66,223 research outputs found
A New Ensemble Learning Method for Temporal Pattern Identification
AbstractIn this paper we present a method for identification of temporal patterns predictive of significant events in a dynamic data system. A new hybrid model using Reconstructed Phase Space (MRPS) and Hidden Markov Model (HMM) is applied to identify temporal patterns. This method constructs phase space embedding by using individual embedding of each variable sequences. We also employ Hidden Markov Models (HMM) to the multivariate sequence data to categorize multi-dimensional data into three states, e.g. normal, patterns and events. A support vector machine optimization method is used to search an optimal classifier to identify temporal patterns that are predictive of future events. We performed two experimental applications using chaotic time series and natural gas usage series related to the natural gas usage forecasting problem. Experiments show that the new method significantly outperforms the original RPS framework and neural network method
Hyper-Spectral Image Analysis with Partially-Latent Regression and Spatial Markov Dependencies
Hyper-spectral data can be analyzed to recover physical properties at large
planetary scales. This involves resolving inverse problems which can be
addressed within machine learning, with the advantage that, once a relationship
between physical parameters and spectra has been established in a data-driven
fashion, the learned relationship can be used to estimate physical parameters
for new hyper-spectral observations. Within this framework, we propose a
spatially-constrained and partially-latent regression method which maps
high-dimensional inputs (hyper-spectral images) onto low-dimensional responses
(physical parameters such as the local chemical composition of the soil). The
proposed regression model comprises two key features. Firstly, it combines a
Gaussian mixture of locally-linear mappings (GLLiM) with a partially-latent
response model. While the former makes high-dimensional regression tractable,
the latter enables to deal with physical parameters that cannot be observed or,
more generally, with data contaminated by experimental artifacts that cannot be
explained with noise models. Secondly, spatial constraints are introduced in
the model through a Markov random field (MRF) prior which provides a spatial
structure to the Gaussian-mixture hidden variables. Experiments conducted on a
database composed of remotely sensed observations collected from the Mars
planet by the Mars Express orbiter demonstrate the effectiveness of the
proposed model.Comment: 12 pages, 4 figures, 3 table
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
Modeling and Classifying Six-Dimensional Trajectories for Teleoperation Under a Time Delay
Within the context of teleoperating the JSC Robonaut humanoid robot under 2-10 second time delays, this paper explores the technical problem of modeling and classifying human motions represented as six-dimensional (position and orientation) trajectories. A dual path research agenda is reviewed which explored both deterministic approaches and stochastic approaches using Hidden Markov Models. Finally, recent results are shown from a new model which represents the fusion of these two research paths. Questions are also raised about the possibility of automatically generating autonomous actions by reusing the same predictive models of human behavior to be the source of autonomous control. This approach changes the role of teleoperation from being a stand-in for autonomy into the first data collection step for developing generative models capable of autonomous control of the robot
Binary hidden Markov models and varieties
The technological applications of hidden Markov models have been extremely
diverse and successful, including natural language processing, gesture
recognition, gene sequencing, and Kalman filtering of physical measurements.
HMMs are highly non-linear statistical models, and just as linear models are
amenable to linear algebraic techniques, non-linear models are amenable to
commutative algebra and algebraic geometry.
This paper closely examines HMMs in which all the hidden random variables are
binary. Its main contributions are (1) a birational parametrization for every
such HMM, with an explicit inverse for recovering the hidden parameters in
terms of observables, (2) a semialgebraic model membership test for every such
HMM, and (3) minimal defining equations for the 4-node fully binary model,
comprising 21 quadrics and 29 cubics, which were computed using Grobner bases
in the cumulant coordinates of Sturmfels and Zwiernik. The new model parameters
in (1) are rationally identifiable in the sense of Sullivant, Garcia-Puente,
and Spielvogel, and each model's Zariski closure is therefore a rational
projective variety of dimension 5. Grobner basis computations for the model and
its graph are found to be considerably faster using these parameters. In the
case of two hidden states, item (2) supersedes a previous algorithm of
Schonhuth which is only generically defined, and the defining equations (3)
yield new invariants for HMMs of all lengths . Such invariants have
been used successfully in model selection problems in phylogenetics, and one
can hope for similar applications in the case of HMMs
- …