A-Type KV Channels in Dorsal Root Ganglion Neurons: Diversity, Function, and Dysfunction

A-type voltage-gated potassium (Kv) channels are major regulators of neuronal excitability that have been mainly characterized in the central nervous system. By contrast, there is a paucity of knowledge about the molecular physiology of these Kv channels in the peripheral nervous system, including highly specialized and heterogenous dorsal root ganglion (DRG) neurons. Although all A-type Kv channels display pore-forming subunits with similar structural properties and fast inactivation, their voltage-, and time-dependent properties and modulation are significantly different. These differences ultimately determine distinct physiological roles of diverse A-type Kv channels, and how their dysfunction might contribute to neurological disorders. The importance of A-type Kv channels in DRG neurons is highlighted by recent studies that have linked their dysfunction to persistent pain sensitization. Here, we review the molecular neurophysiology of A-type Kv channels with an emphasis on those that have been identified and investigated in DRG nociceptors (Kv1.4, Kv3.4, and Kv4s). Also, we discuss evidence implicating these Kv channels in neuropathic pain resulting from injury, and present a perspective of outstanding challenges that must be tackled in order to discover novel treatments for intractable pain disorders

Statistical Aspects of Wasserstein Distances

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover the other distribution. They are ubiquitous in mathematics, with a long history that has seen them catalyse core developments in analysis, optimization, and probability. Beyond their intrinsic mathematical richness, they possess attractive features that make them a versatile tool for the statistician: they can be used to derive weak convergence and convergence of moments, and can be easily bounded; they are well-adapted to quantify a natural notion of perturbation of a probability distribution; and they seamlessly incorporate the geometry of the domain of the distributions in question, thus being useful for contrasting complex objects. Consequently, they frequently appear in the development of statistical theory and inferential methodology, and have recently become an object of inference in themselves. In this review, we provide a snapshot of the main concepts involved in Wasserstein distances and optimal transportation, and a succinct overview of some of their many statistical aspects.Comment: Official version available at https://www.annualreviews.org/doi/full/10.1146/annurev-statistics-030718-10493

An Invitation to Statistics in Wasserstein Space

This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph. ; Gives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature. Presents an up to date overview of the state of the art, including some original results, and discusses open problems. Suitable for self-study or to be used as a graduate level course text. Open access

Transportation-Based Functional ANOVA and PCA for Covariance Operators

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Variance (ANOVA) and a Principal Component Analysis (PCA) of covariance operators, respectively. They arise naturally in functional data analysis, where several populations are to be contrasted relative to the nature of their dispersion around their means, rather than relative to their means themselves. We contribute a novel approach based on optimal (multi)transport, where each covariance can be identified with a a centred Gaussian process of corresponding covariance. By means of constructing the optimal simultaneous coupling of these Gaussian processes, we contrast the (linear) maps that achieve it with the identity with respect to a norm-induced distance. The resulting test statistic, calibrated by permutation, is seen to distinctly outperform the state-of-the-art, and to furnish considerable power even under local alternatives. This effect is seen to be genuinely functional, and is related to the potential for perfect discrimination in infinite dimensions. In the event of a rejection of the null hypothesis stipulating equality, a geometric interpretation of the transport maps allows us to construct a (tangent space) PCA revealing the main modes of variation. As a necessary step to developing our methodology, we prove results on the existence and boundedness of optimal multitransport maps. These are of independent interest in the theory of transport of Gaussian processes. The transportation ANOVA and PCA are illustrated on a variety of simulated and real examples.Comment: 33 page

Camp is for Everyone: Intentional Inclusion of Gender-Expansive Teens at Camp

Camp remains a powerful experience for youth of any age, but special care must be taken to ensure camps are supportive of diverse audiences. This article describes the process by which 4-H camp organizers created a welcoming and affirming camp for teen dependents of active duty, retired, or veteran military personnel, especially those campers who identified as non-binary or LGBTQ+. This included careful consideration of language used in recruitment documents, evaluation documents, volunteer and staff training, as well as communication with campers and families. Through careful planning and implementation, the 4-H adventure camps engaged over 90 teens, and survey results showed statistically significant improvements in camper perceptions of self-worth and satisfaction after their camp experience

Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data

Standard causal discovery methods must fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information - for instance, the dynamics describing the effects of causal relations - which is lost when following this approach. We propose Amortized Causal Discovery, a novel framework that leverages such shared dynamics to learn to infer causal relations from time-series data. This enables us to train a single, amortized model that infers causal relations across samples with different underlying causal graphs, and thus makes use of the information that is shared. We demonstrate experimentally that this approach, implemented as a variational model, leads to significant improvements in causal discovery performance, and show how it can be extended to perform well under hidden confounding

Optimal transport: Fast probabilistic approximation with exact solvers.

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances on finite spaces. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including state-of-the-art solvers and entropically penalized versions. It is based on averaging the exact distances between empirical measures generated from independent samples from the original measures and can easily be tuned towards higher accuracy or shorter computation times. To this end, we give non-asymptotic deviation bounds for its accuracy in the case of discrete optimal transport problems. In particular, we show that in many important instances, including images (2D-histograms), the approximation error is independent of the size of the full problem. We present numerical experiments that demonstrate that a very good approximation in typical applications can be obtained in a computation time that is several orders of magnitude smaller than what is required for exact computation of the full problem

Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment

Automated data-driven decision making systems are increasingly being used to assist, or even replace humans in many settings. These systems function by learning from historical decisions, often taken by humans. In order to maximize the utility of these systems (or, classifiers), their training involves minimizing the errors (or, misclassifications) over the given historical data. However, it is quite possible that the optimally trained classifier makes decisions for people belonging to different social groups with different misclassification rates (e.g., misclassification rates for females are higher than for males), thereby placing these groups at an unfair disadvantage. To account for and avoid such unfairness, in this paper, we introduce a new notion of unfairness, disparate mistreatment, which is defined in terms of misclassification rates. We then propose intuitive measures of disparate mistreatment for decision boundary-based classifiers, which can be easily incorporated into their formulation as convex-concave constraints. Experiments on synthetic as well as real world datasets show that our methodology is effective at avoiding disparate mistreatment, often at a small cost in terms of accuracy.Comment: To appear in Proceedings of the 26th International World Wide Web Conference (WWW), 2017. Code available at: https://github.com/mbilalzafar/fair-classificatio

Fairness-Aware Ranking in Search & Recommendation Systems with Application to LinkedIn Talent Search

We present a framework for quantifying and mitigating algorithmic bias in mechanisms designed for ranking individuals, typically used as part of web-scale search and recommendation systems. We first propose complementary measures to quantify bias with respect to protected attributes such as gender and age. We then present algorithms for computing fairness-aware re-ranking of results. For a given search or recommendation task, our algorithms seek to achieve a desired distribution of top ranked results with respect to one or more protected attributes. We show that such a framework can be tailored to achieve fairness criteria such as equality of opportunity and demographic parity depending on the choice of the desired distribution. We evaluate the proposed algorithms via extensive simulations over different parameter choices, and study the effect of fairness-aware ranking on both bias and utility measures. We finally present the online A/B testing results from applying our framework towards representative ranking in LinkedIn Talent Search, and discuss the lessons learned in practice. Our approach resulted in tremendous improvement in the fairness metrics (nearly three fold increase in the number of search queries with representative results) without affecting the business metrics, which paved the way for deployment to 100% of LinkedIn Recruiter users worldwide. Ours is the first large-scale deployed framework for ensuring fairness in the hiring domain, with the potential positive impact for more than 630M LinkedIn members.Comment: This paper has been accepted for publication at ACM KDD 201