  We are interested in parallelizing the Least Angle Regression (LARS)
algorithm for fitting linear regression models to high-dimensional data. We
consider two parallel and communication avoiding versions of the basic LARS
algorithm. The two algorithms have different asymptotic costs and practical
performance. One offers more speedup and the other produces more accurate
output. The first is bLARS, a block version of LARS algorithm, where we update
b columns at each iteration. Assuming that the data are row-partitioned, bLARS
reduces the number of arithmetic operations, latency, and bandwidth by a factor
of b. The second is Tournament-bLARS (T-bLARS), a tournament version of LARS
where processors compete by running several LARS computations in parallel to
choose b new columns to be added in the solution. Assuming that the data are
column-partitioned, T-bLARS reduces latency by a factor of b. Similarly to
LARS, our proposed methods generate a sequence of linear models. We present
extensive numerical experiments that illustrate speedups up to 4x compared to
LARS without any compromise in solution quality.
