Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

Bayesian methods have garnered huge interest in cognitive science as an approach to models of cognition and perception. On the other hand, Bayesian methods for data analysis have not yet made much headway in cognitive science against the institutionalized inertia of 20th century null hypothesis significance testing (NHST). Ironically, specific Bayesian models of cognition and perception may not long endure the ravages of empirical verification, but generic Bayesian methods for data analysis will eventually dominate. It is time that Bayesian data analysis became the norm for empirical methods in cognitive science. This article reviews a fatal flaw of NHST and introduces the reader to some benefits of Bayesian data analysis. The article presents illustrative examples of multiple comparisons in Bayesian analysis of variance and Bayesian approaches to statistical power. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.

Bayesian data analysis.

Cobb’s concern was a long-worrisome circularity in the sociology of science based on the use of bright lines such as p< 0.05: “We teach it because it’s what we do; we do it because it’s what we teach.” This concern was brought to the attention of the ASA Board. The ASA Board was also stimulated by highly visible discussions over the last few years. For example, ScienceNews (Siegfried 2010) wrote: “It’s science’s dirtiest secret: The ‘scientific method’ of testing hypotheses by statistical analysis stands on a flimsy foundation.” A November 2013, article in Phys.org Science News Wire (2013) cited “numerous deep flaws” in null hypothesis significance testing. A ScienceNews article (Siegfried 2014) on February 7, 2014, said “statistical techniques for testing hypotheses...havemore flaws than Facebook’s privacy policies.” Aweek later, statistician and “Simply Statistics” blogger Jeff Leek responded. “The problem is not that people use P-values poorly,” Leek wrote, “it is that the vast majority of data analysis is not performed by people properly trained to perform data analysis” (Leek 2014). That same week, statistician and science writer Regina Nuzzo published an article in Nature entitled “Scientific Method: Statistical Errors” (Nuzzo 2014). That article is nowone of the most highly viewedNature articles, as reported by altmetric.com (http://www.altmetric.com/details/2115792#score). Of course, it was not simply a matter of responding to some articles in print. The statistical community has been deeply concerned about issues of reproducibility and replicability of scientific conclusions. Without getting into definitions and distinctions of these terms, we observe that much confusion and even doubt about the validity of science is arising. Such doubt can lead to radical choices, such as the one taken by the editors of Basic andApplied Social Psychology, who decided to ban p-values (null hypothesis significance testing) (Trafimow and Marks 2015). Misunderstanding or misuse of statistical inference is only one cause of the “reproducibility crisis” (Peng 2015), but to our community, it is an important one. When the ASA Board decided to take up the challenge of developing a policy statement on p-values and statistical significance, it did so recognizing this was not a lightly taken step. The ASA has not previously taken positions on specific matters of statistical practice. The closest the association has come to this is a statement on the use of value-added models (VAM) for educational assessment (Morganstein and Wasserstein 2014) and a statement on risk-limiting post-election audits (American Statistical Association 2010). However, these were truly policy-related statements. The VAM statement addressed a key educational policy issue, acknowledging the complexity of the issues involved, citing limitations of VAMs as effective performance models, and urging that they be developed and interpreted with the involvement of statisticians. The statement on election auditing was also in response to a major but specific policy issue (close elections in 2008), and said that statistically based election audits should become a routine part of election processes. By contrast, the Board envisioned that the ASA statement on p-values and statistical significance would shed light on an aspect of our field that is too often misunderstood and misused in the broader research community, and, in the process, provides the community a service. The intended audience would be researchers, practitioners, and science writers who are not primarily statisticians. Thus, this statementwould be quite different from anything previously attempted. The Board tasked Wasserstein with assembling a group of experts representing a wide variety of points of view. On behalf of the Board, he reached out to more than two dozen such people, all of whom said theywould be happy to be involved. Several expressed doubt about whether agreement could be reached, but those who did said, in effect, that if there was going to be a discussion, they wanted to be involved. Over the course of many months, group members discussed what format the statement should take, tried to more concretely visualize the audience for the statement, and began to find points of agreement. That turned out to be relatively easy to do, but it was just as easy to find points of intense disagreement. The time came for the group to sit down together to hash out these points, and so in October 2015, 20 members of the group met at the ASA Office in Alexandria, Virginia. The 2-day meeting was facilitated by Regina Nuzzo, and by the end of the meeting, a good set of points around which the statement could be built was developed. The next 3 months saw multiple drafts of the statement, reviewed by group members, by Board members (in a lengthy discussion at the November 2015 ASA Board meeting), and by members of the target audience. Finally, on January 29, 2016, the Executive Committee of the ASA approved the statement. The statement development process was lengthier and more controversial than anticipated. For example, there was considerable discussion about how best to address the issue of multiple potential comparisons (Gelman and Loken 2014). We debated at some length the issues behind the words “a p-value near 0.05 taken by itself offers only weak evidence against the null

