The log-linear group-lasso estimator and its asymptotic properties

We define the group-lasso estimator for the natural parameters of the exponential families of distributions representing hierarchical log-linear models under multinomial sampling scheme. Such estimator arises as the solution of a convex penalized likelihood optimization problem based on the group-lasso penalty. We illustrate how it is possible to construct an estimator of the underlying log-linear model using the blocks of nonzero coefficients recovered by the group-lasso procedure. We investigate the asymptotic properties of the group-lasso estimator as a model selection method in a double-asymptotic framework, in which both the sample size and the model complexity grow simultaneously. We provide conditions guaranteeing that the group-lasso estimator is model selection consistent, in the sense that, with overwhelming probability as the sample size increases, it correctly identifies all the sets of nonzero interactions among the variables. Provided the sequences of true underlying models is sparse enough, recovery is possible even if the number of cells grows larger than the sample size. Finally, we derive some central limit type of results for the log-linear group-lasso estimator.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ364 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The distribution of maxima of approximately Gaussian random fields

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an approximation for the tail of the distribution. For the motivating class of problems this gives approximately the significance level of the maximum score test. The method is based on an application of a likelihood-ratio-identity followed by approximations of local fields. Numerical examples illustrate the accuracy of the approximations.Comment: Published in at http://dx.doi.org/10.1214/07-AOS511 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The importance of N2 leptogenesis

We argue that fast interactions of the lightest singlet neutrino $N_1$ would project part of a preexisting lepton asymmetry $L_p$ onto a direction that is protected from $N_1$ washout effects, thus preventing it from being erased. In particular, we consider an asymmetry generated in $N_2$ decays, assuming that $N_1$ interactions are fast enough to bring $N_1$ into full thermal equilibrium. If $N_1$ decays occur at T\gsim 10^9 GeV, that is, before the muon Yukawa interactions enter into thermal equilibrium, then generically part of $L_p$ survives. In this case some of the constraints implied by the standard $N_1$ leptogenesis scenario hold only if $L_p \approx 0$. For T\lsim 10^9 GeV, $L_p$ is generally erased, unless special alignment/orthogonality conditions in flavor space are realized.Comment: 5 pages. A few clarifications added, conclusions unchanged. Version published in Phys. Rev. Lett. (Title changed in journal

Relating leptogenesis parameters to light neutrino masses

We obtain model independent relations among neutrino masses and leptogenesis parameters. We find exact relations that involve the CP asymmetries $\epsilon_{N_\alpha}$, the washout parameters $\tilde m_\alpha$ and $\theta_{\alpha\beta}$, and the neutrino masses $m_i$ and $M_\alpha$, as well as powerful inequalities that involve just $\tilde m_\alpha$ and $m_i$. We prove that the Yukawa interactions of at least two of the heavy singlet neutrinos are in the strong washout region ($\tilde m_\alpha\gg10^{-3} eV$).Comment: 5 pages, 1 figur

Achieving Both Valid and Secure Logistic Regression Analysis on Aggregated Data from Different Private Sources

Abstract. Preserving the privacy of individual databases when carrying out statistical calculations has a relatively long history in statistics and had been the focus of much recent attention in machine learning. In this paper, we present a protocol for fitting a logistic regression when the data are held by separate parties—without actually combining information sources—by exploiting results from the literature on multi-party secure computation. Our protocol provides only the final result of the calculation compared with other methods that share intermediate values and thus present an opportunity for compromise of values in the individual databases. Our paper has two themes: (1) the development of a secure protocol for computing the logistic parameters, and a demonstration of its performances in practice, and (2) the presentation of an amended protocol that speeds up the computation of the logistic function. We illustrate the nature of the calculations and their accuracy using an extract of data from the Current Population Survey divided between two parties. Throughout, we build our protocol from existing cryptographic primitives, thus the novelty is in designing a concrete procedure for private computation of the logistic regression MLE rather than to propose new cryptographic constructions

First limit on inclusive B→XsννˉB \to X_s \nu \bar\nu decay and constraints on new physics

The inclusive $B \to X_s \nu \bar\nu$ decay rate, on which no experimental bound exists to date, can be constrained by searching for large missing energy events in $B$ decays. Carefully examining the experimental and theoretical aspects of such an analysis, we argue that the published ALEPH limit on \BR(B \to \tau \bar\nu) implies, conservatively, the bound \BR(B \to X_s \nu \bar\nu)<3.9\times10^{-4}, which is less than one order of magnitude above the standard model prediction. The LEP collaborations could significantly improve this bound by a dedicated experimental analysis. We study the constraints this new limit imposes on various extensions of the standard model. We derive new bounds on the couplings of third generation fermions in models with leptoquarks, and in supersymmetric models without R-parity. We also constrain models where new gauge bosons are coupled dominantly to the third generation, such as TopColor models and models based on horizontal gauge symmetries. For models which predict an enhanced effective $bsZ$ vertex, the constraint from $B \to X_s \nu \bar\nu$ is competitive with the limits from inclusive and exclusive $B \to X_s \ell^+ \ell^-$ decays.Comment: 43 pages (paper) + 3 pages (erratum), REVTeX, no figures. Erratum added (Paper unchanged). Two effects neglected in the original analysis are discussed in the Erratum. The numerical estimate of the limit on the branching ratio is weaker by about a factor of thre

Non-Standard Neutrino Interactions and Neutrino Oscillation Experiments

In analyzing neutrino oscillation experiments it is often assumed that while new physics contributes to neutrino masses, neutrino interactions are given by the Standard Model. We develop a formalism to study new physics effects in neutrino interactions using oscillation experiments. We argue that the notion of branching ratio is not appropriate in this case. We show that a neutrino appearance experiment with sensitivity to oscillation probability $P_{ij}^{exp}$ can detect new physics in neutrino interactions if its strength $G_N$ satisfies $(G_N/G_F)^2 \sim P_{ij}^{exp}$. Using our formalism we show how current experiments on neutrino oscillation give bounds on the new interactions in various new physics scenarios.Comment: 10 pages, no figures, revte