887,662 research outputs found
Alternating model trees
Model tree induction is a popular method for tackling regression problems requiring interpretable models. Model trees are decision trees with multiple linear regression models at the leaf nodes. In this paper, we propose a method for growing alternating model trees, a form of option tree for regression problems. The motivation is that alternating decision trees achieve high accuracy in classification problems because they represent an ensemble classifier as a single tree structure. As in alternating decision trees for classifi-cation, our alternating model trees for regression contain splitter and prediction nodes, but we use simple linear regression functions as opposed to constant predictors at the prediction nodes. Moreover, additive regression using forward stagewise modeling is applied to grow the tree rather than a boosting algorithm. The size of the tree is determined using cross-validation. Our empirical results show that alternating model trees achieve significantly lower squared error than standard model trees on several regression datasets
Model Checking Parse Trees
Parse trees are fundamental syntactic structures in both computational
linguistics and compilers construction. We argue in this paper that, in both
fields, there are good incentives for model-checking sets of parse trees for
some word according to a context-free grammar. We put forward the adequacy of
propositional dynamic logic (PDL) on trees in these applications, and study as
a sanity check the complexity of the corresponding model-checking problem:
although complete for exponential time in the general case, we find natural
restrictions on grammars for our applications and establish complexities
ranging from nondeterministic polynomial time to polynomial space in the
relevant cases.Comment: 21 + x page
Potts Model On Random Trees
We study the Potts model on locally tree-like random graphs of arbitrary
degree distribution. Using a population dynamics algorithm we numerically solve
the problem exactly. We confirm our results with simulations. Comparisons with
a previous approach are made, showing where its assumption of uniform local
fields breaks down for networks with nodes of low degree.Comment: 10 pages, 3 figure
Random model trees: an effective and scalable regression method
We present and investigate ensembles of randomized model trees as a novel regression method. Such ensembles combine the scalability of tree-based methods with predictive performance rivaling the state of the art in numeric prediction. An extensive empirical investigation shows that Random Model Trees produce predictive performance which is competitive with state-of-the-art methods like Gaussian Processes Regression or Additive Groves of Regression Trees. The training
and optimization of Random Model Trees scales better than Gaussian Processes Regression to larger datasets, and enjoys a constant advantage over Additive Groves of the order of one to two orders of magnitude
Gibbs properties of the fuzzy Potts model on trees and in mean field
We study Gibbs properties of the fuzzy Potts model in the mean field case
(i.e on a complete graph) and on trees. For the mean field case, a complete
characterization of the set of temperatures for which non-Gibbsianness happens
is given. The results for trees are somewhat less explicit, but we do show for
general trees that non-Gibbsianness of the fuzzy Potts model happens exactly
for those temperatures where the underlying Potts model has multiple Gibbs
measures
Quantitative evaluation of Pandora Temporal Fault Trees via Petri Nets
© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Using classical combinatorial fault trees, analysts are able to assess the effects of combinations of failures on system behaviour but are unable to capture sequence dependent dynamic behaviour. Pandora introduces temporal gates and temporal laws to fault trees to allow sequence-dependent dynamic analysis of events. Pandora can be easily integrated in model-based design and analysis techniques; however, the combinatorial quantification techniques used to solve classical fault trees cannot be applied to temporal fault trees. Temporal fault trees capture state and therefore require a state space solution for quantification of probability. In this paper, we identify Petri Nets as a possible framework for quantifying temporal trees. We describe how Pandora fault trees can be mapped to Petri Nets for dynamic dependability analysis and demonstrate the process on a fault tolerant fuel distribution system model
Stochastic Models for Phylogenetic Trees on Higher-order Taxa
Simple stochastic models for phylogenetic trees on species have been well
studied. But much paleontology data concerns time series or trees on
higher-order taxa, and any broad picture of relationships between extant groups
requires use of higher-order taxa. A coherent model for trees on (say) genera
should involve both a species-level model and a model for the classification
scheme by which species are assigned to genera. We present a general framework
for such models, and describe three alternate classification schemes. Combining
with the species-level model of Aldous-Popovic (2005), one gets models for
higher-order trees, and we initiate analytic study of such models. In
particular we derive formulas for the lifetime of genera, for the distribution
of number of species per genus, and for the offspring structure of the tree on
genera.Comment: 41 pages. Minor revision
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