6,573 research outputs found
Segregating Event Streams and Noise with a Markov Renewal Process Model
DS and MP are supported by EPSRC Leadership Fellowship EP/G007144/1
Learning scalable and transferable multi-robot/machine sequential assignment planning via graph embedding
Can the success of reinforcement learning methods for simple combinatorial
optimization problems be extended to multi-robot sequential assignment
planning? In addition to the challenge of achieving near-optimal performance in
large problems, transferability to an unseen number of robots and tasks is
another key challenge for real-world applications. In this paper, we suggest a
method that achieves the first success in both challenges for robot/machine
scheduling problems.
Our method comprises of three components. First, we show a robot scheduling
problem can be expressed as a random probabilistic graphical model (PGM). We
develop a mean-field inference method for random PGM and use it for Q-function
inference. Second, we show that transferability can be achieved by carefully
designing two-step sequential encoding of problem state. Third, we resolve the
computational scalability issue of fitted Q-iteration by suggesting a heuristic
auction-based Q-iteration fitting method enabled by transferability we
achieved.
We apply our method to discrete-time, discrete space problems (Multi-Robot
Reward Collection (MRRC)) and scalably achieve 97% optimality with
transferability. This optimality is maintained under stochastic contexts. By
extending our method to continuous time, continuous space formulation, we claim
to be the first learning-based method with scalable performance among
multi-machine scheduling problems; our method scalability achieves comparable
performance to popular metaheuristics in Identical parallel machine scheduling
(IPMS) problems
Adaptive probability scheme for behaviour monitoring of the elderly using a specialised ambient device
A Hidden Markov Model (HMM) modified to work in combination with a Fuzzy System is utilised to determine the current behavioural state of the user from information obtained with specialised hardware. Due to the high dimensionality and not-linearly-separable nature of the Fuzzy System and the sensor data obtained with the hardware which informs the state decision, a new method is devised to update the HMM and replace the initial Fuzzy System such that subsequent state decisions are based on the most recent information. The resultant system first reduces the dimensionality of the original information by using a manifold representation in the high dimension which is unfolded in the lower dimension. The data is then linearly separable in the lower dimension where a simple linear classifier, such as the perceptron used here, is applied to determine the probability of the observations belonging to a state. Experiments using the new system verify its applicability in a real scenario
Hierarchical relational models for document networks
We develop the relational topic model (RTM), a hierarchical model of both
network structure and node attributes. We focus on document networks, where the
attributes of each document are its words, that is, discrete observations taken
from a fixed vocabulary. For each pair of documents, the RTM models their link
as a binary random variable that is conditioned on their contents. The model
can be used to summarize a network of documents, predict links between them,
and predict words within them. We derive efficient inference and estimation
algorithms based on variational methods that take advantage of sparsity and
scale with the number of links. We evaluate the predictive performance of the
RTM for large networks of scientific abstracts, web documents, and
geographically tagged news.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS309 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
IMPROVED MULTIPLE BIRDSONG TRACKING WITH DISTRIBUTION DERIVATIVE METHOD AND MARKOV RENEWAL PROCESS CLUSTERING
DS & MP are supported by an EPSRC Leadership Fellowship EP/G007144/1
The Mathematics of Phylogenomics
The grand challenges in biology today are being shaped by powerful
high-throughput technologies that have revealed the genomes of many organisms,
global expression patterns of genes and detailed information about variation
within populations. We are therefore able to ask, for the first time,
fundamental questions about the evolution of genomes, the structure of genes
and their regulation, and the connections between genotypes and phenotypes of
individuals. The answers to these questions are all predicated on progress in a
variety of computational, statistical, and mathematical fields.
The rapid growth in the characterization of genomes has led to the
advancement of a new discipline called Phylogenomics. This discipline results
from the combination of two major fields in the life sciences: Genomics, i.e.,
the study of the function and structure of genes and genomes; and Molecular
Phylogenetics, i.e., the study of the hierarchical evolutionary relationships
among organisms and their genomes. The objective of this article is to offer
mathematicians a first introduction to this emerging field, and to discuss
specific mathematical problems and developments arising from phylogenomics.Comment: 41 pages, 4 figure
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