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

Retarded Learning: Rigorous Results from Statistical Mechanics

We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the scaled critical number of examples below which learning of the direction is impossible. The asymptotic tightness of the bounds suggests an asymptotically optimal method for learning nonsmooth distributions.Comment: 8 pages, 1 figur

Prediction with Expert Advice under Discounted Loss

We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression to this case, propose a suitable new variant of exponential weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte

Multifractality and percolation in the coupling space of perceptrons

The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated analytically using the replica formalism. The storage capacity and the generalization behaviour of the perceptron are shown to be related to properties of $f(\alpha)$ which are correctly described within the replica symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a transition from percolating to non-percolating cells. The existence of empty cells gives rise to singularities in the multifractal spectrum. The analytical results for binary couplings are corroborated by numerical studies.Comment: 13 pages, revtex, 4 eps figures, version accepted for publication in Phys. Rev.

Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks

Random input patterns induce a partition of the coupling space of feed-forward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the spectrum $f(\alpha)$ can be calculated analytically using the replica trick. Phase transition in the multifractal spectrum correspond to the crossover from percolating to non-percolating cell sizes. Instabilities of negative moments are related to the VC-dimension.Comment: 10 pages, Latex, submitted to PR

Cosmological weak lensing with the HST GEMS survey

We present our cosmic shear analysis of GEMS, one of the largest wide-field surveys ever undertaken by the Hubble Space Telescope. Imaged with the Advanced Camera for Surveys (ACS), GEMS spans 795 square arcmin in the Chandra Deep Field South. We detect weak lensing by large-scale structure in high resolution F606W GEMS data from ~60 resolved galaxies per square arcminute. We measure the two-point shear correlation function, the top-hat shear variance and the shear power spectrum, performing an E/B mode decomposition for each statistic. We show that we are not limited by systematic errors and use our results to place joint constraints on the matter density parameter Omega_m and the amplitude of the matter power spectrum sigma_8. We find sigma_8(Omega_m/0.3)^{0.65}=0.68 +/- 0.13 where the 1sigma error includes both our uncertainty on the median redshift of the survey and sampling variance. Removing image and point spread function (PSF) distortions are crucial to all weak lensing analyses. We therefore include a thorough discussion on the degree of ACS PSF distortion and anisotropy which we characterise directly from GEMS data. Consecutively imaged over 20 days, GEMS data also allows us to investigate PSF instability over time. We find that, even in the relatively short GEMS observing period, the ACS PSF ellipticity varies at the level of a few percent which we account for with a semi-time dependent PSF model. Our correction for the temporal and spatial variability of the PSF is shown to be successful through a series of diagnostic tests.Comment: 17 pages, 16 figures. Version accepted by MNRA

The size evolution of galaxies since z~3: combining SDSS, GEMS and FIRES

We present the evolution of the luminosity-size and stellar mass-size relations of luminous (L_V>3.4x10^10h_70^-2L_sun) and of massive (M_*>3x10^10h_70^-2M_sun) galaxies in the last ~11 Gyr. We use very deep near-infrared images of the Hubble Deep Field-South and the MS1054-03 field in the J_s, H and K_s bands from FIRES to retrieve the sizes in the optical rest-frame for galaxies with z>1. We combine our results with those from GEMS at 0.2<z<1 and SDSS at z~0.1 to achieve a comprehensive picture of the optical rest-frame size evolution from z=0 to z=3. Galaxies are differentiated according to their light concentration using the Sersic index n. For less concentrated objects, the galaxies at a given luminosity were typically ~3+-0.5 (+-2 sigma) times smaller at z~2.5 than those we see today. The stellar mass-size relation has evolved less: the mean size at a given stellar mass was \~2+-0.5 times smaller at z~2.5, evolving proportional to (1+z)^{-0.40+-0.06}. Simple scaling relations between dark matter halos and baryons in a hierarchical cosmogony predict a stronger (although consistent within the error bars) than observed evolution of the stellar mass-size relation. The observed luminosity-size evolution out to z~2.5 matches well recent infall model predictions for Milky-Way type objects. For low-n galaxies, the evolution of the stellar mass-size relation would follow naturally if the individual galaxies grow inside-out. For highly concentrated objects, the situation is as follows: at a given luminosity, these galaxies were ~2.7+-1.1 times smaller at z~2.5 (or put differently, were typically ~2.2+-0.7 mag brighter at a given size than they are today), and at a given stellar mass the size has evolved proportional to (1+z)^{-0.45+-0.10}.Comment: Accepted for publication in ApJ. The new version includes several improvements: much accurate size estimations and a better completeness and robustness analysis. Tables of data are included. 29 pages and 14 figures (one low resolution

Safe and complete contig assembly via omnitigs

Contig assembly is the first stage that most assemblers solve when reconstructing a genome from a set of reads. Its output consists of contigs -- a set of strings that are promised to appear in any genome that could have generated the reads. From the introduction of contigs 20 years ago, assemblers have tried to obtain longer and longer contigs, but the following question was never solved: given a genome graph $G$ (e.g. a de Bruijn, or a string graph), what are all the strings that can be safely reported from $G$ as contigs? In this paper we finally answer this question, and also give a polynomial time algorithm to find them. Our experiments show that these strings, which we call omnitigs, are 66% to 82% longer on average than the popular unitigs, and 29% of dbSNP locations have more neighbors in omnitigs than in unitigs.Comment: Full version of the paper in the proceedings of RECOMB 201

Statistical hadronization phenomenology in K/πK/\pi fluctuations at ultra-relativistic energies

We discuss the information that can be obtained from an analysis of fluctuations in heavy ion collisions within the context of the statistical model of particle production. We then examine the recently published experimental data on ratio fluctuations, and use it to obtain constraints on the statistical properties (physically relevant ensemble, degree of chemical equilibration, scaling across energies and system sizes) and freeze-out dynamics (amount of reinteraction between chemical and thermal freeze-out) of the system.Comment: Proceedings, SQM2009. Fig. 4, the main results figure, was wrong due to editing mistake, now correcte