Tree-Independent Dual-Tree Algorithms

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.Comment: accepted in ICML 201

Sampling-based Algorithms for Optimal Motion Planning

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics Researc

Statistical Learning Theory for Location Fingerprinting in Wireless LANs

In this paper, techniques and algorithms developed in the framework of statistical learning theory are analyzed and applied to the problem of determining the location of a wireless device by measuring the signal strengths from a set of access points (location fingerprinting). Statistical Learning Theory provides a rich theoretical basis for the development of models starting from a set of examples. Signal strength measurement is part of the normal operating mode of wireless equipment, in particular Wi-Fi, so that no custom hardware is required. The proposed techniques, based on the Support Vector Machine paradigm, have been implemented and compared, on the same data set, with other approaches considered in the literature. Tests performed in a real-world environment show that results are comparable, with the advantage of a low algorithmic complexity in the normal operating phase. Moreover, the algorithm is particularly suitable for classification, where it outperforms the other techniques

A general guide to applying machine learning to computer architecture

The resurgence of machine learning since the late 1990s has been enabled by significant advances in computing performance and the growth of big data. The ability of these algorithms to detect complex patterns in data which are extremely difficult to achieve manually, helps to produce effective predictive models. Whilst computer architects have been accelerating the performance of machine learning algorithms with GPUs and custom hardware, there have been few implementations leveraging these algorithms to improve the computer system performance. The work that has been conducted, however, has produced considerably promising results. The purpose of this paper is to serve as a foundational base and guide to future computer architecture research seeking to make use of machine learning models for improving system efficiency. We describe a method that highlights when, why, and how to utilize machine learning models for improving system performance and provide a relevant example showcasing the effectiveness of applying machine learning in computer architecture. We describe a process of data generation every execution quantum and parameter engineering. This is followed by a survey of a set of popular machine learning models. We discuss their strengths and weaknesses and provide an evaluation of implementations for the purpose of creating a workload performance predictor for different core types in an x86 processor. The predictions can then be exploited by a scheduler for heterogeneous processors to improve the system throughput. The algorithms of focus are stochastic gradient descent based linear regression, decision trees, random forests, artificial neural networks, and k-nearest neighbors.This work has been supported by the European Research Council (ERC) Advanced Grant RoMoL (Grant Agreemnt 321253) and by the Spanish Ministry of Science and Innovation (contract TIN 2015-65316P).Peer ReviewedPostprint (published version