Convolutional Dictionary Learning: Acceleration and Convergence

Convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian (AL) method or the variant alternating direction method of multipliers (ADMM). When their parameters are properly tuned, AL methods have shown fast convergence in CDL. However, the parameter tuning process is not trivial due to its data dependence and, in practice, the convergence of AL methods depends on the AL parameters for nonconvex CDL problems. To moderate these problems, this paper proposes a new practically feasible and convergent Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The BPG-M-based CDL is investigated with different block updating schemes and majorization matrix designs, and further accelerated by incorporating some momentum coefficient formulas and restarting techniques. All of the methods investigated incorporate a boundary artifacts removal (or, more generally, sampling) operator in the learning model. Numerical experiments show that, without needing any parameter tuning process, the proposed BPG-M approach converges more stably to desirable solutions of lower objective values than the existing state-of-the-art ADMM algorithm and its memory-efficient variant do. Compared to the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large datasets, due to its lower memory requirement and no polynomial computational complexity. Image denoising experiments show that, for relatively strong additive white Gaussian noise, the filters learned by BPG-M-based CDL outperform those trained by the ADMM approach.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Image Processin

FLASH: Randomized Algorithms Accelerated over CPU-GPU for Ultra-High Dimensional Similarity Search

We present FLASH (\textbf{F}ast \textbf{L}SH \textbf{A}lgorithm for \textbf{S}imilarity search accelerated with \textbf{H}PC), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computations and is tailored for high-performance computing platforms. By leveraging a LSH style randomized indexing procedure and combining it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations, we reduce the computational and parallelization costs of similarity search, while retaining sound theoretical guarantees. We evaluate FLASH on several real, high-dimensional datasets from different domains, including text, malicious URL, click-through prediction, social networks, etc. Our experiments shed new light on the difficulties associated with datasets having several million dimensions. Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than FLASH. FLASH is capable of computing an approximate k-NN graph, from scratch, over the full webspam dataset (1.3 billion nonzeros) in less than 10 seconds. Computing a full k-NN graph in less than 10 seconds on the webspam dataset, using brute-force ($n^2D$), will require at least 20 teraflops. We provide CPU and GPU implementations of FLASH for replicability of our results

A novel method for scaling iterative solvers: avoiding latency overhead of parallel sparse-matrix vector multiplies

Cataloged from PDF version of article.In parallel linear iterative solvers, sparse matrix vector multiplication (SpMxV) incurs irregular point-to-point (P2P) communications, whereas inner product computations incur regular collective communications. These P2P communications cause an additional synchronization point with relatively high message latency costs due to small message sizes. In these solvers, each SpMxV is usually followed by an inner product computation that involves the output vector of SpMxV. Here, we exploit this property to propose a novel parallelization method that avoids the latency costs and synchronization overhead of P2P communications. Our method involves a computational and a communication rearrangement scheme. The computational rearrangement provides an alternative method for forming input vector of SpMxV and allows P2P and collective communications to be performed in a single phase. The communication rearrangement realizes this opportunity by embedding P2P communications into global collective communication operations. The proposed method grants a certain value on the maximum number of messages communicated regardless of the sparsity pattern of the matrix. The downside, however, is the increased message volume and the negligible redundant computation. We favor reducing the message latency costs at the expense of increasing message volume. Yet, we propose two iterative-improvement-based heuristics to alleviate the increase in the volume through one-to-one task-to-processor mapping. Our experiments on two supercomputers, Cray XE6 and IBM BlueGene/Q, up to 2,048 processors show that the proposed parallelization method exhibits superior scalable performance compared to the conventional parallelization method

Optimal pre-scheduling of problem remappings

A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal

Generic design of Chinese remaindering schemes

We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a radix ladder, for the intermediate storage and computations. Our design is structured into three main modules: a black box residue computation in charge of computing each residue; a Chinese remaindering controller in charge of launching the computation and of the termination decision; an integer builder in charge of the reconstruction computation. We then show that this design enables many different forms of Chinese remaindering (e.g. deterministic, early terminated, distributed, etc.), easy comparisons between these forms and e.g. user-transparent parallelism at different parallel grains

Flexible and efficient IR using array databases

textabstractThe Matrix Framework is a recent proposal by IR researchers to flexibly represent all important information retrieval models in a single multi-dimensional array framework. Computational support for exactly this framework is provided by the array database system SRAM (Sparse Relational Array Mapping) that works on top of a DBMS. Information retrieval models can be specified in its comprehension-based array query language, in a way that directly corresponds to the underlying mathematical formulas. SRAM efficiently stores sparse arrays in (compressed) relational tables and translates and optimizes array queries into relational queries. In this work, we describe a number of array query optimization rules and demonstrate their effect on text retrieval in the TREC TeraByte track (TREC-TB) efficiency task, using the Okapi BM25 model as our example. It turns out that these optimization rules enable SRAM to automatically translate the BM25 array queries into the relational equivalent of inverted list processing including compression, score materialization and quantization, such as employed by custom-built IR systems. The use of the high-performance MonetDB/X100 relational backend, that provides transparent database compression, allows the system to achieve very fast response times with good precision and low resource usage