7,318 research outputs found
MDL Denoising Revisited
We refine and extend an earlier MDL denoising criterion for wavelet-based
denoising. We start by showing that the denoising problem can be reformulated
as a clustering problem, where the goal is to obtain separate clusters for
informative and non-informative wavelet coefficients, respectively. This
suggests two refinements, adding a code-length for the model index, and
extending the model in order to account for subband-dependent coefficient
distributions. A third refinement is derivation of soft thresholding inspired
by predictive universal coding with weighted mixtures. We propose a practical
method incorporating all three refinements, which is shown to achieve good
performance and robustness in denoising both artificial and natural signals.Comment: Submitted to IEEE Transactions on Information Theory, June 200
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition
We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS)
to regression with functional response. This allows us to simultaneously model
point-wise mean curves, variances and other distributional parameters of the
response in dependence of various scalar and functional covariate effects. In
addition, the scope of distributions is extended beyond exponential families.
The model is fitted via gradient boosting, which offers inherent model
selection and is shown to be suitable for both complex model structures and
highly auto-correlated response curves. This enables us to analyze bacterial
growth in \textit{Escherichia coli} in a complex interaction scenario,
fruitfully extending usual growth models.Comment: bootstrap confidence interval type uncertainty bounds added; minor
changes in formulation
Stochastic collocation on unstructured multivariate meshes
Collocation has become a standard tool for approximation of parameterized
systems in the uncertainty quantification (UQ) community. Techniques for
least-squares regularization, compressive sampling recovery, and interpolatory
reconstruction are becoming standard tools used in a variety of applications.
Selection of a collocation mesh is frequently a challenge, but methods that
construct geometrically "unstructured" collocation meshes have shown great
potential due to attractive theoretical properties and direct, simple
generation and implementation. We investigate properties of these meshes,
presenting stability and accuracy results that can be used as guides for
generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure
Efficient importance sampling for ML estimation of SCD models
The evaluation of the likelihood function of the stochastic conditional duration model requires to compute an integral that has the dimension of the sample size. We apply the efficient importance sampling method for computing this integral. We compare EIS-based ML estimation with QML estimation based on the Kalman filter. We find that EIS-ML estimation is more precise statistically, at a cost of an acceptable loss of quickness of computations. We illustrate this with simulated and real data. We show also that the EIS-ML method is easy to apply to extensions of the SCD model.Stochastic conditional duration, importance sampling
- …