Active Learning with Statistical Models

For many types of machine learning algorithms, one can compute the statistically `optimal' way to select training data. In this paper, we review how optimal data selection techniques have been used with feedforward neural networks. We then show how the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are computationally expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate. Empirically, we observe that the optimality criterion sharply decreases the number of training examples the learner needs in order to achieve good performance.Comment: See http://www.jair.org/ for any accompanying file

Scalable Text and Link Analysis with Mixed-Topic Link Models

Many data sets contain rich information about objects, as well as pairwise relations between them. For instance, in networks of websites, scientific papers, and other documents, each node has content consisting of a collection of words, as well as hyperlinks or citations to other nodes. In order to perform inference on such data sets, and make predictions and recommendations, it is useful to have models that are able to capture the processes which generate the text at each node and the links between them. In this paper, we combine classic ideas in topic modeling with a variant of the mixed-membership block model recently developed in the statistical physics community. The resulting model has the advantage that its parameters, including the mixture of topics of each document and the resulting overlapping communities, can be inferred with a simple and scalable expectation-maximization algorithm. We test our model on three data sets, performing unsupervised topic classification and link prediction. For both tasks, our model outperforms several existing state-of-the-art methods, achieving higher accuracy with significantly less computation, analyzing a data set with 1.3 million words and 44 thousand links in a few minutes.Comment: 11 pages, 4 figure

The sphere packing problem in dimension 24

Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.Comment: 17 page

Red Sequence Cluster Finding in the Millennium Simulation

We investigate halo mass selection properties of red-sequence cluster finders using galaxy populations of the Millennium Simulation (MS). A clear red sequence exists for MS galaxies in massive halos at redshifts z < 1, and we use this knowledge to inform a cluster-finding algorithm applied to 500 Mpc/h projections of the simulated volume. At low redshift (z=0.4), we find that 90% of the clusters found have galaxy membership dominated by a single, real-space halo, and that 10% are blended systems for which no single halo contributes a majority of a cluster's membership. At z=1, the fraction of blends increases to 22%, as weaker redshift evolution in observed color extends the comoving length probed by a fixed range of color. Other factors contributing to the increased blending at high-z include broadening of the red sequence and confusion from a larger number of intermediate mass halos hosting bright red galaxies of magnitude similar to those in higher mass halos. Our method produces catalogs of cluster candidates whose halo mass selection function, p(M|\Ngal,z), is characterized by a bimodal log-normal model with a dominant component that reproduces well the real-space distribution, and a redshift-dependent tail that is broader and displaced by a factor ~2 lower in mass. We discuss implications for X-ray properties of optically selected clusters and offer ideas for improving both mock catalogs and cluster-finding in future surveys.Comment: final version to appear in MNRAS. Appendix added on purity and completeness, small shift in red sequence due to correcting an error in finding i

Feature space analysis for human activity recognition in smart environments

Activity classification from smart environment data is typically done employing ad hoc solutions customised to the particular dataset at hand. In this work we introduce a general purpose collection of features for recognising human activities across datasets of different type, size and nature. The first experimental test of our feature collection achieves state of the art results on well known datasets, and we provide a feature importance analysis in order to compare the potential relevance of features for activity classification in different datasets

Ground states and formal duality relations in the Gaussian core model

We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising anisotropy as well as formal duality relations. These duality relations suggest that the Gaussian core model possesses unexplored symmetries, and they have implications for a broad range of soft-core potentials.Comment: 7 pages, 1 figure, appeared in Physical Review E (http://pre.aps.org

Several new catalysts for reduction of oxygen in fuel cells

Test results prove nickel carbide or nitride, nickel-cobalt carbide, titanium carbide or nitride, and intermetallic compounds of the transition or noble metals to be efficient electrocatalysts for oxygen reduction in alkaline electrolytes in low temperature fuel cells

Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

Real-Time Hyperbola Recognition and Fitting in GPR Data

The problem of automatically recognising and fitting hyperbolae from Ground Penetrating Radar (GPR) images is addressed, and a novel technique computationally suitable for real time on-site application is proposed. After pre-processing of the input GPR images, a novel thresholding method is applied to separate the regions of interest from background. A novel column-connection clustering (C3) algorithm is then applied to separate the regions of interest from each other. Subsequently, a machine learnt model is applied to identify hyperbolic signatures from outputs of the C3 algorithm and a hyperbola is fitted to each such signature with an orthogonal distance hyperbola fitting algorithm. The novel clustering algorithm C3 is a central component of the proposed system, which enables the identification of hyperbolic signatures and hyperbola fitting. Only two features are used in the machine learning algorithm, which is easy to train using a small set of training data. An orthogonal distance hyperbola fitting algorithm for ‘south-opening’ hyperbolae is introduced in this work, which is more robust and accurate than algebraic hyperbola fitting algorithms. The proposed method can successfully recognise and fit hyperbolic signatures with intersections with others, hyperbolic signatures with distortions and incomplete hyperbolic signatures with one leg fully or largely missed. As an additional novel contribution, formulae to compute an initial ‘south-opening’ hyperbola directly from a set of given points are derived, which make the system more efficient. The parameters obtained by fitting hyperbolae to hyperbolic signatures are very important features, they can be used to estimate the location, size of the related target objects, and the average propagation velocity of the electromagnetic wave in the medium. The effectiveness of the proposed system is tested on both synthetic and real GPR data