18,251 research outputs found
Estimating Local Function Complexity via Mixture of Gaussian Processes
Real world data often exhibit inhomogeneity, e.g., the noise level, the
sampling distribution or the complexity of the target function may change over
the input space. In this paper, we try to isolate local function complexity in
a practical, robust way. This is achieved by first estimating the locally
optimal kernel bandwidth as a functional relationship. Specifically, we propose
Spatially Adaptive Bandwidth Estimation in Regression (SABER), which employs
the mixture of experts consisting of multinomial kernel logistic regression as
a gate and Gaussian process regression models as experts. Using the locally
optimal kernel bandwidths, we deduce an estimate to the local function
complexity by drawing parallels to the theory of locally linear smoothing. We
demonstrate the usefulness of local function complexity for model
interpretation and active learning in quantum chemistry experiments and fluid
dynamics simulations.Comment: 19 pages, 16 figure
Parameter estimation and model testing for Markov processes via conditional characteristic functions
Markov processes are used in a wide range of disciplines, including finance.
The transition densities of these processes are often unknown. However, the
conditional characteristic functions are more likely to be available,
especially for L\'{e}vy-driven processes. We propose an empirical likelihood
approach, for both parameter estimation and model specification testing, based
on the conditional characteristic function for processes with either continuous
or discontinuous sample paths. Theoretical properties of the empirical
likelihood estimator for parameters and a smoothed empirical likelihood ratio
test for a parametric specification of the process are provided. Simulations
and empirical case studies are carried out to confirm the effectiveness of the
proposed estimator and test.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ400 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Nonparametric inference of doubly stochastic Poisson process data via the kernel method
Doubly stochastic Poisson processes, also known as the Cox processes,
frequently occur in various scientific fields. In this article, motivated
primarily by analyzing Cox process data in biophysics, we propose a
nonparametric kernel-based inference method. We conduct a detailed study,
including an asymptotic analysis, of the proposed method, and provide
guidelines for its practical use, introducing a fast and stable regression
method for bandwidth selection. We apply our method to real photon arrival data
from recent single-molecule biophysical experiments, investigating proteins'
conformational dynamics. Our result shows that conformational fluctuation is
widely present in protein systems, and that the fluctuation covers a broad
range of time scales, highlighting the dynamic and complex nature of proteins'
structure.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS352 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction
We introduce 'mixed LICORS', an algorithm for learning nonlinear,
high-dimensional dynamics from spatio-temporal data, suitable for both
prediction and simulation. Mixed LICORS extends the recent LICORS algorithm
(Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a
non-parametric, EM-like soft clustering. This retains the asymptotic predictive
optimality of LICORS, but, as we show in simulations, greatly improves
out-of-sample forecasts with limited data. The new method is implemented in the
publicly-available R package "LICORS"
(http://cran.r-project.org/web/packages/LICORS/).Comment: 11 pages; AISTATS 201
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