111,557 research outputs found
Community detection and stochastic block models: recent developments
The stochastic block model (SBM) is a random graph model with planted
clusters. It is widely employed as a canonical model to study clustering and
community detection, and provides generally a fertile ground to study the
statistical and computational tradeoffs that arise in network and data
sciences.
This note surveys the recent developments that establish the fundamental
limits for community detection in the SBM, both with respect to
information-theoretic and computational thresholds, and for various recovery
requirements such as exact, partial and weak recovery (a.k.a., detection). The
main results discussed are the phase transitions for exact recovery at the
Chernoff-Hellinger threshold, the phase transition for weak recovery at the
Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial
recovery, the learning of the SBM parameters and the gap between
information-theoretic and computational thresholds.
The note also covers some of the algorithms developed in the quest of
achieving the limits, in particular two-round algorithms via graph-splitting,
semi-definite programming, linearized belief propagation, classical and
nonbacktracking spectral methods. A few open problems are also discussed
Data Analysis Challenges for the Einstein Telescope
The Einstein Telescope is a proposed third generation gravitational wave
detector that will operate in the region of 1 Hz to a few kHz. As well as the
inspiral of compact binaries composed of neutron stars or black holes, the
lower frequency cut-off of the detector will open the window to a number of new
sources. These will include the end stage of inspirals, plus merger and
ringdown of intermediate mass black holes, where the masses of the component
bodies are on the order of a few hundred solar masses. There is also the
possibility of observing intermediate mass ratio inspirals, where a stellar
mass compact object inspirals into a black hole which is a few hundred to a few
thousand times more massive. In this article, we investigate some of the data
analysis challenges for the Einstein Telescope such as the effects of increased
source number, the need for more accurate waveform models and the some of the
computational issues that a data analysis strategy might face.Comment: 18 pages, Invited review for Einstein Telescope special edition of
GR
Real-time human ambulation, activity, and physiological monitoring:taxonomy of issues, techniques, applications, challenges and limitations
Automated methods of real-time, unobtrusive, human ambulation, activity, and wellness monitoring and data analysis using various algorithmic techniques have been subjects of intense research. The general aim is to devise effective means of addressing the demands of assisted living, rehabilitation, and clinical observation and assessment through sensor-based monitoring. The research studies have resulted in a large amount of literature. This paper presents a holistic articulation of the research studies and offers comprehensive insights along four main axes: distribution of existing studies; monitoring device framework and sensor types; data collection, processing and analysis; and applications, limitations and challenges. The aim is to present a systematic and most complete study of literature in the area in order to identify research gaps and prioritize future research directions
Quality of Information in Mobile Crowdsensing: Survey and Research Challenges
Smartphones have become the most pervasive devices in people's lives, and are
clearly transforming the way we live and perceive technology. Today's
smartphones benefit from almost ubiquitous Internet connectivity and come
equipped with a plethora of inexpensive yet powerful embedded sensors, such as
accelerometer, gyroscope, microphone, and camera. This unique combination has
enabled revolutionary applications based on the mobile crowdsensing paradigm,
such as real-time road traffic monitoring, air and noise pollution, crime
control, and wildlife monitoring, just to name a few. Differently from prior
sensing paradigms, humans are now the primary actors of the sensing process,
since they become fundamental in retrieving reliable and up-to-date information
about the event being monitored. As humans may behave unreliably or
maliciously, assessing and guaranteeing Quality of Information (QoI) becomes
more important than ever. In this paper, we provide a new framework for
defining and enforcing the QoI in mobile crowdsensing, and analyze in depth the
current state-of-the-art on the topic. We also outline novel research
challenges, along with possible directions of future work.Comment: To appear in ACM Transactions on Sensor Networks (TOSN
Phase Transitions in Semidefinite Relaxations
Statistical inference problems arising within signal processing, data mining,
and machine learning naturally give rise to hard combinatorial optimization
problems. These problems become intractable when the dimensionality of the data
is large, as is often the case for modern datasets. A popular idea is to
construct convex relaxations of these combinatorial problems, which can be
solved efficiently for large scale datasets.
Semidefinite programming (SDP) relaxations are among the most powerful
methods in this family, and are surprisingly well-suited for a broad range of
problems where data take the form of matrices or graphs. It has been observed
several times that, when the `statistical noise' is small enough, SDP
relaxations correctly detect the underlying combinatorial structures.
In this paper we develop asymptotic predictions for several `detection
thresholds,' as well as for the estimation error above these thresholds. We
study some classical SDP relaxations for statistical problems motivated by
graph synchronization and community detection in networks. We map these
optimization problems to statistical mechanics models with vector spins, and
use non-rigorous techniques from statistical mechanics to characterize the
corresponding phase transitions. Our results clarify the effectiveness of SDP
relaxations in solving high-dimensional statistical problems.Comment: 71 pages, 24 pdf figure
- …