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This note considers an n-letter alphabet in which the ith letter is accessed with probability p_i. The problem is to design efficient algorithm for constructing near-optimal, depth-constrained Huffman...
Spatial Depth-Based Classification for Functional Data
Functional depths Functional outliers Spatial functional depth Supervised func-tional classification
2013/6/14
We enlarge the available number of functional depths by defining two new depth measures for curves. Both depths are based on a spatial approach: the functional spatial depth (FSD), that shows an inter...
Universal Approximation Depth and Errors of Narrow Belief Networks with Discrete Units
Deep belief network restricted Boltzmann machine universal approxima-tion representational power Kullback-Leibler divergence,q-ary variable
2013/4/28
We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily ...
Depth statistics
Depth statistics
2012/9/19
In 1975 John Tukey proposed a multivariate median which is the ‘deepest’ point in a given data cloud in Rd(Tukey, 1975). In measuring the depth of an arbitrary pointzwith respect to the data, he consi...
Fast nonparametric classification based on data depth
Alpha-procedure zonoid depth DD-plot pattern recog-nition supervised learning, misclassification rate
2012/9/19
A new procedure, calledDDα-procedure, is developed to solve the problem of classifyingd-dimensional objects into q≥2 classes. The pro-cedure is completely nonparametric; it usesq-dimensional depth plo...
General notions of depth for functional data
Multivariate functional depth central regions trimmed regions -depth graph depth location-slope depth grid depth principal component depth
2012/9/17
A data depth measures the centrality of a point with respect to an empirical distribution. Postulates are formulated, which a depth for functional data should satisfy, and a general approach is propos...
Multivariate quantiles and multiple-output regression quantiles：From L1 optimization to halfspace depth
Multivariate quantile quantile regression halfspace depth
2010/3/10
A new multivariate concept of quantile, based on a directional
version of Koenker and Bassett’s traditional regression quantiles, is
introduced for multivariate location and multiple-output regressi...
Discussion of “Multivariate quantiles and multiple-output regression quantiles：From L1 optimization to halfspace depth”
Multivariate quantiles multiple-output regression quantiles L1 optimization halfspace depth
2010/3/10
First I would like to congratulate the authors for developing a new concept
of directional quantile contours. The work will contribute well to the pursuit
of multivariate quantiles. The multiple out...
The Two Step Selection Interview: Combining Standardisation with Depth
step selection interview standardisation depth
2009/4/27
In interviewing in the hiring of personnel has recently been reassessed. Formerly, interview techniques were criticised as being unreliable and invalid. Now, meta analysis indicates that a structured ...
Spatial medians，depth functions and multivariate Jensen's inequality
Spatial medians depth functions multivariate Jensen's inequality
2010/4/26
Spatial medians，depth functions and multivariate Jensen's inequality。
The random Tukey depth
Random Tukey depth one-dimensional projections multidimen-sional data functional data homogeneity test
2010/4/30
The computation of the Tukey depth, also called halfspace depth, is very demanding, even in low
dimensional spaces, because it requires the consideration of all possible one-dimensional projections.I...
Multidimensional trimming based on projection depth
Projection depth depth regions directional radius multivariatetrimmed means influence function breakdown point
2010/4/26
As estimators of location parameters, univariate trimmed means
are well known for their robustness and efficiency. They can serve
as robust alternatives to the sample mean while possessing high effi...