4,372 research outputs found
Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series
The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.National Science Foundation (IIS 0308213, IIS 0329009, CNS 0202067
Four infinite families of chiral -polytopes of type with solvable automorphism groups
We construct four infinite families of chiral -polytopes of type , with , , and automorphisms for
every positive integer , respectively. The automorphism groups of these
polytopes are solvable groups, and when is a power of , they provide
examples with automorphism groups of order where . (On the
other hand, no chiral polytopes of type exist for .) In
particular, our families give a partial answer to a problem proposed by Schulte
and Weiss in [Problems on polytopes, their groups, and realizations, {\em
Period. Math. Hungar.} 53 (2006), 231-255] and a problem proposed by Pellicer
in [Developments and open problems on chiral polytopes, {\em Ars Math. Contemp}
5 (2012), 333-354].Comment: 11pges,1 figures. arXiv admin note: substantial text overlap with
arXiv:1912.0339
Nonparametric inference procedure for percentiles of the random effects distribution in meta-analysis
To investigate whether treating cancer patients with
erythropoiesis-stimulating agents (ESAs) would increase the mortality risk,
Bennett et al. [Journal of the American Medical Association 299 (2008)
914--924] conducted a meta-analysis with the data from 52 phase III trials
comparing ESAs with placebo or standard of care. With a standard parametric
random effects modeling approach, the study concluded that ESA administration
was significantly associated with increased average mortality risk. In this
article we present a simple nonparametric inference procedure for the
distribution of the random effects. We re-analyzed the ESA mortality data with
the new method. Our results about the center of the random effects distribution
were markedly different from those reported by Bennett et al. Moreover, our
procedure, which estimates the distribution of the random effects, as opposed
to just a simple population average, suggests that the ESA may be beneficial to
mortality for approximately a quarter of the study populations. This new
meta-analysis technique can be implemented with study-level summary statistics.
In contrast to existing methods for parametric random effects models, the
validity of our proposal does not require the number of studies involved to be
large. From the results of an extensive numerical study, we find that the new
procedure performs well even with moderate individual study sample sizes.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS280 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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