1,635 research outputs found
Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices
A task-based formulation of Scalable Universal Matrix Multiplication
Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is
applied to the multiplication of hierarchy-free, rank-structured matrices that
appear in the domain of quantum chemistry (QC). The novel features of our
formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and
(2) fine-grained task-based composition. These features make it tolerant of the
load imbalance due to the irregular matrix structure and eliminate all
artifactual sources of global synchronization.Scalability of iterative
computation of square-root inverse of block-rank-sparse QC matrices is
demonstrated; for full-rank (dense) matrices the performance of our SUMMA
formulation usually exceeds that of the state-of-the-art dense MM
implementations (ScaLAPACK and Cyclops Tensor Framework).Comment: 8 pages, 6 figures, accepted to IA3 2015. arXiv admin note: text
overlap with arXiv:1504.0504
Predicting Sparse Clients' Actions with CPOPT-Net in the Banking Environment
The digital revolution of the banking system with evolving European
regulations have pushed the major banking actors to innovate by a newly use of
their clients' digital information. Given highly sparse client activities, we
propose CPOPT-Net, an algorithm that combines the CP canonical tensor
decomposition, a multidimensional matrix decomposition that factorizes a tensor
as the sum of rank-one tensors, and neural networks. CPOPT-Net removes
efficiently sparse information with a gradient-based resolution while relying
on neural networks for time series predictions. Our experiments show that
CPOPT-Net is capable to perform accurate predictions of the clients' actions in
the context of personalized recommendation. CPOPT-Net is the first algorithm to
use non-linear conjugate gradient tensor resolution with neural networks to
propose predictions of financial activities on a public data set
Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors
We present a scalable Bayesian model for low-rank factorization of massive
tensors with binary observations. The proposed model has the following key
properties: (1) in contrast to the models based on the logistic or probit
likelihood, using a zero-truncated Poisson likelihood for binary data allows
our model to scale up in the number of \emph{ones} in the tensor, which is
especially appealing for massive but sparse binary tensors; (2)
side-information in form of binary pairwise relationships (e.g., an adjacency
network) between objects in any tensor mode can also be leveraged, which can be
especially useful in "cold-start" settings; and (3) the model admits simple
Bayesian inference via batch, as well as \emph{online} MCMC; the latter allows
scaling up even for \emph{dense} binary data (i.e., when the number of ones in
the tensor/network is also massive). In addition, non-negative factor matrices
in our model provide easy interpretability, and the tensor rank can be inferred
from the data. We evaluate our model on several large-scale real-world binary
tensors, achieving excellent computational scalability, and also demonstrate
its usefulness in leveraging side-information provided in form of
mode-network(s).Comment: UAI (Uncertainty in Artificial Intelligence) 201
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