Communication Cost for Updating Linear Functions when Message Updates are Sparse: Connections to Maximally Recoverable Codes

We consider a communication problem in which an update of the source message needs to be conveyed to one or more distant receivers that are interested in maintaining specific linear functions of the source message. The setting is one in which the updates are sparse in nature, and where neither the source nor the receiver(s) is aware of the exact {\em difference vector}, but only know the amount of sparsity that is present in the difference-vector. Under this setting, we are interested in devising linear encoding and decoding schemes that minimize the communication cost involved. We show that the optimal solution to this problem is closely related to the notion of maximally recoverable codes (MRCs), which were originally introduced in the context of coding for storage systems. In the context of storage, MRCs guarantee optimal erasure protection when the system is partially constrained to have local parity relations among the storage nodes. In our problem, we show that optimal solutions exist if and only if MRCs of certain kind (identified by the desired linear functions) exist. We consider point-to-point and broadcast versions of the problem, and identify connections to MRCs under both these settings. For the point-to-point setting, we show that our linear-encoder based achievable scheme is optimal even when non-linear encoding is permitted. The theory is illustrated in the context of updating erasure coded storage nodes. We present examples based on modern storage codes such as the minimum bandwidth regenerating codes.Comment: To Appear in IEEE Transactions on Information Theor

Runtime Optimizations for Prediction with Tree-Based Models

Tree-based models have proven to be an effective solution for web ranking as well as other problems in diverse domains. This paper focuses on optimizing the runtime performance of applying such models to make predictions, given an already-trained model. Although exceedingly simple conceptually, most implementations of tree-based models do not efficiently utilize modern superscalar processor architectures. By laying out data structures in memory in a more cache-conscious fashion, removing branches from the execution flow using a technique called predication, and micro-batching predictions using a technique called vectorization, we are able to better exploit modern processor architectures and significantly improve the speed of tree-based models over hard-coded if-else blocks. Our work contributes to the exploration of architecture-conscious runtime implementations of machine learning algorithms

Using Localised ‘Gossip’ to Structure Distributed Learning

The idea of a “memetic” spread of solutions through a human culture in parallel to their development is applied as a distributed approach to learning. Local parts of a problem are associated with a set of overlappingt localities in a space and solutions are then evolved in those localites. Good solutions are not only crossed with others to search for better solutions but also they propogate across the areas of the problem space where they are relatively successful. Thus the whole population co-evolves solutions with the domains in which they are found to work. This approach is compared to the equivalent global evolutionary computation approach with respect to predicting the occcurence of heart disease in the Cleveland data set. It greatly outperforms the global approach, but the space of attributes within which this evolutionary process occurs can effect its efficiency

Using the High Productivity Language Chapel to Target GPGPU Architectures

It has been widely shown that GPGPU architectures offer large performance gains compared to their traditional CPU counterparts for many applications. The downside to these architectures is that the current programming models present numerous challenges to the programmer: lower-level languages, explicit data movement, loss of portability, and challenges in performance optimization. In this paper, we present novel methods and compiler transformations that increase productivity by enabling users to easily program GPGPU architectures using the high productivity programming language Chapel. Rather than resorting to different parallel libraries or annotations for a given parallel platform, we leverage a language that has been designed from first principles to address the challenge of programming for parallelism and locality. This also has the advantage of being portable across distinct classes of parallel architectures, including desktop multicores, distributed memory clusters, large-scale shared memory, and now CPU-GPU hybrids. We present experimental results from the Parboil benchmark suite which demonstrate that codes written in Chapel achieve performance comparable to the original versions implemented in CUDA.NSF CCF 0702260Cray Inc. Cray-SRA-2010-016962010-2011 Nvidia Research Fellowshipunpublishednot peer reviewe

Parallel sparse matrix-vector multiplication as a test case for hybrid MPI+OpenMP programming

We evaluate optimized parallel sparse matrix-vector operations for two representative application areas on widespread multicore-based cluster configurations. First the single-socket baseline performance is analyzed and modeled with respect to basic architectural properties of standard multicore chips. Going beyond the single node, parallel sparse matrix-vector operations often suffer from an unfavorable communication to computation ratio. Starting from the observation that nonblocking MPI is not able to hide communication cost using standard MPI implementations, we demonstrate that explicit overlap of communication and computation can be achieved by using a dedicated communication thread, which may run on a virtual core. We compare our approach to pure MPI and the widely used "vector-like" hybrid programming strategy.Comment: 12 pages, 6 figure