https://www.tandfonline.com/doi/pdf/10.1080/00031305.2016.1154108

The ASA's Statement on p-Values: Context, Process, and Purpose

The analysis of medical images has been woven into the fabric of the pattern analysis and machine intelligence (PAMI) community since the earliest days of these Transactions. Initially, the efforts in this area were seen as applying pattern analysis and computer vision techniques to another interesting dataset. However, over the last two to three decades, the unique nature of the problems presented within this area of study have led to the development of a new discipline in its own right. Examples of these include: the types of image information that are acquired, the fully three-dimensional image data, the nonrigid nature of object motion and deformation, and the statistical variation of both the underlying normal and abnormal ground truth. In this paper, we look at progress in the field over the last 20 years and suggest some of the challenges that remain for the years to come.

https://hal.inria.fr/inria-00615100/document

Medical image analysis: progress over two decades and the challenges ahead

(1998). Human cognitive abilities: A survey of factor analytic studies. Gifted and Talented International: Vol. 13, No. 2, pp. 97-98.

Human cognitive abilities: A survey of factor analytic studies

October 12, 2022 Title A Fast Clustering Algorithm for High Dimensional Data Based on the Gram Matrix Decomposition Version 3.2.4 Author Shahina Rahman [aut], Valen E. Johnson [aut], Suhasini Subba Rao [aut], Rachael Shudde [aut, cre, trl] Maintainer Rachael Shudde <rachael.shudde@gmail.com> Description Clustering algorithm for high dimensional data. Assuming that P feature measurements on N objects are arranged in an N×P matrix X, this package provides clustering based on the left Gram matrix XX^T. To simulate test data, type ``help('simulate_HD_data')'' and to learn how to use the clustering algorithm, type ``help('RJclust')''. To cite this package, type 'citation(``RJcluster'')'. License GPL (>= 2) Encoding UTF-8 Imports Rcpp (>= 1.0.2), matrixStats, infotheo, rlang, stats, graphics, profvis, mclust, foreach, utils LinkingTo Rcpp, RcppArmadillo Suggests testthat (>= 2.1.0), knitr, rmarkdown RoxygenNote 7.1.1 VignetteBuilder knitr Depends R (>= 2.10) NeedsCompilation yes Repository CRAN Date/Publication 2022-02-14 21:30:02 UTC

Package ‘RJcluster’

Clustering is a challenging problem in machine learning in which one attempts to group <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> objects into <inline-formula> <tex-math notation="LaTeX">$K_{0}$ </tex-math></inline-formula> groups based on <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> features measured on each object. In this article, we examine the case where <inline-formula> <tex-math notation="LaTeX">$N \ll P$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$K_{0}$ </tex-math></inline-formula> is not known. Clustering in such high dimensional, small sample size settings has numerous applications in biology, medicine, the social sciences, clinical trials, and other scientific and experimental fields. Whereas most existing clustering algorithms either require the number of clusters to be known a priori or are sensitive to the choice of tuning parameters, our method does not require the prior specification of <inline-formula> <tex-math notation="LaTeX">$K_{0}$ </tex-math></inline-formula> or any tuning parameters. This represents an important advantage for our method because training data are not available in the applications we consider (i.e., in unsupervised learning problems). Without training data, estimating <inline-formula> <tex-math notation="LaTeX">$K_{0}$ </tex-math></inline-formula> and other hyperparameters–and thus applying alternative clustering algorithms–can be difficult and lead to inaccurate results. Our method is based on a simple transformation of the Gram matrix and application of the strong law of large numbers to the transformed matrix. If the correlation between features decays as the number of features grows, we show that the transformed feature vectors concentrate tightly around their respective cluster expectations in a low-dimensional space. This result simplifies the detection and visualization of the unknown cluster configuration. We illustrate the algorithm by applying it to 32 benchmarked microarray datasets, each containing thousands of genomic features measured on a relatively small number of tissue samples. Compared to 21 other commonly used clustering methods, we find that the proposed algorithm is faster and twice as accurate in determining the “best” cluster configuration.

