Related papers: SPIN: A Fast and Scalable Matrix Inversion Method …
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…
With the rapid growth of Next Generation Sequencing (NGS) technologies, large amounts of "omics" data are daily collected and need to be processed. Indexing and compressing large sequences datasets are some of the most important tasks in…
Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to…
We compute the singular values of an $m \times n$ sparse matrix $A$ in a distributed setting, without communication dependence on $m$, which is useful for very large $m$. In particular, we give a simple nonadaptive sampling scheme where the…
We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…
A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…
Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks.…
In the era of big data and cloud computing, large amounts of data are generated from user applications and need to be processed in the datacenter. Data-parallel computing frameworks, such as Apache Spark, are widely used to perform such…
As data volumes grow across applications, analytics of large amounts of data is becoming increasingly important. Big data processing frameworks such as Apache Hadoop, Apache AsterixDB, and Apache Spark have been built to meet this demand. A…
Current deep learning architectures are growing larger in order to learn from complex datasets. These architectures require giant matrix multiplication operations to train millions of parameters. Conversely, there is another growing trend…
A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…
To process data more efficiently, big data frameworks provide data abstractions to developers. However, due to the abstraction, there may be many challenges for developers to understand and debug the data processing code. To uncover the…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call \texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a general sparse matrix…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…