14,571 research outputs found
Optimization of the Asymptotic Property of Mutual Learning Involving an Integration Mechanism of Ensemble Learning
We propose an optimization method of mutual learning which converges into the
identical state of optimum ensemble learning within the framework of on-line
learning, and have analyzed its asymptotic property through the statistical
mechanics method.The proposed model consists of two learning steps: two
students independently learn from a teacher, and then the students learn from
each other through the mutual learning. In mutual learning, students learn from
each other and the generalization error is improved even if the teacher has not
taken part in the mutual learning. However, in the case of different initial
overlaps(direction cosine) between teacher and students, a student with a
larger initial overlap tends to have a larger generalization error than that of
before the mutual learning. To overcome this problem, our proposed optimization
method of mutual learning optimizes the step sizes of two students to minimize
the asymptotic property of the generalization error. Consequently, the
optimized mutual learning converges to a generalization error identical to that
of the optimal ensemble learning. In addition, we show the relationship between
the optimum step size of the mutual learning and the integration mechanism of
the ensemble learning.Comment: 13 pages, 3 figures, submitted to Journal of Physical Society of
Japa
Ensemble learning of linear perceptron; Online learning theory
Within the framework of on-line learning, we study the generalization error
of an ensemble learning machine learning from a linear teacher perceptron. The
generalization error achieved by an ensemble of linear perceptrons having
homogeneous or inhomogeneous initial weight vectors is precisely calculated at
the thermodynamic limit of a large number of input elements and shows rich
behavior. Our main findings are as follows. For learning with homogeneous
initial weight vectors, the generalization error using an infinite number of
linear student perceptrons is equal to only half that of a single linear
perceptron, and converges with that of the infinite case with O(1/K) for a
finite number of K linear perceptrons. For learning with inhomogeneous initial
weight vectors, it is advantageous to use an approach of weighted averaging
over the output of the linear perceptrons, and we show the conditions under
which the optimal weights are constant during the learning process. The optimal
weights depend on only correlation of the initial weight vectors.Comment: 14 pages, 3 figures, submitted to Physical Review
Statistical Mechanics of Nonlinear On-line Learning for Ensemble Teachers
We analyze the generalization performance of a student in a model composed of
nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We
calculate the generalization error of the student analytically or numerically
using statistical mechanics in the framework of on-line learning. We treat two
well-known learning rules: Hebbian learning and perceptron learning. As a
result, it is proven that the nonlinear model shows qualitatively different
behaviors from the linear model. Moreover, it is clarified that Hebbian
learning and perceptron learning show qualitatively different behaviors from
each other. In Hebbian learning, we can analytically obtain the solutions. In
this case, the generalization error monotonically decreases. The steady value
of the generalization error is independent of the learning rate. The larger the
number of teachers is and the more variety the ensemble teachers have, the
smaller the generalization error is. In perceptron learning, we have to
numerically obtain the solutions. In this case, the dynamical behaviors of the
generalization error are non-monotonic. The smaller the learning rate is, the
larger the number of teachers is; and the more variety the ensemble teachers
have, the smaller the minimum value of the generalization error is.Comment: 13 pages, 9 figure
Theoretical study of the (3x2) reconstruction of beta-SiC(001)
By means of ab initio molecular dynamics and band structure calculations, as
well as using calculated STM images, we have singled out one structural model
for the (3x2) reconstruction of the Si-terminated (001) surface of cubic SiC,
amongst several proposed in the literature. This is an alternate dimer-row
model, with an excess Si coverage of 1/3, yielding STM images in good accord
with recent measurements [F.Semond et al. Phys. Rev. Lett. 77, 2013 (1996)].Comment: To be published in PRB Rapid. Com
On balanced complementation for regular t-wise balanced designs
AbstractVanstone has shown a procedure, called r-complementation, to construct a regular pairwise balanced design from an existing regular pairwise balanced design. In this paper, we give a generalization of r-complementation, called balanced complementation. Necessary and sufficient conditions for balanced complementation which gives a regular t-wise balanced design from an existing regular t-wise balanced design are shown. We characterize those aspects of designs which permit balanced complementation. Results obtained here will be applied to construct regular t-wise balanced designs which are useful in Statistics
The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion
For independent nearest-neighbour bond percolation on Z^d with d >> 6, we
prove that the incipient infinite cluster's two-point function and three-point
function converge to those of integrated super-Brownian excursion (ISE) in the
scaling limit. The proof is based on an extension of the new expansion for
percolation derived in a previous paper, and involves treating the magnetic
field as a complex variable. A special case of our result for the two-point
function implies that the probability that the cluster of the origin consists
of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an
error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong
statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic,
and xr package
Statistical Mechanics of Time Domain Ensemble Learning
Conventional ensemble learning combines students in the space domain. On the
other hand, in this paper we combine students in the time domain and call it
time domain ensemble learning. In this paper, we analyze the generalization
performance of time domain ensemble learning in the framework of online
learning using a statistical mechanical method. We treat a model in which both
the teacher and the student are linear perceptrons with noises. Time domain
ensemble learning is twice as effective as conventional space domain ensemble
learning.Comment: 10 pages, 10 figure
Climate change amplifies plant invasion hotspots in Nepal
Aim
Climate change has increased the risk of biological invasions, particularly by increasing the climatically suitable regions for invasive alien species. The distribution of many native and invasive species has been predicted to change under future climate. We performed species distribution modelling of invasive alien plants (IAPs) to identify hotspots under current and future climate scenarios in Nepal, a country ranked among the most vulnerable countries to biological invasions and climate change in the world.
Location
Nepal.
Methods
We predicted climatically suitable niches of 24 out of the total 26 reported IAPs in Nepal under current and future climate (2050 for RCP 6.0) using an ensemble of species distribution models. We also conducted hotspot analysis to highlight the geographic hotspots for IAPs in different climatic zones, land cover, ecoregions, physiography and federal states.
Results
Under future climate, climatically suitable regions for 75% of IAPs will expand in contrast to a contraction of the climatically suitable regions for the remaining 25% of the IAPs. A high proportion of the modelled suitable niches of IAPs occurred on agricultural lands followed by forests. In aggregation, both extent and intensity (invasion hotspots) of the climatically suitable regions for IAPs will increase in Nepal under future climate scenarios. The invasion hotspots will expand towards the high‐elevation mountainous regions. In these regions, land use is rapidly transforming due to the development of infrastructure and expansion of tourism and trade.
Main conclusions
Negative impacts on livelihood, biodiversity and ecosystem services, as well as economic loss caused by IAPs in the future, may be amplified if preventive and control measures are not immediately initiated. Therefore, the management of IAPs in Nepal should account for the vulnerability of climate change‐induced biological invasions into new areas, primarily in the mountains
Statistical Mechanics of Linear and Nonlinear Time-Domain Ensemble Learning
Conventional ensemble learning combines students in the space domain. In this
paper, however, we combine students in the time domain and call it time-domain
ensemble learning. We analyze, compare, and discuss the generalization
performances regarding time-domain ensemble learning of both a linear model and
a nonlinear model. Analyzing in the framework of online learning using a
statistical mechanical method, we show the qualitatively different behaviors
between the two models. In a linear model, the dynamical behaviors of the
generalization error are monotonic. We analytically show that time-domain
ensemble learning is twice as effective as conventional ensemble learning.
Furthermore, the generalization error of a nonlinear model features
nonmonotonic dynamical behaviors when the learning rate is small. We
numerically show that the generalization performance can be improved remarkably
by using this phenomenon and the divergence of students in the time domain.Comment: 11 pages, 7 figure
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