Algorithmic patterns for H\mathcal{H}-matrices on many-core processors

In this work, we consider the reformulation of hierarchical ($\mathcal{H}$) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal{H}$ matrices approximate specific dense matrices, e.g., from discretized integral equations or kernel ridge regression, leading to log-linear time complexity in dense matrix-vector products. The parallelization of $\mathcal{H}$ matrix operations on many-core processors is difficult due to the complex nature of the underlying algorithms. While previous algorithmic advances for many-core hardware focused on accelerating existing $\mathcal{H}$ matrix CPU implementations by many-core processors, we here aim at totally relying on that processor type. As main contribution, we introduce the necessary parallel algorithmic patterns allowing to map the full $\mathcal{H}$ matrix construction and the fast matrix-vector product to many-core hardware. Here, crucial ingredients are space filling curves, parallel tree traversal and batching of linear algebra operations. The resulting model GPU implementation hmglib is the, to the best of the authors knowledge, first entirely GPU-based Open Source $\mathcal{H}$ matrix library of this kind. We conclude this work by an in-depth performance analysis and a comparative performance study against a standard $\mathcal{H}$ matrix library, highlighting profound speedups of our many-core parallel approach

Tensor-on-tensor regression

We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge (L_2) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data. An R package is available at https://github.com/lockEF/MultiwayRegression .Comment: 33 pages, 3 figure

Unconventional machine learning of genome-wide human cancer data

Recent advances in high-throughput genomic technologies coupled with exponential increases in computer processing and memory have allowed us to interrogate the complex aberrant molecular underpinnings of human disease from a genome-wide perspective. While the deluge of genomic information is expected to increase, a bottleneck in conventional high-performance computing is rapidly approaching. Inspired in part by recent advances in physical quantum processors, we evaluated several unconventional machine learning (ML) strategies on actual human tumor data. Here we show for the first time the efficacy of multiple annealing-based ML algorithms for classification of high-dimensional, multi-omics human cancer data from the Cancer Genome Atlas. To assess algorithm performance, we compared these classifiers to a variety of standard ML methods. Our results indicate the feasibility of using annealing-based ML to provide competitive classification of human cancer types and associated molecular subtypes and superior performance with smaller training datasets, thus providing compelling empirical evidence for the potential future application of unconventional computing architectures in the biomedical sciences

Signal and data processing for machine olfaction and chemical sensing: A review

Signal and data processing are essential elements in electronic noses as well as in most chemical sensing instruments. The multivariate responses obtained by chemical sensor arrays require signal and data processing to carry out the fundamental tasks of odor identification (classification), concentration estimation (regression), and grouping of similar odors (clustering). In the last decade, important advances have shown that proper processing can improve the robustness of the instruments against diverse perturbations, namely, environmental variables, background changes, drift, etc. This article reviews the advances made in recent years in signal and data processing for machine olfaction and chemical sensing

Reciprocity Calibration for Massive MIMO: Proposal, Modeling and Validation

This paper presents a mutual coupling based calibration method for time-division-duplex massive MIMO systems, which enables downlink precoding based on uplink channel estimates. The entire calibration procedure is carried out solely at the base station (BS) side by sounding all BS antenna pairs. An Expectation-Maximization (EM) algorithm is derived, which processes the measured channels in order to estimate calibration coefficients. The EM algorithm outperforms current state-of-the-art narrow-band calibration schemes in a mean squared error (MSE) and sum-rate capacity sense. Like its predecessors, the EM algorithm is general in the sense that it is not only suitable to calibrate a co-located massive MIMO BS, but also very suitable for calibrating multiple BSs in distributed MIMO systems. The proposed method is validated with experimental evidence obtained from a massive MIMO testbed. In addition, we address the estimated narrow-band calibration coefficients as a stochastic process across frequency, and study the subspace of this process based on measurement data. With the insights of this study, we propose an estimator which exploits the structure of the process in order to reduce the calibration error across frequency. A model for the calibration error is also proposed based on the asymptotic properties of the estimator, and is validated with measurement results.Comment: Submitted to IEEE Transactions on Wireless Communications, 21/Feb/201

A concept for a fuel efficient flight planning aid for general aviation

A core equation for estimation of fuel burn from path profile data was developed. This equation was used as a necessary ingredient in a dynamic program to define a fuel efficient flight path. The resultant algorithm is oriented toward use by general aviation. The pilot provides a description of the desired ground track, standard aircraft parameters, and weather at selected waypoints. The algorithm then derives the fuel efficient altitudes and velocities at the waypoints

autoAx: An Automatic Design Space Exploration and Circuit Building Methodology utilizing Libraries of Approximate Components

Approximate computing is an emerging paradigm for developing highly energy-efficient computing systems such as various accelerators. In the literature, many libraries of elementary approximate circuits have already been proposed to simplify the design process of approximate accelerators. Because these libraries contain from tens to thousands of approximate implementations for a single arithmetic operation it is intractable to find an optimal combination of approximate circuits in the library even for an application consisting of a few operations. An open problem is "how to effectively combine circuits from these libraries to construct complex approximate accelerators". This paper proposes a novel methodology for searching, selecting and combining the most suitable approximate circuits from a set of available libraries to generate an approximate accelerator for a given application. To enable fast design space generation and exploration, the methodology utilizes machine learning techniques to create computational models estimating the overall quality of processing and hardware cost without performing full synthesis at the accelerator level. Using the methodology, we construct hundreds of approximate accelerators (for a Sobel edge detector) showing different but relevant tradeoffs between the quality of processing and hardware cost and identify a corresponding Pareto-frontier. Furthermore, when searching for approximate implementations of a generic Gaussian filter consisting of 17 arithmetic operations, the proposed approach allows us to identify approximately $10^3$ highly important implementations from $10^{23}$ possible solutions in a few hours, while the exhaustive search would take four months on a high-end processor.Comment: Accepted for publication at the Design Automation Conference 2019 (DAC'19), Las Vegas, Nevada, US

Lecture notes on ridge regression

The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a penalty (i.e. a function of regression coefficients). The ridge penalty is the sum of squared regression coefficients, giving rise to ridge regression. Here many aspect of ridge regression are reviewed e.g. moments, mean squared error, its equivalence to constrained estimation, and its relation to Bayesian regression. Finally, its behaviour and use are illustrated in simulation and on omics data. Subsequently, ridge regression is generalized to allow for a more general penalty. The ridge penalization framework is then translated to logistic regression and its properties are shown to carry over. To contrast ridge penalized estimation, the final chapter introduces its lasso counterpart