Human Papillomavirus: How Social Ideologies Influence Medical Policy and Care

The purpose of this paper is to discuss the ways in which new advances in the production of a vaccine against human papillomavirus (HPV) have been received by both the general public and the medical community. Despite its high prevalence in the general population, as a sexually transmitted infection, there is a great deal of shame and stigma associated with contracting the virus (Waller, et. al. 2007). HPV is a disease of disparities in that ethnic and sexual minorities are disproportionately affected. Since the HPV vaccine is most effective at both a younger age, and before the first sexual experience, it is important to protect the future sexual health of individuals. The debate is still ongoing in many states about whether the HPV vaccine should be a part of required school vaccinations for those entering the sixth grade. Many moral conservatives fear that forced vaccination infringes on parental rights and encourages sexual promiscuity before marriage. Abstinence-only messages being taught in schools has only served to amplify a sex-negative ideology in American culture. It is important for health care professionals to be aware of the social perspective of HPV and address these concerns, especially with their at risk patients. By addressing disparities, parent and provider views of vaccination, and sexual stigmas, vaccine uptake in all adolescents will be improved. Implementing a vaccine mandate for school entry will ensure that those at most risk of being affected will be reached

Online Learning with Multiple Operator-valued Kernels

We consider the problem of learning a vector-valued function f in an online learning setting. The function f is assumed to lie in a reproducing Hilbert space of operator-valued kernels. We describe two online algorithms for learning f while taking into account the output structure. A first contribution is an algorithm, ONORMA, that extends the standard kernel-based online learning algorithm NORMA from scalar-valued to operator-valued setting. We report a cumulative error bound that holds both for classification and regression. We then define a second algorithm, MONORMA, which addresses the limitation of pre-defining the output structure in ONORMA by learning sequentially a linear combination of operator-valued kernels. Our experiments show that the proposed algorithms achieve good performance results with low computational cost

M-Power Regularized Least Squares Regression

Regularization is used to find a solution that both fits the data and is sufficiently smooth, and thereby is very effective for designing and refining learning algorithms. But the influence of its exponent remains poorly understood. In particular, it is unclear how the exponent of the reproducing kernel Hilbert space~(RKHS) regularization term affects the accuracy and the efficiency of kernel-based learning algorithms. Here we consider regularized least squares regression (RLSR) with an RKHS regularization raised to the power of m, where m is a variable real exponent. We design an efficient algorithm for solving the associated minimization problem, we provide a theoretical analysis of its stability, and we compare its advantage with respect to computational complexity, speed of convergence and prediction accuracy to the classical kernel ridge regression algorithm where the regularization exponent m is fixed at 2. Our results show that the m-power RLSR problem can be solved efficiently, and support the suggestion that one can use a regularization term that grows significantly slower than the standard quadratic growth in the RKHS norm

Analysis of the limiting spectral measure of large random matrices of the separable covariance type

Consider the random matrix $\Sigma = D^{1/2} X \widetilde D^{1/2}$ where $D$ and $\widetilde D$ are deterministic Hermitian nonnegative matrices with respective dimensions $N \times N$ and $n \times n$, and where $X$ is a random matrix with independent and identically distributed centered elements with variance $1/n$. Assume that the dimensions $N$ and $n$ grow to infinity at the same pace, and that the spectral measures of $D$ and $\widetilde D$ converge as $N,n \to\infty$ towards two probability measures. Then it is known that the spectral measure of $\Sigma\Sigma^*$ converges towards a probability measure $\mu$ characterized by its Stieltjes Transform. In this paper, it is shown that $\mu$ has a density away from zero, this density is analytical wherever it is positive, and it behaves in most cases as $\sqrt{|x - a|}$ near an edge $a$ of its support. A complete characterization of the support of $\mu$ is also provided. \\ Beside its mathematical interest, this analysis finds applications in a certain class of statistical estimation problems.Comment: Correction of the proof of Lemma 3.

