189 research outputs found
A Generative Model of Natural Texture Surrogates
Natural images can be viewed as patchworks of different textures, where the
local image statistics is roughly stationary within a small neighborhood but
otherwise varies from region to region. In order to model this variability, we
first applied the parametric texture algorithm of Portilla and Simoncelli to
image patches of 64X64 pixels in a large database of natural images such that
each image patch is then described by 655 texture parameters which specify
certain statistics, such as variances and covariances of wavelet coefficients
or coefficient magnitudes within that patch.
To model the statistics of these texture parameters, we then developed
suitable nonlinear transformations of the parameters that allowed us to fit
their joint statistics with a multivariate Gaussian distribution. We find that
the first 200 principal components contain more than 99% of the variance and
are sufficient to generate textures that are perceptually extremely close to
those generated with all 655 components. We demonstrate the usefulness of the
model in several ways: (1) We sample ensembles of texture patches that can be
directly compared to samples of patches from the natural image database and can
to a high degree reproduce their perceptual appearance. (2) We further
developed an image compression algorithm which generates surprisingly accurate
images at bit rates as low as 0.14 bits/pixel. Finally, (3) We demonstrate how
our approach can be used for an efficient and objective evaluation of samples
generated with probabilistic models of natural images.Comment: 34 pages, 9 figure
Breaking the waves: asymmetric random periodic features for low-bitrate kernel machines
Many signal processing and machine learning applications are built from
evaluating a kernel on pairs of signals, e.g. to assess the similarity of an
incoming query to a database of known signals. This nonlinear evaluation can be
simplified to a linear inner product of the random Fourier features of those
signals: random projections followed by a periodic map, the complex
exponential. It is known that a simple quantization of those features
(corresponding to replacing the complex exponential by a different periodic map
that takes binary values, which is appealing for their transmission and
storage), distorts the approximated kernel, which may be undesirable in
practice. Our take-home message is that when the features of only one of the
two signals are quantized, the original kernel is recovered without distortion;
its practical interest appears in several cases where the kernel evaluations
are asymmetric by nature, such as a client-server scheme. Concretely, we
introduce the general framework of asymmetric random periodic features, where
the two signals of interest are observed through random periodic features:
random projections followed by a general periodic map, which is allowed to be
different for both signals. We derive the influence of those periodic maps on
the approximated kernel, and prove uniform probabilistic error bounds holding
for all signal pairs from an infinite low-complexity set. Interestingly, our
results allow the periodic maps to be discontinuous, thanks to a new
mathematical tool, i.e. the mean Lipschitz smoothness. We then apply this
generic framework to semi-quantized kernel machines (where only one signal has
quantized features and the other has classical random Fourier features), for
which we show theoretically that the approximated kernel remains unchanged
(with the associated error bound), and confirm the power of the approach with
numerical simulations
The complexity of quantum support vector machines
Quantum support vector machines employ quantum circuits to define the kernel
function. It has been shown that this approach offers a provable exponential
speedup compared to any known classical algorithm for certain data sets. The
training of such models corresponds to solving a convex optimization problem
either via its primal or dual formulation. Due to the probabilistic nature of
quantum mechanics, the training algorithms are affected by statistical
uncertainty, which has a major impact on their complexity. We show that the
dual problem can be solved in quantum circuit
evaluations, where denotes the size of the data set and the
solution accuracy compared to the ideal result from exact expectation values,
which is only obtainable in theory. We prove under an empirically motivated
assumption that the kernelized primal problem can alternatively be solved in
evaluations by
employing a generalization of a known classical algorithm called Pegasos.
Accompanying empirical results demonstrate these analytical complexities to be
essentially tight. In addition, we investigate a variational approximation to
quantum support vector machines and show that their heuristic training achieves
considerably better scaling in our experiments.Comment: v2: published versio
Infusing Definiteness into Randomness: Rethinking Composition Styles for Deep Image Matting
We study the composition style in deep image matting, a notion that
characterizes a data generation flow on how to exploit limited foregrounds and
random backgrounds to form a training dataset. Prior art executes this flow in
a completely random manner by simply going through the foreground pool or by
optionally combining two foregrounds before foreground-background composition.