https://ieeexplore.ieee.org/ielx7/6287639/6514899/09934902.pdf

A Hyperparameter-Free, Fast and Efficient Framework to Detect Clusters From Limited Samples Based on Ultra High-Dimensional Features

Uniformly most powerful Bayesian tests (UMPBT's) are an objective class of Bayesian hypothesis tests that can be considered the Bayesian counterpart of classical uniformly most powerful tests. Because the rejection regions of UMPBT's can be matched to the rejection regions of classical uniformly most powerful tests (UMPTs), UMPBT's provide a mechanism for calibrating Bayesian evidence thresholds, Bayes factors, classical significance levels and p-values. The purpose of this article is to expand the application of UMPBT's outside the class of exponential family models. Specifically, we introduce sufficient conditions for the existence of UMPBT's and propose a unified approach for their derivation. An important application of our methodology is the extension of UMPBT's to testing whether the non-centrality parameter of a chi-squared distribution is zero. The resulting tests have broad applicability, providing default alternative hypotheses to compute Bayes factors in, for example, Pearson's chi-squared test for goodness-of-fit, tests of independence in contingency tables, and likelihood ratio, score and Wald tests.

/pdf/on-the-existence-of-uniformly-most-powerful-bayesian-tests-3pjjgzq06i.pdf

On the Existence of Uniformly Most Powerful Bayesian Tests With Application to Non-Central Chi-Squared Tests.

days (range, 34-71 days). The removal of the tumor volume from analysis was possible using a threshold planning dose. The median of the mean standard uptake value in the lung that received 0-5 Gy was 0.51 (range, 0.35-1.15), 5-10 Gy was 0.77 (range, 0.40-1.36), 10-20 Gy was 0.80 (range, 0.40-1.69), and >20 Gy was 1.08 (range, 0.55-2.70). A hierarchical linear regression model of the radiation dose and normalized FDG uptake per case found an adequate fit with the linear model, and the addition of quadratic and logarithmic functions did not improve the fit. The 18 cases had a posterior mean of slopes range of 0.0011-0.064. The slope of this relationship varied over an order of magnitude, reflecting the range of the underlying pulmonary biological response to radiation among the study population. Matthew McCurdy1,2, Josue Martinez3, Rick Castillo4, Nicolas Zouain2, and Thomas Guerrero4 1Baylor College of Medicine, Houston, TX, 2University of North Dakota School of Medicine & Health Sciences, Fargo and Grand Forks, ND 3Texas A&M University, College Station, TX, 4The University of Texas M.D. Anderson Cancer Center, Houston, TX

http://www.drzouain.com/Upload/file_56_4.pdf

Radiation Pneumonitis: Pulmonary Metabolic Response to Radiation in Lung Cancer Patients

Efficient variable selection in high-dimensional cancer genomic studies is critical for discovering genes associated with specific cancer types and for predicting response to treatment. Censored survival data is prevalent in such studies. In this article we introduce a Bayesian variable selection procedure that uses a mixture prior composed of a point mass at zero and an inverse moment prior in conjunction with the partial likelihood defined by the Cox proportional hazard model. The procedure is implemented in the R package BVSNLP, which supports parallel computing and uses a stochastic search method to explore the model space. Bayesian model averaging is used for prediction. The proposed algorithm provides better performance than other variable selection procedures in simulation studies, and appears to provide more consistent variable selection when applied to actual genomic datasets.

Valen E. Johnson

Papers

Package ‘RJcluster’

A Hyperparameter-Free, Fast and Efficient Framework to Detect Clusters From Limited Samples Based on Ultra High-Dimensional Features

On the Existence of Uniformly Most Powerful Bayesian Tests With Application to Non-Central Chi-Squared Tests.

Radiation Pneumonitis: Pulmonary Metabolic Response to Radiation in Lung Cancer Patients

Bayesian Variable Selection in High Dimensional Survival Time Cancer Genomic Datasets using Nonlocal Priors