We present a system that enables rapid model experimentation for tera-scale machine learning with trillions of non-zero features, billions of training examples, and millions of parameters. Our contribution to the literature is a new method (SA L-BFGS) for changing batch L-BFGS to perform in near real-time by using statistical tools to balance the contributions of previous weights, old training examples, and new training examples to achieve fast convergence with few iterations. The result is, to our knowledge, the most scalable and flexible linear learning system reported in the literature, beating standard practice with the current best system (Vowpal Wabbit and AllReduce). Using the KDD Cup 2012 data set from Tencent, Inc. we provide experimental results to verify the performance of this method.

As an important tool for information filtering in the era of socialized web, recommender systems have witnessed rapid development in the last decade. As benefited from the better interpretability, neighborhood-based collaborative filtering techniques, such as item-based collaborative filtering adopted by Amazon, have gained a great success in many practical recommender systems. However, the neighborhood-based collaborative filtering method suffers from the rating bound problem, i.e., the rating on a target item that this method estimates is bounded by the observed ratings of its all neighboring items. Therefore, it cannot accurately estimate the unobserved rating on a target item, if its ground truth rating is actually higher (lower) than the highest (lowest) rating over all items in its neighborhood. In this paper, we address this problem by formalizing rating estimation as a task of recovering a scalar rating function. With a linearity assumption, we infer all the ratings by optimizing the low-order norm, e.g., the $l_1/2$-norm, of the second derivative of the target scalar function, while remaining its observed ratings unchanged. Experimental results on three real datasets, namely Douban, Goodreads and MovieLens, demonstrate that the proposed approach can well overcome the rating bound problem. Particularly, it can significantly improve the accuracy of rating estimation by 37% than the conventional neighborhood-based methods.

In this work we develop Curvature Propagation (CP), a general technique for efficiently computing unbiased approximations of the Hessian of any function that is computed using a computational graph. At the cost of roughly two gradient evaluations, CP can give a rank-1 approximation of the whole Hessian, and can be repeatedly applied to give increasingly precise unbiased estimates of any or all of the entries of the Hessian. Of particular interest is the diagonal of the Hessian, for which no general approach is known to exist that is both efficient and accurate. We show in experiments that CP turns out to work well in practice, giving very accurate estimates of the Hessian of neural networks, for example, with a relatively small amount of work. We also apply CP to Score Matching, where a diagonal of a Hessian plays an integral role in the Score Matching objective, and where it is usually computed exactly using inefficient algorithms which do not scale to larger and more complex models.

We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes. Due to the inherent conjugacy of the GPs, one can analytically marginalize the GPs and compute the conditional likelihood of the observations given the partition tree. This property allows for efficient inference of the partition itself, for which we employ graph-theoretic techniques. We apply the multiresolution GP to the analysis of Magnetoencephalography (MEG) recordings of brain activity.

Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alpha-mixtures, with a particular form of mixing component relating to each agent's wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts.

Clustering evaluation measures are frequently used to evaluate the performance of algorithms. However, most measures are not properly normalized and ignore some information in the inherent structure of clusterings. We model the relation between two clusterings as a bipartite graph and propose a general component-based decomposition formula based on the components of the graph. Most existing measures are examples of this formula. In order to satisfy consistency in the component, we further propose a split-merge framework for comparing clusterings of different data sets. Our framework gives measures that are conditionally normalized, and it can make use of data point information, such as feature vectors and pairwise distances. We use an entropy-based instance of the framework and a coreference resolution data set to demonstrate empirically the utility of our framework over other measures.

We introduce a method for constructing skills capable of solving tasks drawn from a distribution of parameterized reinforcement learning problems. The method draws example tasks from a distribution of interest and uses the corresponding learned policies to estimate the topology of the lower-dimensional piecewise-smooth manifold on which the skill policies lie. This manifold models how policy parameters change as task parameters vary. The method identifies the number of charts that compose the manifold and then applies non-linear regression in each chart to construct a parameterized skill by predicting policy parameters from task parameters. We evaluate our method on an underactuated simulated robotic arm tasked with learning to accurately throw darts at a parameterized target location.

We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to nonsmooth problems that are difficult to optimize, and we propose in this paper a suitable version of an accelerated proximal method to solve them. We prove convergence of a nested procedure, obtained composing an accelerated proximal method with an inner algorithm for computing the proximity operator. By exploiting the geometrical properties of the penalty, we devise a new active set strategy, thanks to which the inner iteration is relatively fast, thus guaranteeing good computational performances of the overall algorithm. Our approach allows to deal with high dimensional problems without pre-processing for dimensionality reduction, leading to better computational and prediction performances with respect to the state-of-the art methods, as shown empirically both on toy and real data.

Supply chain management is a very dynamic operation research problem where one has to quickly adapt according to the changes perceived in environment in order to maximize the benefit or minimize the loss. Therefore we require a system which changes as per the changing requirements. Multi agent system technology in recent times has emerged as a possible way of efficient solution implementation for many such complex problems. Our research here focuses on building a Multi Agent System (MAS), which implements a modified version of Gravitational Search swarm intelligence Algorithm (GSA) to find out an optimal strategy in managing the demand supply chain. We target the grains distribution system among various centers of Food Corporation of India (FCI) as application domain. We assume centers with larger stocks as objects of greater mass and vice versa. Applying Newtonian law of gravity as suggested in GSA, larger objects attract objects of smaller mass towards itself, creating a virtual grain supply source. As heavier object sheds its mass by supplying some to the one in demand, it loses its gravitational pull and thus keeps the whole system of supply chain per-fectly in balance. The multi agent system helps in continuous updation of the whole system with the help of autonomous agents which react to the change in environment and act accordingly. This model also reduces the communication bottleneck to greater extents.

We develop an improved bound for the approximation error of the Nystr\"{o}m method under the assumption that there is a large eigengap in the spectrum of kernel matrix. This is based on the empirical observation that the eigengap has a significant impact on the approximation error of the Nystr\"{o}m method. Our approach is based on the concentration inequality of integral operator and the theory of matrix perturbation. Our analysis shows that when there is a large eigengap, we can improve the approximation error of the Nystr\"{o}m method from $O(N/m^{1/4})$ to $O(N/m^{1/2})$ when measured in Frobenius norm, where $N$ is the size of the kernel matrix, and $m$ is the number of sampled columns.