RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections

In high dimensions, the classical Hotelling's $T^2$ test tends to have low power or becomes undefined due to singularity of the sample covariance matrix. In this paper, this problem is overcome by projecting the data matrix onto lower dimensional subspaces through multiplication by random matrices. We propose RAPTT (RAndom Projection T-Test), an exact test for equality of means of two normal populations based on projected lower dimensional data. RAPTT does not require any constraints on the dimension of the data or the sample size. A simulation study indicates that in high dimensions the power of this test is often greater than that of competing tests. The advantage of RAPTT is illustrated on high-dimensional gene expression data involving the discrimination of tumor and normal colon tissues

Expandable Factor Analysis

Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable inference in factor models when the number of factors is unknown. The method relies on a continuous shrinkage prior for efficient maximum a posteriori estimation of a low-rank and sparse loadings matrix. The structure of the prior leads to an estimation algorithm that accommodates uncertainty in the number of factors. We propose an information criterion to select the hyperparameters of the prior. Expandable factor analysis has better false discovery rates and true positive rates than its competitors across diverse simulations. We apply the proposed approach to a gene expression study of aging in mice, illustrating superior results relative to four competing methods.Comment: 28 pages, 4 figure

The Importance of Being Early

The assumption that the penalty for being early is less than that for being late was put forward by Vickrey (1963) who analyzed how commuters compare penalties in the form of schedule delay (due to peak hour congestion), against penalties in the form of reaching their destination (ahead or behind their desired time of arrival). This assumption has been tested by many researchers since then for various applications, especially in modeling congestion pricing (Arnott et al., 1990) where it is critical to understand the tradeoff between schedule delay and travel delay. Key findings are summarized in the second section of this paper. This research aims to test this hypothesis of earliness being less expensive than lateness using empirical data at different levels and across different regions. New methods to estimate the ratio of earliness to lateness for different types of datasets are developed, which could be used by agencies to implement control policies like congestion pricing or other schemes more accurately. Travel survey data from metropolitan areas provide individual travel patterns while loop detector data provide link level traffic flow data.Schedule Delay, Travel Time, Traffic, Travel Behavior.

Structure of the species-energy relationship

The relationship between energy availability and species richness (the species-energy relationship) is one of the best documented macroecological phenomena. However, the structure of species distribution along the gradient, the proximate driver of the relationship, is poorly known. Here, using data on the distribution of birds in southern Africa, for which species richness increases linearly with energy availability, we provide an explicit determination of this structure. We show that most species exhibit increasing occupancy towards more productive regions (occurring in more grid cells within a productivity class). However, average reporting rates per species within occupied grid cells, a correlate of local density, do not show a similar increase. The mean range of used energy levels and the mean geographical range size of species in southern Africa decreases along the energy gradient, as most species are present at high productivity levels but only some can extend their ranges towards lower levels. Species turnover among grid cells consequently decreases towards high energy levels. In summary, these patterns support the hypothesis that higher productivity leads to more species by increasing the probability of occurrence of resources that enable the persistence of viable populations, without necessarily affecting local population densities

Efficient Defenses Against Adversarial Attacks

Following the recent adoption of deep neural networks (DNN) accross a wide range of applications, adversarial attacks against these models have proven to be an indisputable threat. Adversarial samples are crafted with a deliberate intention of undermining a system. In the case of DNNs, the lack of better understanding of their working has prevented the development of efficient defenses. In this paper, we propose a new defense method based on practical observations which is easy to integrate into models and performs better than state-of-the-art defenses. Our proposed solution is meant to reinforce the structure of a DNN, making its prediction more stable and less likely to be fooled by adversarial samples. We conduct an extensive experimental study proving the efficiency of our method against multiple attacks, comparing it to numerous defenses, both in white-box and black-box setups. Additionally, the implementation of our method brings almost no overhead to the training procedure, while maintaining the prediction performance of the original model on clean samples.Comment: 16 page

Dynamic systems approaches and levels of analysis in the nervous system.

Various analyses are applied to physiological signals. While epistemological diversity is necessary to address effects at different levels, there is often a sense of competition between analyses rather than integration. This is evidenced by the differences in the criteria needed to claim understanding in different approaches. In the nervous system, neuronal analyses that attempt to explain network outputs in cellular and synaptic terms are rightly criticized as being insufficient to explain global effects, emergent or otherwise, while higher-level statistical and mathematical analyses can provide quantitative descriptions of outputs but can only hypothesize on their underlying mechanisms. The major gap in neuroscience is arguably our inability to translate what should be seen as complementary effects between levels. We thus ultimately need approaches that allow us to bridge between different spatial and temporal levels. Analytical approaches derived from critical phenomena in the physical sciences are increasingly being applied to physiological systems, including the nervous system, and claim to provide novel insight into physiological mechanisms and opportunities for their control. Analyses of criticality have suggested several important insights that should be considered in cellular analyses. However, there is a mismatch between lower-level neurophysiological approaches and statistical phenomenological analyses that assume that lower-level effects can be abstracted away, which means that these effects are unknown or inaccessible to experimentalists. As a result experimental designs often generate data that is insufficient for analyses of criticality. This review considers the relevance of insights from analyses of criticality to neuronal network analyses, and highlights that to move the analyses forward and close the gap between the theoretical and neurobiological levels, it is necessary to consider that effects at each level are complementary rather than in competition.Vipin Srivastava would like to thank the Department of Science and Technology, Government of India for support under their cognitive science research initiative.This is the final published version. It was originally published by Frontiers at http://journal.frontiersin.org/Journal/10.3389/fphys.2013.00015/full