A Primer on Causality in Data Science

Many questions in Data Science are fundamentally causal in that our objective is to learn the effect of some exposure, randomized or not, on an outcome interest. Even studies that are seemingly non-causal, such as those with the goal of prediction or prevalence estimation, have causal elements, including differential censoring or measurement. As a result, we, as Data Scientists, need to consider the underlying causal mechanisms that gave rise to the data, rather than simply the pattern or association observed in those data. In this work, we review the 'Causal Roadmap' of Petersen and van der Laan (2014) to provide an introduction to some key concepts in causal inference. Similar to other causal frameworks, the steps of the Roadmap include clearly stating the scientific question, defining of the causal model, translating the scientific question into a causal parameter, assessing the assumptions needed to express the causal parameter as a statistical estimand, implementation of statistical estimators including parametric and semi-parametric methods, and interpretation of our findings. We believe that using such a framework in Data Science will help to ensure that our statistical analyses are guided by the scientific question driving our research, while avoiding over-interpreting our results. We focus on the effect of an exposure occurring at a single time point and highlight the use of targeted maximum likelihood estimation (TMLE) with Super Learner.Comment: 26 pages (with references); 4 figure

Institutions and Economic Outcomes: A Dominance Based Analysis of Causality and Multivariate Welfare With Discrete and Continuous Variables

One of the central issues in welfare economics is the measurement of overall wellbeing and, to this end, the interaction between institutions (polity) and growth is paramount. Individual welfare depends on both economic and political factors but the continuous nature of economic variables combined with the discrete nature of political ones renders conventional multivariate techniques problematic. In this paper, we propose a multivariate dominance test based on the comparison of mixtures of continuous and discrete distributions to examine changes in welfare. Our results suggest that, while economic growth exerted a positive impact from 1960 to 2000, declines in polity over the earlier part of this period were sufficient to produce a decline in overall wellbeing until the mid-1970s. Subsequent increases in polity then reversed the trend and, ultimately, wellbeing in 2000 was higher than that in 1960. To be sure, economic and political variables are correlated and, based on the dominance of polity in our multivariate results, we conjecture that this correlation is predominantly due to a causal link from polity to growth. While the development literature is rife with debates over whether it is institutions that cause growth or growth that causes institutions, we argue that the relevant question is not which hypothesis is correct but, rather, which hypothesis dominates. Since standard regression techniques have difficulty capturing non-linear dependence, especially when one of the variables is an index with limited variation, we propose a causality dominance test to examine this aspect of the growth-institutions nexus and indeed find evidence that the causal effects of polity on growth dominate those of growth on polity, particularly when the data are population weighted.Growth, Polity, Causality, Multivariate Wellbeing

Deterministic equivalents for certain functionals of large random matrices

Consider an $N\times n$ random matrix $Y_n=(Y^n_{ij})$ where the entries are given by $Y^n_{ij}=\frac{\sigma_{ij}(n)}{\sqrt{n}}X^n_{ij}$, the $X^n_{ij}$ being independent and identically distributed, centered with unit variance and satisfying some mild moment assumption. Consider now a deterministic $N\times n$ matrix A_n whose columns and rows are uniformly bounded in the Euclidean norm. Let $\Sigma_n=Y_n+A_n$. We prove in this article that there exists a deterministic $N\times N$ matrix-valued function T_n(z) analytic in $\mathbb{C}-\mathbb{R}^+$ such that, almost surely, $$\lim_{n\to+\infty,N/n\to c}\biggl(\frac{1}{N}\operatorname {Trace}(\Sigma_n\Sigma_n^T-zI_N)^{-1}-\frac{1}{N}\operatorname {Trace}T_n(z)\biggr)=0.$$ Otherwise stated, there exists a deterministic equivalent to the empirical Stieltjes transform of the distribution of the eigenvalues of $\Sigma_n\Sigma_n^T$. For each n, the entries of matrix T_n(z) are defined as the unique solutions of a certain system of nonlinear functional equations. It is also proved that $\frac{1}{N}\operatorname {Trace} T_n(z)$ is the Stieltjes transform of a probability measure $\pi_n(d\lambda)$, and that for every bounded continuous function f, the following convergence holds almost surely $$\frac{1}{N}\sum_{k=1}^Nf(\lambda_k)-\int_0^{\infty}f(\lambda)\pi _n(d\lambda)\mathop {\longrightarrow}_{n\to\infty}0,$$ where the $(\lambda_k)_{1\le k\le N}$ are the eigenvalues of $\Sigma_n\Sigma_n^T$. This work is motivated by the context of performance evaluation of multiple inputs/multiple output (MIMO) wireless digital communication channels. As an application, we derive a deterministic equivalent to the mutual information: $$C_n(\sigma^2)=\frac{1}{N}\mathbb{E}\log \det\biggl(I_N+\frac{\Sigma_n\Sigma_n^T}{\sigma^2}\biggr),$$ where $\sigma^2$ is a known parameter.Comment: Published at http://dx.doi.org/10.1214/105051606000000925 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org