94,514 research outputs found
Branch merging on continuum trees with applications to regenerative tree growth
We introduce a family of branch merging operations on continuum trees and
show that Ford CRTs are distributionally invariant. This operation is new even
in the special case of the Brownian CRT, which we explore in more detail. The
operations are based on spinal decompositions and a regenerativity preserving
merging procedure of -strings of beads, that is, random
intervals equipped with a random discrete measure
arising in the limit of ordered -Chinese restaurant
processes as introduced recently by Pitman and Winkel. Indeed, we iterate the
branch merging operation recursively and give an alternative approach to the
leaf embedding problem on Ford CRTs related to -regenerative tree growth processes.Comment: 40 pages, 5 figure
Decision Stream: Cultivating Deep Decision Trees
Various modifications of decision trees have been extensively used during the
past years due to their high efficiency and interpretability. Tree node
splitting based on relevant feature selection is a key step of decision tree
learning, at the same time being their major shortcoming: the recursive nodes
partitioning leads to geometric reduction of data quantity in the leaf nodes,
which causes an excessive model complexity and data overfitting. In this paper,
we present a novel architecture - a Decision Stream, - aimed to overcome this
problem. Instead of building a tree structure during the learning process, we
propose merging nodes from different branches based on their similarity that is
estimated with two-sample test statistics, which leads to generation of a deep
directed acyclic graph of decision rules that can consist of hundreds of
levels. To evaluate the proposed solution, we test it on several common machine
learning problems - credit scoring, twitter sentiment analysis, aircraft flight
control, MNIST and CIFAR image classification, synthetic data classification
and regression. Our experimental results reveal that the proposed approach
significantly outperforms the standard decision tree learning methods on both
regression and classification tasks, yielding a prediction error decrease up to
35%
When a quantum measurement can be implemented locally ... and when it cannot
Local operations on subsystems and classical communication between parties
(LOCC) constitute the most general protocols available on spatially separated
quantum systems. Every LOCC protocol implements a separable generalized
measurement -- a complete measurement for which every outcome corresponds to a
tensor product of operators on individual subsystems -- but it is known that
there exist separable measurements that cannot be implemented by LOCC. A
longstanding problem in quantum information theory is to understand the
difference between LOCC and the full set of separable measurements. In this
paper, we show how to construct an LOCC protocol to implement an arbitrary
separable measurement, except that with those measurements for which no LOCC
protocol exists, the method shows explicitly that this is the case.Comment: 21 pages, 7 figures. Extensively revised to include details of all
arguments, explicitly proving all results in full rigor. Version 3 has
sections reordered and other restructuring, but otherwise contains the same
discussion as version
Evaluating Semi-Analytic Halo Merging Histories
We evaluate the accuracy of semi-analytic merger-trees by comparing them with
the merging histories of dark-matter halos in N-body simulations, focusing on
the joint distribution of the number of progenitors and their masses. We first
confirm that the halo mass function as predicted directly by the
Press-Schechter (PS) model deviates from the simulations by up to 50% depending
on the mass scale and redshift, while the means of the projected distributions
of progenitor number and mass for a halo of a given mass are more accurately
predicted by the Extended PS model. We then use the full merger trees to study
the joint distribution as a function of redshift and parent-halo mass. We find
that while the deviation of the mean quantities due to the inaccuracy of the
Extended PS model partly propagates into the higher moments of the
distribution, the merger-tree procedure does not introduce a significant
additional source of error. In particular, certain properties of the merging
history such as the mass ratio of the progenitors and the total accretion rate
are reproduced quite accurately for galaxy sized halos (\sim 10^{12}\msun),
and less so for larger masses. We conclude that although there could be deviations in the absolute numbers and masses of progenitors and in the
higher order moment of these distributions, the relative properties of
progenitors for a given halo are reproduced fairly well by the merger trees.
They can thus provide a useful framework for modelling galaxy formation once
the above-mentioned limitations are taken into account.Comment: 10 pages including 9 figures, submitted to MNRA
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