzen window estimates, and visual fidelity of samples---are largely
independent of each other when the data is high-dimensional. Good performance
with respect to one criterion therefore need not imply good performance with
respect to the other criteria. Our results show that extrapolation from one
criterion to another is not warranted and generative models need to be
evaluated directly with respect to the application(s) they were intended for.
In addition, we provide examples demonstrating that Parzen window estimates
should generally be avoided
Nonlinear time-series analysis revisited
In 1980 and 1981, two pioneering papers laid the foundation for what became
known as nonlinear time-series analysis: the analysis of observed
data---typically univariate---via dynamical systems theory. Based on the
concept of state-space reconstruction, this set of methods allows us to compute
characteristic quantities such as Lyapunov exponents and fractal dimensions, to
predict the future course of the time series, and even to reconstruct the
equations of motion in some cases. In practice, however, there are a number of
issues that restrict the power of this approach: whether the signal accurately
and thoroughly samples the dynamics, for instance, and whether it contains
noise. Moreover, the numerical algorithms that we use to instantiate these
ideas are not perfect; they involve approximations, scale parameters, and
finite-precision arithmetic, among other things. Even so, nonlinear time-series
analysis has been used to great advantage on thousands of real and synthetic
data sets from a wide variety of systems ranging from roulette wheels to lasers
to the human heart. Even in cases where the data do not meet the mathematical
or algorithmic requirements to assure full topological conjugacy, the results
of nonlinear time-series analysis can be helpful in understanding,
characterizing, and predicting dynamical systems
Entropy-based parametric estimation of spike train statistics
We consider the evolution of a network of neurons, focusing on the asymptotic
behavior of spikes dynamics instead of membrane potential dynamics. The spike
response is not sought as a deterministic response in this context, but as a
conditional probability : "Reading out the code" consists of inferring such a
probability. This probability is computed from empirical raster plots, by using
the framework of thermodynamic formalism in ergodic theory. This gives us a
parametric statistical model where the probability has the form of a Gibbs
distribution. In this respect, this approach generalizes the seminal and
profound work of Schneidman and collaborators. A minimal presentation of the
formalism is reviewed here, while a general algorithmic estimation method is
proposed yielding fast convergent implementations. It is also made explicit how
several spike observables (entropy, rate, synchronizations, correlations) are
given in closed-form from the parametric estimation. This paradigm does not
only allow us to estimate the spike statistics, given a design choice, but also
to compare different models, thus answering comparative questions about the
neural code such as : "are correlations (or time synchrony or a given set of
spike patterns, ..) significant with respect to rate coding only ?" A numerical
validation of the method is proposed and the perspectives regarding spike-train
code analysis are also discussed.Comment: 37 pages, 8 figures, submitte
Anticipated climate and land-cover changes reveal refuge areas for Borneo's orang-utans
Habitat loss and climate change pose a double jeopardy for many threatened taxa, making the identification of optimal
habitat for the future a conservation priority. Using a case study of the endangered Bornean orang-utan, we identify
environmental refuges by integrating bioclimatic models with projected deforestation and oil-palm agriculture
suitability from the 1950s to 2080s. We coupled a maximum entropy algorithm with information on habitat needs to
predict suitable habitat for the present day and 1950s. We then projected to the 2020s, 2050s and 2080s in models
incorporating only land-cover change, climate change or both processes combined. For future climate, we incorporated
projections from four model and emission scenario combinations. For future land cover, we developed spatial
deforestation predictions from 10 years of satellite data. Refuges were delineated as suitable forested habitats identified
by all models that were also unsuitable for oil palm – a major threat to tropical biodiversity. Our analyses indicate
that in 2010 up to 260 000 km2 of Borneo was suitable habitat within the core orang-utan range; an 18–24%
reduction since the 1950s. Land-cover models predicted further decline of 15–30% by the 2080s. Although habitat
extent under future climate conditions varied among projections, there was majority consensus, particularly in northeastern
and western regions. Across projections habitat loss due to climate change alone averaged 63% by 2080, but
74% when also considering land-cover change. Refuge areas amounted to 2000–42 000 km2 depending on thresholds
used, with 900–17 000 km2 outside the current species range. We demonstrate that efforts to halt deforestation could
mediate some orang-utan habitat loss, but further decline of the most suitable areas is to be expected given projected
changes to climate. Protected refuge areas could therefore become increasingly important for ongoing translocation
efforts. We present an approach to help identify such areas for highly threatened species given environmental
changes expected this century
On the Use of Complexity Algorithms: a Cautionary Lesson from Climate Research
Complexity algorithms provide information about datasets which is radically different from classical moment statistics. Instead of focusing on the divergences from central values, they quantify other characteristics such as order, pattern repetitions, or the existence of attractors. However, those analyses must be done with the proper statistical treatment, which is, unfortunately, not always the case. In this contribution, I provide an example of the hazards of applying complexity measures without sufficient care by correcting a previously published analysis that aimed to quantify the complexity of climate. I clarify some misconceptions about the use of Sample Entropy and revise the incorrect assessments and conclusions drawn from the previous misapplication of the methods
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