9,551 research outputs found

    End-to-End Differentiable Proving

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    We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules.Comment: NIPS 2017 camera-ready, NIPS 201

    Surrogate Functions for Maximizing Precision at the Top

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    The problem of maximizing precision at the top of a ranked list, often dubbed Precision@k (prec@k), finds relevance in myriad learning applications such as ranking, multi-label classification, and learning with severe label imbalance. However, despite its popularity, there exist significant gaps in our understanding of this problem and its associated performance measure. The most notable of these is the lack of a convex upper bounding surrogate for prec@k. We also lack scalable perceptron and stochastic gradient descent algorithms for optimizing this performance measure. In this paper we make key contributions in these directions. At the heart of our results is a family of truly upper bounding surrogates for prec@k. These surrogates are motivated in a principled manner and enjoy attractive properties such as consistency to prec@k under various natural margin/noise conditions. These surrogates are then used to design a class of novel perceptron algorithms for optimizing prec@k with provable mistake bounds. We also devise scalable stochastic gradient descent style methods for this problem with provable convergence bounds. Our proofs rely on novel uniform convergence bounds which require an in-depth analysis of the structural properties of prec@k and its surrogates. We conclude with experimental results comparing our algorithms with state-of-the-art cutting plane and stochastic gradient algorithms for maximizing [email protected]: To appear in the the proceedings of the 32nd International Conference on Machine Learning (ICML 2015

    Online Matrix Completion and Online Robust PCA

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    This work studies two interrelated problems - online robust PCA (RPCA) and online low-rank matrix completion (MC). In recent work by Cand\`{e}s et al., RPCA has been defined as a problem of separating a low-rank matrix (true data), L:=[1,2,t,,tmax]L:=[\ell_1, \ell_2, \dots \ell_{t}, \dots , \ell_{t_{\max}}] and a sparse matrix (outliers), S:=[x1,x2,xt,,xtmax]S:=[x_1, x_2, \dots x_{t}, \dots, x_{t_{\max}}] from their sum, M:=L+SM:=L+S. Our work uses this definition of RPCA. An important application where both these problems occur is in video analytics in trying to separate sparse foregrounds (e.g., moving objects) and slowly changing backgrounds. While there has been a large amount of recent work on both developing and analyzing batch RPCA and batch MC algorithms, the online problem is largely open. In this work, we develop a practical modification of our recently proposed algorithm to solve both the online RPCA and online MC problems. The main contribution of this work is that we obtain correctness results for the proposed algorithms under mild assumptions. The assumptions that we need are: (a) a good estimate of the initial subspace is available (easy to obtain using a short sequence of background-only frames in video surveillance); (b) the t\ell_t's obey a `slow subspace change' assumption; (c) the basis vectors for the subspace from which t\ell_t is generated are dense (non-sparse); (d) the support of xtx_t changes by at least a certain amount at least every so often; and (e) algorithm parameters are appropriately setComment: Presented at ISIT (IEEE Intnl. Symp. on Information Theory), 2015. Submitted to IEEE Transactions on Information Theory. This version: changes are in blue; the main changes are just to explain the model assumptions better (added based on ISIT reviewers' comments

    The MDS Queue: Analysing the Latency Performance of Erasure Codes

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    In order to scale economically, data centers are increasingly evolving their data storage methods from the use of simple data replication to the use of more powerful erasure codes, which provide the same level of reliability as replication but at a significantly lower storage cost. In particular, it is well known that Maximum-Distance-Separable (MDS) codes, such as Reed-Solomon codes, provide the maximum storage efficiency. While the use of codes for providing improved reliability in archival storage systems, where the data is less frequently accessed (or so-called "cold data"), is well understood, the role of codes in the storage of more frequently accessed and active "hot data", where latency is the key metric, is less clear. In this paper, we study data storage systems based on MDS codes through the lens of queueing theory, and term this the "MDS queue." We analytically characterize the (average) latency performance of MDS queues, for which we present insightful scheduling policies that form upper and lower bounds to performance, and are observed to be quite tight. Extensive simulations are also provided and used to validate our theoretical analysis. We also employ the framework of the MDS queue to analyse different methods of performing so-called degraded reads (reading of partial data) in distributed data storage

    Tensile testing of cellulose based natural fibers for structural composite applications

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    A series of tensile tests were conducted on a Lloyd LRX tensile testing machine for numerous natural fibers deemed potential candidates for development in composite applications. The tensile tests were conducted on the fibers jute, kenaf, flax, abaca, sisal, hemp, and coir for samples exposed to moisture conditions of (1) room temperature and humidity, (2) 65% moisture content, (3) 90% moisture content, and (4) soaked fiber. These seven fibers were then tested for the four conditions and the mechanical properties of tensile strength, tensile strain to failure, and Young's modulus were calculated for the results. These results were then compared and verified with those from the literature, with some of the fibers showing distinctly promising potential. Additionally, a study on the effect of alkalization using 3% NaOH solution was carried out on flax, kenaf, abaca, and sisal to observe impact that this common fiber pre-treatment process has on fiber mechanical properties. The result of the investigation indicated that over treatment of natural fibers using NaOH could have a negative effect on the base fiber properties. It is consequently apparent that a treatment time of less than 10 min is sufficient to remove hemicelluloses and to give the optimum effect
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