19,631 research outputs found
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
Cortical spatio-temporal dimensionality reduction for visual grouping
The visual systems of many mammals, including humans, is able to integrate
the geometric information of visual stimuli and to perform cognitive tasks
already at the first stages of the cortical processing. This is thought to be
the result of a combination of mechanisms, which include feature extraction at
single cell level and geometric processing by means of cells connectivity. We
present a geometric model of such connectivities in the space of detected
features associated to spatio-temporal visual stimuli, and show how they can be
used to obtain low-level object segmentation. The main idea is that of defining
a spectral clustering procedure with anisotropic affinities over datasets
consisting of embeddings of the visual stimuli into higher dimensional spaces.
Neural plausibility of the proposed arguments will be discussed
Event-based Vision: A Survey
Event cameras are bio-inspired sensors that differ from conventional frame
cameras: Instead of capturing images at a fixed rate, they asynchronously
measure per-pixel brightness changes, and output a stream of events that encode
the time, location and sign of the brightness changes. Event cameras offer
attractive properties compared to traditional cameras: high temporal resolution
(in the order of microseconds), very high dynamic range (140 dB vs. 60 dB), low
power consumption, and high pixel bandwidth (on the order of kHz) resulting in
reduced motion blur. Hence, event cameras have a large potential for robotics
and computer vision in challenging scenarios for traditional cameras, such as
low-latency, high speed, and high dynamic range. However, novel methods are
required to process the unconventional output of these sensors in order to
unlock their potential. This paper provides a comprehensive overview of the
emerging field of event-based vision, with a focus on the applications and the
algorithms developed to unlock the outstanding properties of event cameras. We
present event cameras from their working principle, the actual sensors that are
available and the tasks that they have been used for, from low-level vision
(feature detection and tracking, optic flow, etc.) to high-level vision
(reconstruction, segmentation, recognition). We also discuss the techniques
developed to process events, including learning-based techniques, as well as
specialized processors for these novel sensors, such as spiking neural
networks. Additionally, we highlight the challenges that remain to be tackled
and the opportunities that lie ahead in the search for a more efficient,
bio-inspired way for machines to perceive and interact with the world
25 Years of Self-Organized Criticality: Numerical Detection Methods
The detection and characterization of self-organized criticality (SOC), in
both real and simulated data, has undergone many significant revisions over the
past 25 years. The explosive advances in the many numerical methods available
for detecting, discriminating, and ultimately testing, SOC have played a
critical role in developing our understanding of how systems experience and
exhibit SOC. In this article, methods of detecting SOC are reviewed; from
correlations to complexity to critical quantities. A description of the basic
autocorrelation method leads into a detailed analysis of application-oriented
methods developed in the last 25 years. In the second half of this manuscript
space-based, time-based and spatial-temporal methods are reviewed and the
prevalence of power laws in nature is described, with an emphasis on event
detection and characterization. The search for numerical methods to clearly and
unambiguously detect SOC in data often leads us outside the comfort zone of our
own disciplines - the answers to these questions are often obtained by studying
the advances made in other fields of study. In addition, numerical detection
methods often provide the optimum link between simulations and experiments in
scientific research. We seek to explore this boundary where the rubber meets
the road, to review this expanding field of research of numerical detection of
SOC systems over the past 25 years, and to iterate forwards so as to provide
some foresight and guidance into developing breakthroughs in this subject over
the next quarter of a century.Comment: Space Science Review series on SO
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