SciPy is an open source scientific computing library for the Python programming language. SciPy 1.0 was released in late 2017, about 16 years after the original version 0.1 release. SciPy has become a de facto standard for leveraging scientific algorithms in the Python programming language, with more than 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories, and millions of downloads per year. This includes usage of SciPy in almost half of all machine learning projects on GitHub, and usage by high profile projects including LIGO gravitational wave analysis and creation of the first-ever image of a black hole (M87). The library includes functionality spanning clustering, Fourier transforms, integration, interpolation, file I/O, linear algebra, image processing, orthogonal distance regression, minimization algorithms, signal processing, sparse matrix handling, computational geometry, and statistics. In this work, we provide an overview of the capabilities and development practices of the SciPy library and highlight some recent technical developments.

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SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python

Publisher Summary This chapter focuses on the modern notion of short-term memory, called working memory. Working memory refers to the temporary maintenance of information that was just experienced or just retrieved from long-term memory but no longer exists in the external environment. These internal representations are short-lived, but can be maintained for longer periods of time through active rehearsal strategies, and can be subjected to various operations that manipulate the information in such a way that makes it useful for goal-directed behavior. Working memory is a system that is critically important in cognition and seems necessary in the course of performing many other cognitive functions, such as reasoning, language comprehension, planning, and spatial processing. This chapter demonstrates the functional importance of dopamine to working memory function in several ways. Elucidation of the cognitive and neural mechanisms underlying human working memory is an important focus of cognitive neuroscience and neurology for much of the past decade. One conclusion that arises from research is that working memory, a faculty that enables temporary storage and manipulation of information in the service of behavioral goals, can be viewed as neither a unitary, nor a dedicated system. Data from numerous neuropsychological and neurophysiological studies in animals and humans demonstrates that a network of brain regions, including the prefrontal cortex, is critical for the active maintenance of internal representations.

Chapter 11 Working memory

Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

With the increase in genomewide experiments and the sequencing of multiple genomes, the analysis of large data sets has become commonplace in biology. It is often the case that thousands of features in a genomewide data set are tested against some null hypothesis, where a number of features are expected to be significant. Here we propose an approach to measuring statistical significance in these genomewide studies based on the concept of the false discovery rate. This approach offers a sensible balance between the number of true and false positives that is automatically calibrated and easily interpreted. In doing so, a measure of statistical significance called the q value is associated with each tested feature. The q value is similar to the well known p value, except it is a measure of significance in terms of the false discovery rate rather than the false positive rate. Our approach avoids a flood of false positive results, while offering a more liberal criterion than what has been used in genome scans for linkage.

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Statistical significance for genomewide studies

Boosting is one of the most important recent developments in classification methodology. Boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced. For many classification algorithms, this simple strategy results in dramatic improvements in performance. We show that this seemingly mysterious phenomenon can be understood in terms of well-known statistical principles, namely additive modeling and maximum likelihood. For the two-class problem, boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum Bernoulli likelihood as a criterion. We develop more direct approximations and show that they exhibit nearly identical results to boosting. Direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations, and far superior in some. We suggest a minor modification to boosting that can reduce computation, often by factors of 10 to 50. Finally, we apply these insights to produce an alternative formulation of boosting decision trees. This approach, based on best-first truncated tree induction, often leads to better performance, and can provide interpretable descriptions of the aggregate decision rule. It is also much faster computationally, making it more suitable to large-scale data mining applications.

/pdf/additive-logistic-regression-a-statistical-view-of-boosting-1d1knlp5yb.pdf

Additive Logistic Regression : A Statistical View of Boosting

We examine Cosmic Microwave Background (CMB) temperature power spectra from the BOOMERANG, MAXIMA, and DASI experiments. We non-parametrically estimate the true power spectrum with no model assumptions. This is a significant departure from previous research which used either cosmological models or some other parameterized form (e.g. parabolic fits). Our non-parametric estimate is practically indistinguishable from the best fit cosmological model, thus lending independent support to the underlying physics that governs these models. We also generate a confidence set for the non-parametric fit and extract confidence intervals for the numbers, locations, and heights of peaks and the successive peak-to-peak height ratios. At the 95%, 68%, and 40% confidence levels, we find functions that fit the data with one, two, and three peaks respectively (0 8 sigma level. If we assume that there are three peaks in the data, we find their locations to be within l_1 = (118,300), l_2 = (377,650), and l_3 = (597,900). We find the ratio of the first peak-height to the second (Delta T_1)/(Delta T_2)^2= (1.06, 4.27) and the second to the third (Delta T_2)/(Delta T_3)^2= (0.41, 2.5). All measurements are for 95% confidence. If the standard errors on the temperature measurements were reduced to a third of what they are currently, as we expect to be achieved by the MAP and Planck CMB experiments, we could eliminate two-peak models at the 95% confidence limit. The non-parametric methodology discussed in this paper has many astrophysical applications.

A Non-parametric Analysis of the CMB Power Spectrum

We present initial results on the use of Mixture Models for density estimation in large astronomical databases. We provide herein both the theoretical and experimental background for using a mixture model of Gaussians based on the Expectation Maximization (EM) Algorithm. Applying these analyses to simulated data sets we show that the EM algorithm - using the both the AIC & BIC penalized likelihood to score the fit - can out-perform the best kernel density estimate of the distribution while requiring no ``fine-tuning'' of the input algorithm parameters. We find that EM can accurately recover the underlying density distribution from point processes thus providing an efficient adaptive smoothing method for astronomical source catalogs. To demonstrate the general application of this statistic to astrophysical problems we consider two cases of density estimation; the clustering of galaxies in redshift space and the clustering of stars in color space. From these data we show that EM provides an adaptive smoothing of the distribution of galaxies in redshift space (describing accurately both the small and large-scale features within the data) and a means of identifying outliers in multi-dimensional color-color space (e.g. for the identification of high redshift QSOs). Automated tools such as those based on the EM algorithm will be needed in the analysis of the next generation of astronomical catalogs (2MASS, FIRST, PLANCK, SDSS) and ultimately in the development of the National Virtual Observatory.

Computational AstroStatistics: Fast Algorithms and Efficient Statistics for Density Estimation in Large Astronomical Datasets

Estimation of Correlations in Large Samples

With the onset of large, systematically selected spectroscopic surveys we have the opportunity to understand the distribution and evolution of galaxies in terms of the mix of their spectral population. In this proceedings we describe a series of statistical techniques, ranging from Karhunen-Lo’eve transform to wavelet transforms, that are being applied to the spectra from the Sloan Digital Sky Survey in order to define a statistically robust and objective spectral classification scheme. The approach we describe for the classification of galaxy, stellar and QSO spectra is at the interface of astrophysics, statistics and computer science. To enable these techniques to be applied and interpreted successfully requires both robust statistical inference together with fast and efficient computer algorithms. Combining these three disciplines we can fully exploit the wealth of physical information present within the SDSS spectra.

Automated Classification Techniques for Large Spectroscopic Surveys

Traditionally, statistical computing courses have taught the syntax of a particular programming language or specific statistical computation methods. Since the publication of Nolan and Temple Lang ...

https://www.tandfonline.com/doi/pdf/10.1080/10691898.2020.1845109

Christopher R. Genovese

Papers

A Non-parametric Analysis of the CMB Power Spectrum

Computational AstroStatistics: Fast Algorithms and Efficient Statistics for Density Estimation in Large Astronomical Datasets

Estimation of Correlations in Large Samples

Automated Classification Techniques for Large Spectroscopic Surveys

Expanding the scope of statistical computing: Training statisticians to be software engineers