Parallelizing Deadlock Resolution in Symbolic Synthesis of Distributed Programs

Previous work has shown that there are two major complexity barriers in the synthesis of fault-tolerant distributed programs: (1) generation of fault-span, the set of states reachable in the presence of faults, and (2) resolving deadlock states, from where the program has no outgoing transitions. Of these, the former closely resembles with model checking and, hence, techniques for efficient verification are directly applicable to it. Hence, we focus on expediting the latter with the use of multi-core technology. We present two approaches for parallelization by considering different design choices. The first approach is based on the computation of equivalence classes of program transitions (called group computation) that are needed due to the issue of distribution (i.e., inability of processes to atomically read and write all program variables). We show that in most cases the speedup of this approach is close to the ideal speedup and in some cases it is superlinear. The second approach uses traditional technique of partitioning deadlock states among multiple threads. However, our experiments show that the speedup for this approach is small. Consequently, our analysis demonstrates that a simple approach of parallelizing the group computation is likely to be the effective method for using multi-core computing in the context of deadlock resolution

Massively-Parallel Feature Selection for Big Data

We present the Parallel, Forward-Backward with Pruning (PFBP) algorithm for feature selection (FS) in Big Data settings (high dimensionality and/or sample size). To tackle the challenges of Big Data FS PFBP partitions the data matrix both in terms of rows (samples, training examples) as well as columns (features). By employing the concepts of $p$-values of conditional independence tests and meta-analysis techniques PFBP manages to rely only on computations local to a partition while minimizing communication costs. Then, it employs powerful and safe (asymptotically sound) heuristics to make early, approximate decisions, such as Early Dropping of features from consideration in subsequent iterations, Early Stopping of consideration of features within the same iteration, or Early Return of the winner in each iteration. PFBP provides asymptotic guarantees of optimality for data distributions faithfully representable by a causal network (Bayesian network or maximal ancestral graph). Our empirical analysis confirms a super-linear speedup of the algorithm with increasing sample size, linear scalability with respect to the number of features and processing cores, while dominating other competitive algorithms in its class

Uncertainty quantification for radio interferometric imaging: II. MAP estimation

Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Statistical sampling approaches to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling, can in principle recover the full posterior distribution of the image, from which uncertainties can then be quantified. However, for massive data sizes, like those anticipated from the Square Kilometre Array (SKA), it will be difficult if not impossible to apply any MCMC technique due to its inherent computational cost. We formulate Bayesian inference problems with sparsity-promoting priors (motivated by compressive sensing), for which we recover maximum a posteriori (MAP) point estimators of radio interferometric images by convex optimisation. Exploiting recent developments in the theory of probability concentration, we quantify uncertainties by post-processing the recovered MAP estimate. Three strategies to quantify uncertainties are developed: (i) highest posterior density credible regions; (ii) local credible intervals (cf. error bars) for individual pixels and superpixels; and (iii) hypothesis testing of image structure. These forms of uncertainty quantification provide rich information for analysing radio interferometric observations in a statistically robust manner. Our MAP-based methods are approximately $10^5$ times faster computationally than state-of-the-art MCMC methods and, in addition, support highly distributed and parallelised algorithmic structures. For the first time, our MAP-based techniques provide a means of quantifying uncertainties for radio interferometric imaging for realistic data volumes and practical use, and scale to the emerging big-data era of radio astronomy.Comment: 13 pages, 10 figures, see companion article in this arXiv listin

Parallel/distributed direct method for solving linear systems

A new family of parallel schemes for directly solving linear systems is presented and analyzed. It is shown that these schemes exhibit a near optimal performance and enjoy several important features: (1) For large enough linear systems, the design of the appropriate paralleled algorithm is insensitive to the number of processors as its performance grows monotonically with them; (2) It is especially good for large matrices, with dimensions large relative to the number of processors in the system; (3) It can be used in both distributed parallel computing environments and tightly coupled parallel computing systems; and (4) This set of algorithms can be mapped onto any parallel architecture without any major programming difficulties or algorithmical changes

Nested Sequential Monte Carlo Methods

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.Comment: Extended version of paper published in Proceedings of the 32nd International Conference on Machine Learning (ICML), Lille, France, 201