Loo.py: transformation-based code generation for GPUs and CPUs

Today's highly heterogeneous computing landscape places a burden on programmers wanting to achieve high performance on a reasonably broad cross-section of machines. To do so, computations need to be expressed in many different but mathematically equivalent ways, with, in the worst case, one variant per target machine. Loo.py, a programming system embedded in Python, meets this challenge by defining a data model for array-style computations and a library of transformations that operate on this model. Offering transformations such as loop tiling, vectorization, storage management, unrolling, instruction-level parallelism, change of data layout, and many more, it provides a convenient way to capture, parametrize, and re-unify the growth among code variants. Optional, deep integration with numpy and PyOpenCL provides a convenient computing environment where the transition from prototype to high-performance implementation can occur in a gradual, machine-assisted form

Dimension Reduction by Mutual Information Discriminant Analysis

In the past few decades, researchers have proposed many discriminant analysis (DA) algorithms for the study of high-dimensional data in a variety of problems. Most DA algorithms for feature extraction are based on transformations that simultaneously maximize the between-class scatter and minimize the withinclass scatter matrices. This paper presents a novel DA algorithm for feature extraction using mutual information (MI). However, it is not always easy to obtain an accurate estimation for high-dimensional MI. In this paper, we propose an efficient method for feature extraction that is based on one-dimensional MI estimations. We will refer to this algorithm as mutual information discriminant analysis (MIDA). The performance of this proposed method was evaluated using UCI databases. The results indicate that MIDA provides robust performance over different data sets with different characteristics and that MIDA always performs better than, or at least comparable to, the best performing algorithms.Comment: 13pages, 3 tables, International Journal of Artificial Intelligence & Application

A methodology pruning the search space of six compiler transformations by addressing them together as one problem and by exploiting the hardware architecture details

Today’s compilers have a plethora of optimizations-transformations to choose from, and the correct choice, order as well parameters of transformations have a significant/large impact on performance; choosing the correct order and parameters of optimizations has been a long standing problem in compilation research, which until now remains unsolved; the separate sub-problems optimization gives a different schedule/binary for each sub-problem and these schedules cannot coexist, as by refining one degrades the other. Researchers try to solve this problem by using iterative compilation techniques but the search space is so big that it cannot be searched even by using modern supercomputers. Moreover, compiler transformations do not take into account the hardware architecture details and data reuse in an efficient way. In this paper, a new iterative compilation methodology is presented which reduces the search space of six compiler transformations by addressing the above problems; the search space is reduced by many orders of magnitude and thus an efficient solution is now capable to be found. The transformations are the following: loop tiling (including the number of the levels of tiling), loop unroll, register allocation, scalar replacement, loop interchange and data array layouts. The search space is reduced (a) by addressing the aforementioned transformations together as one problem and not separately, (b) by taking into account the custom hardware architecture details (e.g., cache size and associativity) and algorithm characteristics (e.g., data reuse). The proposed methodology has been evaluated over iterative compilation and gcc/icc compilers, on both embedded and general purpose processors; it achieves significant performance gains at many orders of magnitude lower compilation time

Tied factor analysis for face recognition across large pose differences

Face recognition algorithms perform very unreliably when the pose of the probe face is different from the gallery face: typical feature vectors vary more with pose than with identity. We propose a generative model that creates a one-to-many mapping from an idealized “identity” space to the observed data space. In identity space, the representation for each individual does not vary with pose. We model the measured feature vector as being generated by a pose-contingent linear transformation of the identity variable in the presence of Gaussian noise. We term this model “tied” factor analysis. The choice of linear transformation (factors) depends on the pose, but the loadings are constant (tied) for a given individual. We use the EM algorithm to estimate the linear transformations and the noise parameters from training data. We propose a probabilistic distance metric that allows a full posterior over possible matches to be established. We introduce a novel feature extraction process and investigate recognition performance by using the FERET, XM2VTS, and PIE databases. Recognition performance compares favorably with contemporary approaches

Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions

We put forth two physics-informed neural network (PINN) schemes based on Miura transformations and the novelty of this research is the incorporation of Miura transformation constraints into neural networks to solve nonlinear PDEs. The most noteworthy advantage of our method is that we can simply exploit the initial-boundary data of a solution of a certain nonlinear equation to obtain the data-driven solution of another evolution equation with the aid of PINNs and during the process, the Miura transformation plays an indispensable role of a bridge between solutions of two separate equations. It is tailored to the inverse process of the Miura transformation and can overcome the difficulties in solving solutions based on the implicit expression. Moreover, two schemes are applied to perform abundant computational experiments to effectively reproduce dynamic behaviors of solutions for the well-known KdV equation and mKdV equation. Significantly, new data-driven solutions are successfully simulated and one of the most important results is the discovery of a new localized wave solution: kink-bell type solution of the defocusing mKdV equation and it has not been previously observed and reported to our knowledge. It provides a possibility for new types of numerical solutions by fully leveraging the many-to-one relationship between solutions before and after Miura transformations. Performance comparisons in different cases as well as advantages and disadvantages analysis of two schemes are also discussed. On the basis of the performance of two schemes and no free lunch theorem, they both have their own merits and thus more appropriate one should be chosen according to specific cases

Aitchison's Compositional Data Analysis 40 Years On: A Reappraisal

The development of John Aitchison's approach to compositional data analysis is followed since his paper read to the Royal Statistical Society in 1982. Aitchison's logratio approach, which was proposed to solve the problematic aspects of working with data with a fixed sum constraint, is summarized and reappraised. It is maintained that the principles on which this approach was originally built, the main one being subcompositional coherence, are not required to be satisfied exactly -- quasi-coherence is sufficient, that is near enough to being coherent for all practical purposes. This opens up the field to using simpler data transformations, such as power transformations, that permit zero values in the data. The additional principle of exact isometry, which was subsequently introduced and not in Aitchison's original conception, imposed the use of isometric logratio transformations, but these are complicated and problematic to interpret, involving ratios of geometric means. If this principle is regarded as important in certain analytical contexts, for example unsupervised learning, it can be relaxed by showing that regular pairwise logratios, as well as the alternative quasi-coherent transformations, can also be quasi-isometric, meaning they are close enough to exact isometry for all practical purposes. It is concluded that the isometric and related logratio transformations such as pivot logratios are not a prerequisite for good practice, although many authors insist on their obligatory use. This conclusion is fully supported here by case studies in geochemistry and in genomics, where the good performance is demonstrated of pairwise logratios, as originally proposed by Aitchison, or Box-Cox power transforms of the original compositions where no zero replacements are necessary.Comment: 26 pages, 18 figures, plus Supplementary Material. This is a complete revision of the first version of this paper, placing the geochemical example upfront and adding a large section on CoDA of wide matrice