9,551 research outputs found
End-to-End Differentiable Proving
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
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
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),
and a sparse
matrix (outliers), from their
sum, . 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
's obey a `slow subspace change' assumption; (c) the basis vectors for
the subspace from which is generated are dense (non-sparse); (d) the
support of 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
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
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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