Explicit Learning Curves for Transduction and Application to Clustering and Compression Algorithms

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined. The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapnik's basic results is a rather tight error bound for transductive classification based on an exact computation of the hypergeometric tail. While tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapnik's transductive bound. This characterization is obtained using concentration inequalities for the tail of sums of random variables obtained by sampling without replacement. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space

Generalized hardi invariants by method of tensor contraction

pre-printWe propose a 3D object recognition technique to construct rotation invariant feature vectors for high angular resolution diffusion imaging (HARDI). This method uses the spherical harmonics (SH) expansion and is based on generating rank-1 contravariant tensors using the SH coefficients, and contracting them with covariant tensors to obtain invariants. The proposed technique enables the systematic construction of invariants for SH expansions of any order using simple mathematical operations. In addition, it allows construction of a large set of invariants, even for low order expansions, thus providing rich feature vectors for image analysis tasks such as classification and segmentation. In this paper, we use this technique to construct feature vectors for eighth-order fiber orientation distributions (FODs) reconstructed using constrained spherical deconvolution (CSD). Using simulated and in vivo brain data, we show that these invariants are robust to noise, enable voxel-wise classification, and capture meaningful information on the underlying white matter structure

On Prediction Using Variable Order Markov Models

This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We focus on six prominent prediction algorithms, including Context Tree Weighting (CTW), Prediction by Partial Match (PPM) and Probabilistic Suffix Trees (PSTs). We discuss the properties of these algorithms and compare their performance using real life sequences from three domains: proteins, English text and music pieces. The comparison is made with respect to prediction quality as measured by the average log-loss. We also compare classification algorithms based on these predictors with respect to a number of large protein classification tasks. Our results indicate that a "decomposed" CTW (a variant of the CTW algorithm) and PPM outperform all other algorithms in sequence prediction tasks. Somewhat surprisingly, a different algorithm, which is a modification of the Lempel-Ziv compression algorithm, significantly outperforms all algorithms on the protein classification problems

Can We Learn to Beat the Best Stock

A novel algorithm for actively trading stocks is presented. While traditional expert advice and "universal" algorithms (as well as standard technical trading heuristics) attempt to predict winners or trends, our approach relies on predictable statistical relations between all pairs of stocks in the market. Our empirical results on historical markets provide strong evidence that this type of technical trading can "beat the market" and moreover, can beat the best stock in the market. In doing so we utilize a new idea for smoothing critical parameters in the context of expert learning

Modulated Floquet Topological Insulators

Floquet topological insulators are topological phases of matter generated by the application of time-periodic perturbations on otherwise conventional insulators. We demonstrate that spatial variations in the time-periodic potential lead to localized quasi-stationary states in two-dimensional systems. These states include one-dimensional interface modes at the nodes of the external potential, and fractionalized excitations at vortices of the external potential. We also propose a setup by which light can induce currents in these systems. We explain these results by showing a close analogy to px+ipy superconductors

Ground-based observations of the relations between lightning charge-moment-change and the physical and optical properties of column sprites

Optical observations of 66 sprites, using a calibrated commercial CCD camera, were conducted in 2009-2010 and 2010-2011 winter seasons as part of the ILAN (Imaging of Lightning And Nocturnal flashes) campaign in the vicinity of Israel and the eastern Mediterranean. We looked for correlations between the properties of parent lightning (specifically, the charge moment change; CMC) to the properties of column sprites, such as the measured radiance, the length and the number of column elements in each sprite event. The brightness of sprites positively correlates with the CMC (0.7) and so does the length of sprite elements (0.83). These results are in agreement with previous studies, and support the QE model of sprite generation. © 2013 Elsevier Ltd

Learning with a Drifting Target Concept

We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target concept that can change on each round. One of our main contributions is a refinement of the best previous results for polynomial-time algorithms for the space of linear separators under a uniform distribution. We also provide general results for an algorithm capable of adapting to a variable rate of drift of the target concept. Some of the results also describe an active learning variant of this setting, and provide bounds on the number of queries for the labels of points in the sequence sufficient to obtain the stated bounds on the error rates

A global atmospheric electricity monitoring network for climate and geophysical research

The Global atmospheric Electric Circuit (GEC) is a fundamental coupling network of the climate system connecting electrically disturbed weather regions with fair weather regions across the planet. The GEC sustains the fair weather electric field (or potential gradient, PG) which is present globally and can be measured routinely at the surface using durable instrumentation such as modern electric field mills, which are now widely deployed internationally. In contrast to lightning or magnetic fields, fair weather PG cannot be measured remotely. Despite the existence of many PG datasets (both contemporary and historical), few attempts have been made to coordinate and integrate these fragmented surface measurements within a global framework. Such a synthesis is important elvinin order to fully study major influences on the GEC such as climate variations and space weather effects, as well as more local atmospheric electrical processes such as cloud electrification, lightning initiation, and dust and aerosol charging. The GloCAEM (Global Coordination of Atmospheric Electricity Measurements) project has brought together experts in atmospheric electricity to make the first steps towards an effective global network for atmospheric electricity monitoring, which will provide data in near real time. Data from all sites are available in identically-formatted files, at both one second and one minute temporal resolution, along with meteorological data (wherever available) for ease of interpretation of electrical measurements. This work describes the details of the GloCAEM database and presents what is likely to be the largest single analysis of PG data performed from multiple datasets at geographically distinct locations. Analysis of the diurnal variation in PG from all 17 GloCAEM sites demonstrates that the majority of sites show two daily maxima, characteristic of local influences on the PG, such as the sunrise effect. Data analysis methods to minimise such effects are presented and recommendations provided on the most suitable GloCAEM sites for the study of various scientific phenomena. The use of the dataset for a further understanding of the GEC is also demonstrated, in particular for more detailed characterization of day-to-day global circuit variability. Such coordinated effort enables deeper insight into PG phenomenology which goes beyond single-location PG measurements, providing a simple measurement of global thunderstorm variability on a day-to-day timescale. The creation of the GloCAEM database is likely to enable much more effective study of atmospheric electricity variables than has ever been possible before, which will improve our understanding of the role of atmospheric electricity in the complex processes underlying weather and climate

Cosmic ray measurements in the atmosphere at several latitudes in October, 2014

Cosmic ray fluxes in the atmosphere were recorded during balloon flights in October 2014 in northern Murmansk region, Apatity (Russia; 67o33’N, 33o24’E), in Antarctica (observatory Mirny; 66o33’S, 93o00’E), in Moscow (Russia; 55o45’N, 37o37’E), in Reading (United King-dom; 51o27’N, 0o 58’W), in Mitzpe-Ramon (Israel; 30o36’N, 34o48’E) and in Zaragoza (Spain; 41o9’N, 0o54’W). Two type of cosmic ray detectors were used, namely, (1) the standard ra-diosonde and its modification constructed at the Lebedev Physical Institute (Moscow, Russia) and (2) the device manufactured at the Reading University (Reading, United Kingdom). We compare and analyze obtained data and focus on the estimation of the cosmic ray latitudinal effect in the atmosphere