4,457 research outputs found
Coupling geometry on binary bipartite networks: hypotheses testing on pattern geometry and nestedness
Upon a matrix representation of a binary bipartite network, via the
permutation invariance, a coupling geometry is computed to approximate the
minimum energy macrostate of a network's system. Such a macrostate is supposed
to constitute the intrinsic structures of the system, so that the coupling
geometry should be taken as information contents, or even the nonparametric
minimum sufficient statistics of the network data. Then pertinent null and
alternative hypotheses, such as nestedness, are to be formulated according to
the macrostate. That is, any efficient testing statistic needs to be a function
of this coupling geometry. These conceptual architectures and mechanisms are by
and large still missing in community ecology literature, and rendered
misconceptions prevalent in this research area. Here the algorithmically
computed coupling geometry is shown consisting of deterministic multiscale
block patterns, which are framed by two marginal ultrametric trees on row and
column axes, and stochastic uniform randomness within each block found on the
finest scale. Functionally a series of increasingly larger ensembles of matrix
mimicries is derived by conforming to the multiscale block configurations. Here
matrix mimicking is meant to be subject to constraints of row and column sums
sequences. Based on such a series of ensembles, a profile of distributions
becomes a natural device for checking the validity of testing statistics or
structural indexes. An energy based index is used for testing whether network
data indeed contains structural geometry. A new version block-based nestedness
index is also proposed. Its validity is checked and compared with the existing
ones. A computing paradigm, called Data Mechanics, and its application on one
real data network are illustrated throughout the developments and discussions
in this paper
A Time Series Model of Multiple Structural changes in Level, Trend and Variance
We consider a deterministically trending dynamic time series model in which multiple changes in level, trend and error variance are modeled explicitly and the number but not the timing of the changes are known. Estimation of the model is made possible by the use of the Gibbs sampler. The determination of the number of structural breaks and the form of structural change is considered as a problem of model selection and we compare the use of marginal likelihoods, posterior odds ratios and Schwarz' BIC model selection criterion to select the most appropriate model from the data. We evaluate the efficacy of the Bayesian approach using a small Monte Carlo experiment. As empirical examples, we investigate structural changes in the U.S. ex-post real interest rate and in a long time series of U.S. GDP.BIC, Gibbs sampling, multiple structural changes, posterior odds ratio
Maximal inequality of Stochastic convolution driven by compensated Poisson random measures in Banach spaces
Let be a Banach space such that, for some , the
function is of class and its first and second
Fr\'{e}chet derivatives are bounded by some constant multiples of -th
power of the norm and -th power of the norm and let be a
-semigroup of contraction type on . We consider the
following stochastic convolution process \begin{align*}
u(t)=\int_0^t\int_ZS(t-s)\xi(s,z)\,\tilde{N}(\mathrm{d} s,\mathrm{d} z), \;\;\;
t\geq 0, \end{align*} where is a compensated Poisson random measure
on a measurable space and is an -predictable function. We
prove that there exists a c\`{a}dl\`{a}g modification a of the
process which satisfies the following maximal inequality \begin{align*}
\mathbb{E} \sup_{0\leq s\leq t} \|\tilde{u}(s)\|^{q^\prime}\leq C\ \mathbb{E}
\left(\int_0^t\int_Z \|\xi(s,z) \|^{p}\,N(\mathrm{d} s,\mathrm{d}
z)\right)^{\frac{q^\prime}{p}}, \end{align*} for all and
with .Comment: This version is only very slightly updated as compared to the one
from September 201
Deep Anchored Convolutional Neural Networks
Convolutional Neural Networks (CNNs) have been proven to be extremely
successful at solving computer vision tasks. State-of-the-art methods favor
such deep network architectures for its accuracy performance, with the cost of
having massive number of parameters and high weights redundancy. Previous works
have studied how to prune such CNNs weights. In this paper, we go to another
extreme and analyze the performance of a network stacked with a single
convolution kernel across layers, as well as other weights sharing techniques.
We name it Deep Anchored Convolutional Neural Network (DACNN). Sharing the same
kernel weights across layers allows to reduce the model size tremendously, more
precisely, the network is compressed in memory by a factor of L, where L is the
desired depth of the network, disregarding the fully connected layer for
prediction. The number of parameters in DACNN barely increases as the network
grows deeper, which allows us to build deep DACNNs without any concern about
memory costs. We also introduce a partial shared weights network (DACNN-mix) as
well as an easy-plug-in module, coined regulators, to boost the performance of
our architecture. We validated our idea on 3 datasets: CIFAR-10, CIFAR-100 and
SVHN. Our results show that we can save massive amounts of memory with our
model, while maintaining a high accuracy performance.Comment: This paper is accepted to 2019 IEEE/CVF Conference on Computer Vision
and Pattern Recognition Workshops (CVPRW
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