Acceleration of Sparse Vector Autoregressive Modeling Using GPUs Autoregressive modeling is a standard approach to mathematically describe the behavior of a time series. The vector autoregressive model (VAR) describes the behavior of multiple time series. The VAR modeling is a fundamental approach which has applications in multiple domains such as time series forecasting, Granger causality, system identification and stochastic control. Solving high dimensional VAR model requires the use of sparse regression techniques from machine learning. Efficient algorithms to solve the sparse regression problems are too slow to be useful in solving large high dimensional sparse VAR modeling problems. Earlier application of sparse VAR modeling in the neuroimaging domain required the use of the IBMs Blue Gene supercomputers. In this paper we describe an approach to accelerate large scale sparse VAR problems when solved using the lasso regression algorithm on stateoftheart GPUs. Our accelerated implementation on NVIDIA GTX 1080 GPU takes a few seconds to solve the problem, reaching up to 4 TFLOPs of singleprecision performance which is close to 55% of its peak matrixmultiply (GEMM) performance.

Discovering Sparse and Ununiform Lag Structure Using VAR Models with Latent Group LASSO Structurally regularized learning methods have been attracting attention in the field of statistics, machine learning, and signal processing as useful analysis tools for learning in highdimensional settings. Using these methods, specific structure can be represented in parameters. In multivariate time series data, it is important to capture timedelay structure where necessary lag length to explain each variable is different. In this paper, we deal with a problem to discover the optimal number of order for each variable in VAR models. When we apply conventional structurally regularized learning methods such as Group Lasso, some problems, which include loss of necessary coefficients, occur. To overcome these problems, we propose a method based on the Latent Group LASSO regularization. To apply it to VAR models, we introduce overlapped coefficient groups in time direction and use a heavytailed distribution, such as Studentu0027s tdistribution, as a prior to enhance its sparsity. We evaluated the effectiveness of the proposed method using artificial data and actual data set (Beijing PM2.5 data set). As the result, we obtained the sparse models that capture ununiform timedelay structure represented by fewer variables with the same degree of forecast accuracy comparing with ordinary VAR models.