High-Speed Function Approximation

We address a new learning problem where the goal is to build a predictive model that minimizes prediction time (the time taken to make a prediction) subject to a constraint on model accuracy. Our solution is a generic framework that leverages existing data mining algorithms without requiring any modifications to these algorithms. We show a first application of our framework to a combustion simulation problem. Our experimental evaluation shows significant improvements over existing methods; prediction time typically is improved by a factor between 2 and 6.

[1]  Javier D. Bruguera,et al.  Faithful powering computation using table look-up and a fused accumulation tree , 2001, Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001.

[2]  Marios Hadjieleftheriou,et al.  R-Trees - A Dynamic Index Structure for Spatial Searching , 2008, ACM SIGSPATIAL International Workshop on Advances in Geographic Information Systems.

[3]  Hans-Peter Kriegel,et al.  The R*-tree: an efficient and robust access method for points and rectangles , 1990, SIGMOD '90.

[4]  Sunil Arya,et al.  Accounting for boundary effects in nearest-neighbor searching , 1996, Discret. Comput. Geom..

[5]  Rich Caruana,et al.  Data mining in metric space: an empirical analysis of supervised learning performance criteria , 2004, ROCAI.

[6]  Robert A. Jacobs,et al.  Hierarchical Mixtures of Experts and the EM Algorithm , 1993, Neural Computation.

[7]  Luís Torgo,et al.  Kernel Regression Trees , 2007 .

[8]  Christos Faloutsos,et al.  Deflating the dimensionality curse using multiple fractal dimensions , 2000, Proceedings of 16th International Conference on Data Engineering (Cat. No.00CB37073).

[9]  Christian Böhm,et al.  Searching in high-dimensional spaces: Index structures for improving the performance of multimedia databases , 2001, CSUR.

[10]  Marco Patella,et al.  Bulk Loading the M-tree , 2001 .

[11]  Johannes Gehrke,et al.  Indexing for function approximation , 2006, VLDB.

[12]  J. Grcar,et al.  Scaling and efficiency of PRISM in adaptive simulations of turbulent premixed flames , 1999 .

[13]  Rich Caruana,et al.  Model compression , 2006, KDD '06.

[14]  Robert W. Dibble,et al.  Pdf Modeling of Turbulent Nonpremixed Methane Jet Flames , 1989 .

[15]  Stephen B. Pope,et al.  Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation , 1997 .

[16]  Christos Faloutsos,et al.  On packing R-trees , 1993, CIKM '93.

[17]  Paul E. Plassmann,et al.  A Scientific On-line Database for Efficient Function Approximation , 2003, ICCSA.

[18]  Stefan Schaal,et al.  Real-time robot learning with locally weighted statistical learning , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[19]  Anand Sivasubramaniam,et al.  Analyzing range queries on spatial data , 2000, Proceedings of 16th International Conference on Data Engineering (Cat. No.00CB37073).

[20]  Johannes Gehrke,et al.  SECRET: a scalable linear regression tree algorithm , 2002, KDD.

[21]  Christian Böhm,et al.  A cost model for nearest neighbor search in high-dimensional data space , 1997, PODS.

[22]  P. Chaudhuri,et al.  Piecewise polynomial regression trees , 1994 .

[23]  Ambuj K. Singh,et al.  Modeling high-dimensional index structures using sampling , 2001, SIGMOD '01.

[24]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[25]  Christos Faloutsos,et al.  Beyond uniformity and independence: analysis of R-trees using the concept of fractal dimension , 1994, PODS.

[26]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .

[27]  Thomas G. Dietterich What is machine learning? , 2020, Archives of Disease in Childhood.

[28]  Timos K. Sellis,et al.  A model for the prediction of R-tree performance , 1996, PODS.

[29]  Hans-Jörg Schek,et al.  A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces , 1998, VLDB.

[30]  Jean-Michel Muller,et al.  "Partially rounded" small-order approximations for accurate, hardware-oriented, table-based methods , 2003, Proceedings 2003 16th IEEE Symposium on Computer Arithmetic.

[31]  Aram Karalic Linear Regression in Regression Tree Leaves , 1992 .