A Bayesian hierarchical framework with a Gaussian copula and a generalized extreme value (GEV) marginal distribution is proposed for the description of spatial dependencies in data. This spatial copula model was applied to extreme summer temperatures over the Extremadura Region, in the southwest of Spain, during the period 1980–2015, and compared with the spatial noncopula model. The Bayesian hierarchical model was implemented with a Monte Carlo Markov Chain (MCMC) method that allows the distribution of the model’s parameters to be estimated. The results show the GEV distribution’s shape parameter to take constant negative values, the location parameter to be altitude dependent, and the scale parameter values to be concentrated around the same value throughout the region. Further, the spatial copula model chosen presents lower deviance information criterion (DIC) values when spatial distributions are assumed for the GEV distribution’s location and scale parameters than when the scale parameter is taken to be constant over the region.
Over the last years, a surge of empirical studies converged on complexity-related measures as reliable markers of consciousness across many different conditions, such as sleep, anesthesia, hallucinatory states, coma, and related disorders. Most of these measures were independently proposed by researchers endorsing disparate frameworks and employing different methods and techniques. Since this body of evidence has not been systematically reviewed and coherently organized so far, this positive trend has remained somewhat below the radar. The aim of this paper is to make this consilience of evidence in the science of consciousness explicit. We start with a systematic assessment of the growing literature on complexity-related measures and identify their common denominator, tracing it back to core theoretical principles and predictions put forward more than 20 years ago. In doing this, we highlight a consistent trajectory spanning two decades of consciousness research and provide a provisional taxonomy of the present literature. Finally, we consider all of the above as a positive ground to approach new questions and devise future experiments that may help consolidate and further develop a promising field where empirical research on consciousness appears to have, so far, naturally converged.
Making scientific information machine-readable greatly facilitates its re-use. Many scientific articles have the goal to test a hypothesis, so making the tests of statistical predictions easier to find and access could be very beneficial. We propose an approach that can be used to make hypothesis tests machine readable. We believe there are two benefits to specifying a hypothesis test in a way that a computer can evaluate whether the statistical prediction is corroborated or not. First, hypothesis test will become more transparent, falsifiable, and rigorous. Second, scientists will benefit if information related to hypothesis tests in scientific articles is easily findable and re-usable, for example when performing meta-analyses, during peer review, and when examining meta-scientific research questions. We examine what a machine readable hypothesis test should look like, and demonstrate the feasibility of machine readable hypothesis tests in a real-life example using the fully operational prototype R package scienceverse.
Spatial Statistics and Disease Mapping Paper Session at the 2016 American Association of Geographers Annual Meeting.https://github.com/maps-apps-n/geography-thesis/blob/master/TBIncidenceConfPaper.pdf tl;dr A multi-variate multi-level regression analysis proposes primary schools as major hotspot sources of TB incidence in Bolivia per geographical coverage .
We present a new paradigm for Neural ODE algorithms, called ODEtoODE, where time-dependent parameters of the main flow evolve according to a matrix flow on the orthogonal group O(d). This nested system of two flows, where the parameter-flow is constrained to lie on the compact manifold, provides stability and effectiveness of training and provably solves the gradient vanishing-explosion problem which is intrinsically related to training deep neural network architectures such as Neural ODEs. Consequently, it leads to better downstream models, as we show on the example of training reinforcement learning policies with evolution strategies, and in the supervised learning setting, by comparing with previous SOTA baselines. We provide strong convergence results for our proposed mechanism that are independent of the depth of the network, supporting our empirical studies. Our results show an intriguing connection between the theory of deep neural networks and the field of matrix flows on compact manifolds.
Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient, constant memory backpropagation. Neural ODEs are universal approximators only when they are non-autonomous, that is, the dynamics depends explicitly on time. We propose a novel family of Neural ODEs with time-varying weights, where time-dependence is non-parametric, and the smoothness of weight trajectories can be explicitly controlled to allow a tradeoff between expressiveness and efficiency. Using this enhanced expressiveness, we outperform previous Neural ODE variants in both speed and representational capacity, ultimately outperforming standard ResNet and CNN models on select image classification and video prediction tasks.
We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can be also used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.
Across scientific disciplines, there is a rapidly growing recognition of the need for more statistically robust, transparent approaches to data visualization. Complementary to this, many scientists have called for plotting tools that accurately and transparently convey key aspects of statistical effects and raw data with minimal distortion. Previously common approaches, such as plotting conditional mean or median barplots together with error-bars have been criticized for distorting effect size, hiding underlying patterns in the raw data, and obscuring the assumptions upon which the most commonly used statistical tests are based. Here we describe a data visualization approach which overcomes these issues, providing maximal statistical information while preserving the desired 'inference at a glance' nature of barplots and other similar visualization devices. These "raincloud plots" can visualize raw data, probability density, and key summary statistics such as median, mean, and relevant confidence intervals in an appealing and flexible format with minimal redundancy. In this tutorial paper, we provide basic demonstrations of the strength of raincloud plots and similar approaches, outline potential modifications for their optimal use, and provide open-source code for their streamlined implementation in R, Python and Matlab ( https://github.com/RainCloudPlots/RainCloudPlots). Readers can investigate the R and Python tutorials interactively in the browser using Binder by Project Jupyter.