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Page 35 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
Given a model M of ZFC, the authors study the measure algebra B of Borel sets of reals modulo the class / of null sets and the class Ra(M) of reals random over M, often inside models strictly larger than  ...  Ambos-Spies [same journal 31 (1985), no. 5, 461-477; MR 87d:03113] initiated the study of splitting of r.e. sets by build- ing an r.e. set A such that for any splitting into r.e. sets Ap and A), Ao and  ... 

Efficient Bulk Loading of Large High-Dimensional Indexes [chapter]

Christian Böhm, Hans-Peter Kriegel
1999 Lecture Notes in Computer Science  
Decisions of the split strategy can be made according to a sample of the data set which is selected automatically.  ...  The sort algorithm is a variant of the well-known Quicksort algorithm, enhanced to work on secondary storage. The index construction has a runtime complexity of O(n log n).  ...  Average Case Complexity of Our Technique Our technique has an average case complexity of O(n log n) unless the split strategy has a complexity worse than O(n).  ... 
doi:10.1007/3-540-48298-9_27 fatcat:o7rigkj2kze67git2eywhkmivu

Page 1701 of Mathematical Reviews Vol. , Issue 87d [page]

1987 Mathematical Reviews  
On the other hand, extensions of the Sacks splitting theorem such as the Robinson splitting theorem are not proved by producing set splittings.  ...  Section 1 recalls some basic recur- sion theory, including the recursion theorem and Rice’s theorem, and presents some results of Blum on size complexity and dynamic complexity (including the Trakhtenbrot  ... 

Knowledge-Based, Central Nervous System (CNS) Lead Selection and Lead Optimization for CNS Drug Discovery

Arup K. Ghose, Torsten Herbertz, Robert L. Hudkins, Bruce D. Dorsey, John P. Mallamo
2011 ACS Chemical Neuroscience  
habits, an artificial data set was generated for illustrating variable and split selection in recursive partitioning.  ...  Each tree in the ensemble is built based on the principle of recursive partitioning, where the feature space is recursively split into regions containing observations with similar response values.  ...  An Introduction to Recursive Partitioning 35  ... 
doi:10.1021/cn200100h pmid:22267984 pmcid:PMC3260741 fatcat:p5u2ylcmsrabdkek2plrw4udhe

Recursive partitioning for monotone missing at random longitudinal markers

Shannon Stock, Victor DeGruttola
2012 Statistics in Medicine  
This recursive partitioning approach for continuous longitudinal data uses the kernel of a U-statistic as the splitting criterion, and avoids the need for parametric assumptions regarding the relationship  ...  accommodates a large set of genetic or other covariates and a longitudinal response.  ...  The recursive partitioning process accurately identified the correct splits for more than 89% of data sets in each simulation.  ... 
doi:10.1002/sim.5574 pmid:22941582 pmcid:PMC3754451 fatcat:njdhr4n655e4hfs25flxogaj5m

An introduction to recursive partitioning: Rationale, application, and characteristics of classification and regression trees, bagging, and random forests

Carolin Strobl, James Malley, Gerhard Tutz
2009 Psychological methods  
Especially random forests, which can deal with large numbers of predictor variables even in the presence of complex interactions, have been applied successfully in genetics, clinical medicine, and bioinformatics  ...  The aim of this work is to introduce the principles of the standard recursive partitioning methods as well as recent methodological improvements, to illustrate their usage for low and high-dimensional  ...  is also randomized by means of random sampling from the set of all predictor variables to make the resulting set of trees even more diverse.  ... 
doi:10.1037/a0016973 pmid:19968396 pmcid:PMC2927982 fatcat:sjmucxyhu5eupnh3x3drb4qmuy

Cost-complexity pruning of random forests [article]

Kiran Bangalore Ravi, Jean Serra
2017 arXiv   pre-print
We study the effect of using the out-of-bag samples to improve the generalization error first of the decision trees and second the random forest by post-pruning.  ...  Random forests perform bootstrap-aggregation by sampling the training samples with replacement. This enables the evaluation of out-of-bag error which serves as a internal cross-validation mechanism.  ...  As shown in figure 1 the set of splits over which the splitting measure is minimized is determined by the coordinates of the training set points.  ... 
arXiv:1703.05430v2 fatcat:upxal4sqtjglvnuccrx5b5m5pi

On Learning a Hidden Directed Graph with Path Queries [article]

Mano Vikash Janardhanan, Lev Reyzin
2021 arXiv   pre-print
In this paper, we consider the problem of reconstructing a directed graph using path queries.  ...  In this query model of learning, a graph is hidden from the learner, and the learner can access information about it with path queries.  ...  Upper bound Our main result is an upper bound on the query complexity of Algorithm 1 which is a clean recursive randomized algorithm for learning an almost-tree.  ... 
arXiv:2002.11541v2 fatcat:e7zilyzdaval3hg4y4rmsoxcky