In this work, we first show that naive foreground combination can be
problematic and therefore derive an alternative formulation to reasonably
combine foregrounds. Our second contribution is an observation that matting
performance can benefit from a certain occurrence frequency of combined
foregrounds and their associated source foregrounds during training. Inspired
by this, we introduce a novel composition style that binds the source and
combined foregrounds in a definite triplet. In addition, we also find that
different orders of foreground combination lead to different foreground
patterns, which further inspires a quadruplet-based composition style. Results
under controlled experiments on four matting baselines show that our
composition styles outperform existing ones and invite consistent performance
improvement on both composited and real-world datasets. Code is available at:
https://github.com/coconuthust/composition_stylesComment: Accepted to AAAI 2023; 11 pages, 9 figures; Code is available at
https://github.com/coconuthust/composition_style
Diffusion in multiscale spacetimes
We study diffusion processes in anomalous spacetimes regarded as models of
quantum geometry. Several types of diffusion equation and their solutions are
presented and the associated stochastic processes are identified. These results
are partly based on the literature in probability and percolation theory but
their physical interpretation here is different since they apply to quantum
spacetime itself. The case of multiscale (in particular, multifractal)
spacetimes is then considered through a number of examples and the most general
spectral-dimension profile of multifractional spaces is constructed.Comment: 23 pages, 5 figures. v2: discussion improved, typos corrected,
references adde
Statistical Inference for Propagation Processes on Complex Networks
Die Methoden der Netzwerktheorie erfreuen sich wachsender Beliebtheit, da sie die Darstellung von komplexen Systemen durch Netzwerke erlauben. Diese werden nur mit einer Menge von Knoten erfasst, die durch Kanten verbunden werden. Derzeit verfügbare Methoden beschränken sich hauptsächlich auf die deskriptive Analyse der Netzwerkstruktur. In der hier vorliegenden Arbeit werden verschiedene Ansätze für die Inferenz über Prozessen in komplexen Netzwerken vorgestellt. Diese Prozesse beeinflussen messbare Größen in Netzwerkknoten und werden durch eine Menge von Zufallszahlen beschrieben. Alle vorgestellten Methoden sind durch praktische Anwendungen motiviert, wie die Übertragung von Lebensmittelinfektionen, die Verbreitung von Zugverspätungen, oder auch die Regulierung von genetischen Effekten. Zunächst wird ein allgemeines dynamisches Metapopulationsmodell für die Verbreitung von Lebensmittelinfektionen vorgestellt, welches die lokalen Infektionsdynamiken mit den netzwerkbasierten Transportwegen von kontaminierten Lebensmitteln zusammenführt. Dieses Modell ermöglicht die effiziente Simulationen verschiedener realistischer Lebensmittelinfektionsepidemien. Zweitens wird ein explorativer Ansatz zur Ursprungsbestimmung von Verbreitungsprozessen entwickelt. Auf Grundlage einer netzwerkbasierten Redefinition der geodätischen Distanz können komplexe Verbreitungsmuster in ein systematisches, kreisrundes Ausbreitungsschema projiziert werden. Dies gilt genau dann, wenn der Ursprungsnetzwerkknoten als Bezugspunkt gewählt wird. Die Methode wird erfolgreich auf den EHEC/HUS Epidemie 2011 in Deutschland angewandt. Die Ergebnisse legen nahe, dass die Methode die aufwändigen Standarduntersuchungen bei Lebensmittelinfektionsepidemien sinnvoll ergänzen kann. Zudem kann dieser explorative Ansatz zur Identifikation von Ursprungsverspätungen in Transportnetzwerken angewandt werden. Die Ergebnisse von umfangreichen Simulationsstudien mit verschiedenstensten Übertragungsmechanismen lassen auf eine allgemeine Anwendbarkeit des Ansatzes bei der Ursprungsbestimmung von Verbreitungsprozessen in vielfältigen Bereichen hoffen. Schließlich wird gezeigt, dass kernelbasierte Methoden eine Alternative für die statistische Analyse von Prozessen in Netzwerken darstellen können. Es wurde ein netzwerkbasierter Kern für den logistischen Kernel Machine Test entwickelt, welcher die nahtlose Integration von biologischem Wissen in die Analyse von Daten aus genomweiten Assoziationsstudien erlaubt. Die Methode wird erfolgreich bei der Analyse genetischer Ursachen für rheumatische Arthritis und Lungenkrebs getestet. Zusammenfassend machen die Ergebnisse der vorgestellten Methoden deutlich, dass die Netzwerk-theoretische Analyse von Verbreitungsprozessen einen wesentlichen Beitrag zur Beantwortung verschiedenster Fragestellungen in unterschiedlichen Anwendungen liefern kann
Resource optimization of edge servers dealing with priority-based workloads by utilizing service level objective-aware virtual rebalancing
IoT enables profitable communication between sensor/actuator devices and the cloud. Slow network causing Edge data to lack Cloud analytics hinders real-time analytics adoption. VRebalance solves priority-based workload performance for stream processing at the Edge. BO is used in VRebalance to prioritize workloads and find optimal resource configurations for efficient resource management. Apache Storm platform was used with RIoTBench IoT benchmark tool for real-time stream processing. Tools were used to evaluate VRebalance. Study shows VRebalance is more effective than traditional methods, meeting SLO targets despite system changes. VRebalance decreased SLO violation rates by almost 30% for static priority-based workloads and 52.2% for dynamic priority-based workloads compared to hill climbing algorithm. Using VRebalance decreased SLO violations by 66.1% compared to Apache Storm\u27s default allocation
Machine learning at the atomic-scale
Statistical learning algorithms are finding more and more applications in
science and technology. Atomic-scale modeling is no exception, with machine
learning becoming commonplace as a tool to predict energy, forces and
properties of molecules and condensed-phase systems. This short review
summarizes recent progress in the field, focusing in particular on the problem
of representing an atomic configuration in a mathematically robust and
computationally efficient way. We also discuss some of the regression
algorithms that have been used to construct surrogate models of atomic-scale
properties. We then show examples of how the optimization of the
machine-learning models can both incorporate and reveal insights onto the
physical phenomena that underlie structure-property relations
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