arXiv subjects

Bradley Lowery

Publications and source records attributed to Bradley Lowery.

3 recordsLinked to original sources

arXiv2019

Functional Ratings in Sports

In this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a teams average point differential adjusted for strength of schedule. Using two team's functional ratings we can predict the expected point differential at any time in the game. We looked at three variations of our model accounting for home-court advantage in different ways. We use the 2018-2019 NCAA Division 1 men's college basketball season to test the models and determined that home-court advantage is statistically important but does not differ between teams.

stat.AP↗

arXiv2019

A Tight I/O Lower Bound for Matrix Multiplication

A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of segments needed to perform $C:=AB$, for distinct matrices $A$, $B$, and $C$, where each segment is a series of operations involving $M$ reads and writes to and from fast memory, and $M$ is the size of fast memory. A lower bound on the number of segments was then determined by obtaining an upper bound on the number of elementary multiplications performed per segment. This paper follows the same high level approach, but improves the lower bound by (1) transforming algorithms for MMM so that they perform all computation via fused multiply-add instructions (FMAs) and using this to reason about only the cost associated with reading the matrices, and (2) decoupling the per-segment I/O cost from the size of fast memory. For $n \times n$ matrices, the lower bound's leading-order term is $2n^3/\sqrt{M}$. A theoretical algorithm whose leading terms attains this is introduced. To what extent the state-of-the-art Goto's Algorithm attains the lower bound is discussed.

cs.CC↗

arXiv2014

Designing LU-QR hybrid solvers for performance and stability

This paper introduces hybrid LU-QR al- gorithms for solving dense linear systems of the form Ax = b. Throughout a matrix factorization, these al- gorithms dynamically alternate LU with local pivoting and QR elimination steps, based upon some robustness criterion. LU elimination steps can be very efficiently parallelized, and are twice as cheap in terms of floating- point operations, as QR steps. However, LU steps are not necessarily stable, while QR steps are always stable. The hybrid algorithms execute a QR step when a robustness criterion detects some risk for instability, and they execute an LU step otherwise. Ideally, the choice between LU and QR steps must have a small computational overhead and must provide a satisfactory level of stability with as few QR steps as possible. In this paper, we introduce several robustness criteria and we establish upper bounds on the growth factor of the norm of the updated matrix incurred by each of these criteria. In addition, we describe the implementation of the hybrid algorithms through an exten- sion of the PaRSEC software to allow for dynamic choices during execution. Finally, we analyze both stability and performance results compared to state-of-the-art linear solvers on parallel distributed multicore platforms.

math.NA↗