Reconstructing Biological and Digital Phylogenetic Trees in Parallel

Ramtin Afshar, Michael T. Goodrich, Pedro Matias, Martha C. Osegueda, Peter Sanders, Fabrizio Grandoni, Grzegorz Herman
2020 European Symposium on Algorithms  
query complexities for the problems we study.  ...  Our results are all asymptotically optimal and improve the asymptotic (sequential) query complexity for one of the problems we study.  ...  The expected query complexity Q(n) of Algorithm 2 is dominated by the two recursive calls Q n d+2 and Q n(d+1) d+2 and the calls to find-splitting-edge.  ... 
doi:10.4230/lipics.esa.2020.3 dblp:conf/esa/AfsharGMO20 fatcat:twxeirj7vbgrrmye7xt7gx2oce

Selection in the Presence of Memory Faults, with Applications to In-place Resilient Sorting [article]

Tsvi Kopelowitz, Nimrod Talmon
2012 arXiv   pre-print
Besides the deterministic algorithm, a randomized resilient selection algorithm is developed, which is simpler than the deterministic one, and has O(n + α) expected time complexity and O(1) space complexity  ...  The main focus of this work is designing algorithms for solving the selection problem in the presence of memory faults.  ...  There exists a deterministic resilient splitting algorithm with worstcase time complexity O(αn), and a randomized in-place resilient splitting algorithm with expected time complexity O(αn). Proof.  ... 
arXiv:1204.5229v2 fatcat:uwkvz3dre5hbhgow2c6pa74fd4

Willows: a memory efficient tree and forest construction package

Heping Zhang, Minghui Wang, Xiang Chen
2009 BMC Bioinformatics  
In addition, this package can easily set different options (e.g., algorithms and specifications) and predict the class of test samples.  ...  Results: Using the recursive partitioning technique, we developed a new software package, Willows, to maximize the utility of the computer memory and make it feasible to analyze massive genotype data.  ...  This manuscript was not prepared in collaboration with investigators of the Framingham Heart Study and does not necessarily reflect the opinions or views of the Framingham Heart Study, Boston University  ... 
doi:10.1186/1471-2105-10-130 pmid:19416535 pmcid:PMC2683818 fatcat:c64dnltbzrhntmcyzxzgfvjnta

ToPs: Ensemble Learning With Trees of Predictors

Jinsung Yoon, William R. Zame, Mihaela van der Schaar
2018 IEEE Transactions on Signal Processing  
The (locally) optimal tree of predictors is derived recursively; each step involves jointly optimizing the split of the terminal nodes of the previous tree and the choice of learner and training set (hence  ...  predictor) for each set in the split.  ...  Proof of computational complexity of one recursive step:Statement: The computational complexity of one recursive step for constructing tree of predictors grows asM i=1 O(N D × T i(N, D)). Proof.  ... 
doi:10.1109/tsp.2018.2807402 fatcat:urhxyu3suzej7oc25vevm5gvaq

Divide and Conquer Networks [article]

Alex Nowak-Vila, David Folqué, Joan Bruna
2018 arXiv   pre-print
Thanks to the dynamic programming nature of our model, we show significant improvements in terms of generalization error and computational complexity.  ...  Moreover, thanks to the dynamic aspect of our architecture, we can incorporate the computational complexity as a regularization term that can be optimized by backpropagation.  ...  The strategy for this task consists of splitting the set of points into two disjoint subsets and solving the problem recursively for each.  ... 
arXiv:1611.02401v7 fatcat:wigbigmipfdjrmgfc3yjz3vhzm

policytree: Policy learning via doubly robust empirical welfare maximization over trees

Erik Sverdrup, Ayush Kanodia, Zhengyuan Zhou, Susan Athey, Stefan Wager
2020 Journal of Open Source Software  
For each split candidate, the point is moved from the right set to the left set for all dimensions. This proceeds recursively to enumerate the reward in all possible splits.  ...  node, right node, total reward, action) 2 if k = 0 then Recursive Case We propose the time complexity for k >= 1 (1 or more splits) to be O(P k N k (log N + D)).  ... 
doi:10.21105/joss.02232 fatcat:vc4djy37efd6vib5rfdi75elvm

Reconstructing Biological and Digital Phylogenetic Trees in Parallel [article]

Ramtin Afshar, Michael T. Goodrich, Pedro Matias, Martha C. Osegueda
2020 arXiv   pre-print
query complexities for the problems we study.  ...  Our results are all asymptotically optimal and improve the asymptotic (sequential) query complexity for one of the problems we study.  ...  Our reconstruction algorithm is therefore a randomized recursive algorithm that takes as input a set of vertices, V , with a (known) root vertex r ∈ V , and returns the edge set, E, for V .  ... 
arXiv:2006.15259v2 fatcat:mlhibauvgfeh3dx3q4b23rphge
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