as well as a large number of features N, while each example has only s << N non-zero features. This paper presents a Cutting-Plane Algorithm for training linear SVMs that provably has training time O(sn) for classification problems and O(sn log(n)) for ordinal regression problems. The algorithm

run-time of our method is Õ(d/(λɛ)), where d is a bound on the number of non-zero features in each example. Since the run-time does not depend directly on the size of the training set, the resulting algorithm is especially suited for learning from large datasets. Our approach also extends to non

Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zero-dimensional or one-dimensional aggregates. Applications need the N-dimensional generalization

marginals at the last two iterations. We only plot the diseases which had non-negligible posterior probability. Loopy Belief Propagation . s---=-o� . a-----' range of prior To test this hypothesis, we reparameterized the pyra mid network as follows: we set the prior probability of the "1"

The observation of the neutrinos arrived from Supernova LMC-’87A shows, with a good confidence level, the existence of two massive neutrinos. For the unobserved third neutrino mass, could speculate two possibilities either that this mass is close to one of the two observed values or that this neutrino has a negligible electronic flavor component. 1

in this sequence could be efficiently solved using the constrained concave-convex procedure (CCCP). Moreover, we prove theoretically that the CPMMC algorithm takes time O(sn) to converge with guaranteed accuracy, where n is the total number of samples in the dataset and s is the average number of non-zero features

computation and the use of regularization techniques. Our theoretical analysis shows that SRDA can be computed with O(ms) time and O(ms) memory, where s( ≤ n) is the average number of non-zero features in each sample. Extensive experimental results on four real world data sets demonstrate the effectiveness

for at most s of n inputs. Second, we show that the problem of minimizing the number of non-zero input weights used (without misclassifying training examples) is both NP-hard and difficult to approximate. Keywords: linear threshold, minimization, learning, complexity, approximation algorithm. Minimum Feature

of the proposed methods, when learning from data with utility scores, is O(tms), where t is the required number of iterations, m the number of training examples and s the average number of non-zero features per example. In addition, the complexity of learning from pairwise preferences is O(tms+tl), where l

similarity. We describe OASIS, a method for learning pairwise similarity that is fast and scales linearly with the number of objects and the number of non-zero features. Scalability is achieved through online learning of a bilinear model over sparse representations using a large margin criterion