Research on distributed machine learning algorithms has focused primarily on one of two extremes - algorithms that obey strict concurrency constraints or algorithms that obey few or no such constraints. We consider an intermediate alternative in which algorithms optimistically assume that conflicts are unlikely and if conflicts do arise a conflict-resolution protocol is invoked. We view this "optimistic concurrency control" paradigm as particularly appropriate for large-scale machine learning algorithms, particularly in the unsupervised setting. We demonstrate our approach in three problem areas: clustering, feature learning and online facility location. We evaluate our methods via large-scale experiments in a cluster computing environment.
A great amount of work addresses scalable clustering algorithms @cite_22 @cite_11 @cite_18 . Many algorithms with provable approximation factors are streaming algorithms and inherently use hierarchies, or related divide-and-conquer approaches . The approximation factors in such algorithms multiply across levels , and demand a careful tradeoff between communication and approximation quality that is obviated in our framework. Other approaches use core sets @cite_13 @cite_17 . A lot of methods @cite_5 @cite_1 @cite_8 first collect a set of centers and then re-cluster them, and therefore need to communicate all intermediate centers. Our approach avoids that, since a center causes no rejections in the epochs after it is established: the rejection rate does not grow with @math . Still, as our examples demonstrate, our OCC framework can easily integrate and exploit many of the ideas in the cited works.
@cite_18 @cite_11 @cite_22 @cite_8 @cite_1 @cite_5 @cite_13 @cite_17
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We present parallel and sequential dense QR factorization algorithms that are both optimal (up to polylogarithmic factors) in the amount of communication they perform and just as stable as Householder QR. We prove optimality by deriving new lower bounds for the number of multiplications done by “non-Strassen-like” QR, and using these in known communication lower bounds that are proportional to the number of multiplications. We not only show that our QR algorithms attain these lower bounds (up to polylogarithmic factors), but that existing LAPACK and ScaLAPACK algorithms perform asymptotically more communication. We derive analogous communication lower bounds for LU factorization and point out recent LU algorithms in the literature that attain at least some of these lower bounds. The sequential and parallel QR algorithms for tall and skinny matrices lead to significant speedups in practice over some of the existing algorithms, including LAPACK and ScaLAPACK, for example, up to 6.7 times over ScaLAPACK. A performance model for the parallel algorithm for general rectangular matrices predicts significant speedups over ScaLAPACK. This paper provides new algorithms for distributed clustering for two popular center-based objectives, @math -median and @math -means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following a classic approach in clustering by har2004coresets , we reduce the problem of finding a clustering with low cost to the problem of finding a coreset' of small size. We provide a distributed method for constructing a global coreset which improves over the previous methods by reducing the communication complexity, and which works over general communication topologies. We provide experimental evidence for this approach on both synthetic and real data sets. Harvesting relational facts from Web sources has received great attention for automatically constructing large knowledge bases. Stateof-the-art approaches combine pattern-based gathering of fact candidates with constraint-based reasoning. However, they still face major challenges regarding the trade-offs between precision, recall, and scalability. Techniques that scale well are susceptible to noisy patterns that degrade precision, while techniques that employ deep reasoning for high precision cannot cope with Web-scale data. This paper presents a scalable system, called PROSPERA, for high-quality knowledge harvesting. We propose a new notion of ngram-itemsets for richer patterns, and use MaxSat-based constraint reasoning on both the quality of patterns and the validity of fact candidates.We compute pattern-occurrence statistics for two benefits: they serve to prune the hypotheses space and to derive informative weights of clauses for the reasoner. The paper shows how to incorporate these building blocks into a scalable architecture that can parallelize all phases on a Hadoop-based distributed platform. Our experiments with the ClueWeb09 corpus include comparisons to the recent ReadTheWeb experiment. We substantially outperform these prior results in terms of recall, with the same precision, while having low run-times. We present a new method for clustering based on compression. The method does not use subject-specific features or background knowledge, and works as follows: First, we determine a parameter-free, universal, similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the noncomputable notion of Kolmogorov complexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics, we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis.