How good are your fits? Unbinned multivariate goodness-of-fit tests in high energy physics

Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned methods for determining the goodness of fit of the p.d.f. to the data. The application and performance of each method is discussed in the context of a real-life high energy physics analysis (a Dalitz-plot analysis). Several of the methods presented in this paper can also be used for the non-parametric determination of whether two samples originate from the same parent p.d.f. This can be used, e.g., to determine the quality of a detector Monte Carlo simulation without the need for a parametric expression of the efficiency.Comment: 32 pages, 12 figure

Mining Contrast Subspaces

In this paper, we tackle a novel problem of mining contrast subspaces. Given a set of multidimensional objects in two classes C+  and C− and a query object o, we want to find top-k subspaces S that maximize the ratio of likelihood of o in C+  against that in C−. We demonstrate that this problem has important applications, and at the same time, is very challenging. It even does not allow polynomial time approximation. We present CSMiner, a mining method with various pruning techniques. CSMiner is substantially faster than the baseline method. Our experimental results on real data sets verify the effectiveness and efficiency of our method

Simultaneous interval regression for K-nearest neighbor

International audienceIn some regression problems, it may be more reasonable to predict intervals rather than precise values. We are interested in finding intervals which simultaneously for all input instances x ∈X contain a β proportion of the response values. We name this problem simultaneous interval regression. This is similar to simultaneous tolerance intervals for regression with a high confidence level γ ≈ 1 and several authors have already treated this problem for linear regression. Such intervals could be seen as a form of confidence envelop for the prediction variable given any value of predictor variables in their domain. Tolerance intervals and simultaneous tolerance intervals have not yet been treated for the K-nearest neighbor (KNN) regression method. The goal of this paper is to consider the simultaneous interval regression problem for KNN and this is done without the homoscedasticity assumption. In this scope, we propose a new interval regression method based on KNN which takes advantage of tolerance intervals in order to choose, for each instance, the value of the hyper-parameter K which will be a good trade-off between the precision and the uncertainty due to the limited sample size of the neighborhood around each instance. In the experiment part, our proposed interval construction method is compared with a more conventional interval approximation method on six benchmark regression data sets

Kernel density classification and boosting: an L2 sub analysis

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research

Effect of FCNC mediated Z boson on lepton flavor violating decays

We study the three body lepton flavor violating (LFV) decays $\mu^- \to e^- e^+ e^-$, $\tau^- \to l_i^- l_j^+ l_j^-$ and the semileptonic decay $\tau \to \mu \phi$ in the flavor changing neutral current (FCNC) mediated $Z$ boson model. We also calculate the branching ratios for LFV leptonic B decays, $B_{d,s} \to \mu e$, $B_{d,s} \to \tau e$, $B_{d,s} \to \tau \mu$ and the conversion of muon to electron in Ti nucleus. The new physics parameter space is constrained by using the experimental limits on $\mu^- \to e^- e^+ e^-$ and $\tau^- \to \mu^- \mu^+ \mu^-$. We find that the branching ratios for $\tau \to eee$ and $\tau \to \mu \phi$ processes could be as large as $\sim {\cal O}(10^{-8})$ and ${\rm Br}B_{d,s} \to \tau \mu, \tau e) \sim {\cal O}(10^{-10})$. For other LFV B decays the branching ratios are found to be too small to be observed in the near future.Comment: 15 pages, 8 figures, typos corrected, one more section added, version to appear in EPJ

Adaptive Density Estimation on the Circle by Nearly-Tight Frames

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the so-called Mexican needlets, which describe a nearly-tight frame on the circle. We study the asymptotic behaviour of the $L^{2}$-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.Comment: 30 pages, 3 figure

Simulation techniques for cosmological simulations

Modern cosmological observations allow us to study in great detail the evolution and history of the large scale structure hierarchy. The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological model, requires precise modelling of the observed structure. In this paper we briefly review the current most effective techniques of large scale structure simulations, emphasising both their advantages and shortcomings. Starting with basics of the direct N-body simulations appropriate to modelling cold dark matter evolution, we then discuss the direct-sum technique GRAPE, particle-mesh (PM) and hybrid methods, combining the PM and the tree algorithms. Simulations of baryonic matter in the Universe often use hydrodynamic codes based on both particle methods that discretise mass, and grid-based methods. We briefly describe Eulerian grid methods, and also some variants of Lagrangian smoothed particle hydrodynamics (SPH) methods.Comment: 42 pages, 16 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 12; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

Fermi 130 GeV gamma-ray excess and dark matter annihilation in sub-haloes and in the Galactic centre

We analyze publicly available Fermi-LAT high-energy gamma-ray data and confirm the existence of clear spectral feature peaked at E=130GeV. Scanning over the Galaxy we identify several disconnected regions where the observed excess originates from. Our best optimized fit is obtained for the central region of Galaxy with a clear peak at 130GeV with local statistical significance 4.5 sigma. The observed excess is not correlated with Fermi bubbles. We compute the photon spectra induced by dark matter annihilations into two and four standard model particles, the latter via two light intermediate states, and fit the spectra with data. Since our fits indicate sharper and higher signal peak than in the previous works, data favors dark matter direct two-body annihilation channels into photons or other channels giving only line-like spectra. If Einasto halo profile correctly predicts the central cusp of Galaxy, dark matter annihilation cross-section to two photons is of order ten percent of the standard thermal freeze-out cross-section. The large dark matter two-body annihilation cross-section to photons may signal a new resonance that should be searched for at the CERN LHC experiments.Comment: Addendum included on the double peak structure of the excess seen due to new improved Fermi-LAT energy resolutio

Tune in to your emotions: a robust personalized affective music player

The emotional power of music is exploited in a personalized affective music player (AMP) that selects music for mood enhancement. A biosignal approach is used to measure listeners’ personal emotional reactions to their own music as input for affective user models. Regression and kernel density estimation are applied to model the physiological changes the music elicits. Using these models, personalized music selections based on an affective goal state can be made. The AMP was validated in real-world trials over the course of several weeks. Results show that our models can cope with noisy situations and handle large inter-individual differences in the music domain. The AMP augments music listening where its techniques enable automated affect guidance. Our approach provides valuable insights for affective computing and user modeling, for which the AMP is a suitable carrier application