35,490 research outputs found
Lasso Estimation of an Interval-Valued Multiple Regression Model
A multiple interval-valued linear regression model considering all the
cross-relationships between the mids and spreads of the intervals has been
introduced recently. A least-squares estimation of the regression parameters
has been carried out by transforming a quadratic optimization problem with
inequality constraints into a linear complementary problem and using Lemke's
algorithm to solve it. Due to the irrelevance of certain cross-relationships,
an alternative estimation process, the LASSO (Least Absolut Shrinkage and
Selection Operator), is developed. A comparative study showing the differences
between the proposed estimators is provided
Linear regression for numeric symbolic variables: an ordinary least squares approach based on Wasserstein Distance
In this paper we present a linear regression model for modal symbolic data.
The observed variables are histogram variables according to the definition
given in the framework of Symbolic Data Analysis and the parameters of the
model are estimated using the classic Least Squares method. An appropriate
metric is introduced in order to measure the error between the observed and the
predicted distributions. In particular, the Wasserstein distance is proposed.
Some properties of such metric are exploited to predict the response variable
as direct linear combination of other independent histogram variables. Measures
of goodness of fit are discussed. An application on real data corroborates the
proposed method
Parametric Regression on the Grassmannian
We address the problem of fitting parametric curves on the Grassmann manifold
for the purpose of intrinsic parametric regression. As customary in the
literature, we start from the energy minimization formulation of linear
least-squares in Euclidean spaces and generalize this concept to general
nonflat Riemannian manifolds, following an optimal-control point of view. We
then specialize this idea to the Grassmann manifold and demonstrate that it
yields a simple, extensible and easy-to-implement solution to the parametric
regression problem. In fact, it allows us to extend the basic geodesic model to
(1) a time-warped variant and (2) cubic splines. We demonstrate the utility of
the proposed solution on different vision problems, such as shape regression as
a function of age, traffic-speed estimation and crowd-counting from
surveillance video clips. Most notably, these problems can be conveniently
solved within the same framework without any specifically-tailored steps along
the processing pipeline.Comment: 14 pages, 11 figure
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