Bayesian Variable Selection for Ultrahigh-dimensional Sparse Linear Models

We propose a Bayesian variable selection procedure for ultrahigh-dimensional linear regression models. The number of regressors involved in regression, $p_n$, is allowed to grow exponentially with $n$. Assuming the true model to be sparse, in the sense that only a small number of regressors contribute to this model, we propose a set of priors suitable for this regime. The model selection procedure based on the proposed set of priors is shown to be variable selection consistent when all the $2^{p_n}$ models are considered. In the ultrahigh-dimensional setting, selection of the true model among all the $2^{p_n}$ possible ones involves prohibitive computation. To cope with this, we present a two-step model selection algorithm based on screening and Gibbs sampling. The first step of screening discards a large set of unimportant covariates, and retains a smaller set containing all the active covariates with probability tending to one. In the next step, we search for the best model among the covariates obtained in the screening step. This procedure is computationally quite fast, simple and intuitive. We demonstrate competitive performance of the proposed algorithm for a variety of simulated and real data sets when compared with several frequentist, as well as Bayesian methods

Linear Estimating Equations for Exponential Families with Application to Gaussian Linear Concentration Models

In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator of Hyv\"arinen (2005) provides an alternative where this normalization constant is not required. The corresponding estimating equations become linear for an exponential family. The score matching estimator is shown to be consistent and asymptotically normally distributed for such models, although not necessarily efficient. Gaussian linear concentration models are examples of such families. For linear concentration models that are also linear in the covariance we show that the score matching estimator is identical to the maximum likelihood estimator, hence in such cases it is also efficient. Gaussian graphical models and graphical models with symmetries form particularly interesting subclasses of linear concentration models and we investigate the potential use of the score matching estimator for this case

Finding robust solutions to stable marriage

We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An (a,b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs. In this context, we define the most robust stable matching as a (1,b)-supermatch where b is minimum. We show that checking whether a given stable matching is a (1,b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches

“Style City” How London became a Fashion Capital

The book explains and explores in a critical as well as a celebratory way the birth of today’s London Designer identity and the evolution of London Fashion Week. It starts in the mid-Seventies when the cultural recognition of British fashion designers scarcely existed. It covers the rise of Vivienne Westwood, John Galliano, Katharine Hamnett and many others who were to become household names. But at the same time, it relates the persistent failure of the British government and the clothing industry to respond to successive opportunities, leaving designers to create an industry for themselves. It ends with British designers established worldwide and London Fashion Week as one of the world’s four premier fashion events

On the Invariance of G\"odel's Second Theorem with regard to Numberings

The prevalent interpretation of G\"odel's Second Theorem states that a sufficiently adequate and consistent theory does not prove its consistency. It is however not entirely clear how to justify this informal reading, as the formulation of the underlying mathematical theorem depends on several arbitrary formalisation choices. In this paper I examine the theorem's dependency regarding G\"odel numberings. I introduce deviant numberings, yielding provability predicates satisfying L\"ob's conditions, which result in provable consistency sentences. According to the main result of this paper however, these "counterexamples" do not refute the theorem's prevalent interpretation, since once a natural class of admissible numberings is singled out, invariance is maintained.Comment: Forthcoming in The Review of Symbolic Logi