9,888 research outputs found
Optimal designs for rational function regression
We consider optimal non-sequential designs for a large class of (linear and
nonlinear) regression models involving polynomials and rational functions with
heteroscedastic noise also given by a polynomial or rational weight function.
The proposed method treats D-, E-, A-, and -optimal designs in a
unified manner, and generates a polynomial whose zeros are the support points
of the optimal approximate design, generalizing a number of previously known
results of the same flavor. The method is based on a mathematical optimization
model that can incorporate various criteria of optimality and can be solved
efficiently by well established numerical optimization methods. In contrast to
previous optimization-based methods proposed for similar design problems, it
also has theoretical guarantee of its algorithmic efficiency; in fact, the
running times of all numerical examples considered in the paper are negligible.
The stability of the method is demonstrated in an example involving high degree
polynomials. After discussing linear models, applications for finding locally
optimal designs for nonlinear regression models involving rational functions
are presented, then extensions to robust regression designs, and trigonometric
regression are shown. As a corollary, an upper bound on the size of the support
set of the minimally-supported optimal designs is also found. The method is of
considerable practical importance, with the potential for instance to impact
design software development. Further study of the optimality conditions of the
main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory
and additional example
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
Herding as a Learning System with Edge-of-Chaos Dynamics
Herding defines a deterministic dynamical system at the edge of chaos. It
generates a sequence of model states and parameters by alternating parameter
perturbations with state maximizations, where the sequence of states can be
interpreted as "samples" from an associated MRF model. Herding differs from
maximum likelihood estimation in that the sequence of parameters does not
converge to a fixed point and differs from an MCMC posterior sampling approach
in that the sequence of states is generated deterministically. Herding may be
interpreted as a"perturb and map" method where the parameter perturbations are
generated using a deterministic nonlinear dynamical system rather than randomly
from a Gumbel distribution. This chapter studies the distinct statistical
characteristics of the herding algorithm and shows that the fast convergence
rate of the controlled moments may be attributed to edge of chaos dynamics. The
herding algorithm can also be generalized to models with latent variables and
to a discriminative learning setting. The perceptron cycling theorem ensures
that the fast moment matching property is preserved in the more general
framework
Cultural Values and Cross-cultural Video Consumption on YouTube
Video-sharing social media like YouTube provide access to diverse cultural
products from all over the world, making it possible to test theories that the
Web facilitates global cultural convergence. Drawing on a daily listing of
YouTube's most popular videos across 58 countries, we investigate the
consumption of popular videos in countries that differ in cultural values,
language, gross domestic product, and Internet penetration rate. Although
online social media facilitate global access to cultural products, we find this
technological capability does not result in universal cultural convergence.
Instead, consumption of popular videos in culturally different countries
appears to be constrained by cultural values. Cross-cultural convergence is
more advanced in cosmopolitan countries with cultural values that favor
individualism and power inequality
Causal Inference through a Witness Protection Program
One of the most fundamental problems in causal inference is the estimation of
a causal effect when variables are confounded. This is difficult in an
observational study, because one has no direct evidence that all confounders
have been adjusted for. We introduce a novel approach for estimating causal
effects that exploits observational conditional independencies to suggest
"weak" paths in a unknown causal graph. The widely used faithfulness condition
of Spirtes et al. is relaxed to allow for varying degrees of "path
cancellations" that imply conditional independencies but do not rule out the
existence of confounding causal paths. The outcome is a posterior distribution
over bounds on the average causal effect via a linear programming approach and
Bayesian inference. We claim this approach should be used in regular practice
along with other default tools in observational studies.Comment: 41 pages, 7 figure
The remittances behaviour of the second generation in Europe: altruism or self-interest?
Whereas most research on remittances focuses on first-generation migrants, the aim of this paper is to investigate the remitting behaviour of the host country-born children of migrants - the second generation - in various European cities. Some important studies found that migrant transnationalism is not only a phenomenon for the first generation, but
also apply to the second and higher generations, through, among other things, family visits, elder care, and remittances. At the same time, the maintenance of a strong ethnic identity in the ‘host’ society does not necessarily mean that second-generation migrants have strong transnational ties to their ‘home’ country.
The data used in this paper is from “The Integration of the European Second Generation” (TIES) project. The survey collected information on approximately 6,250 individuals aged 18-35 with at least one migrant parent from Morocco, Turkey or former Yugoslavia, in 15 European cities, regrouped in 8 ‘countries’. For the purpose of this paper, only
analyses for Austria (Linz and Vienna); Switzerland (Basle and Zurich); Germany (Berlin and Frankfurt); France (Paris and Strasbourg); the Netherlands (Amsterdam and Rotterdam); Spain (Barcelona and Madrid); and Sweden (Stockholm) will be presented.
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