The usage of psychological networks that conceptualize behavior as a complex interplay of psychological and other components has gained increasing popularity in various research fields. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online.

/pdf/estimating-psychological-networks-and-their-accuracy-a-ljt6ufq2za.pdf

Estimating Psychological Networks and their Accuracy : A tutorial paper

We propose an independence criterion based on the eigen-spectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

Measuring statistical dependence with Hilbert-Schmidt norms

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.

Machine Learning for Fluid Mechanics

Recent years have seen an emergence of network modeling applied to moods, attitudes, and problems in the realm of psychology. In this framework, psychological variables are understood to directly affect each other rather than being caused by an unobserved latent entity. In this tutorial, we introduce the reader to estimating the most popular network model for psychological data: the partial correlation network. We describe how regularization techniques can be used to efficiently estimate a parsimonious and interpretable network structure in psychological data. We show how to perform these analyses in R and demonstrate the method in an empirical example on post-traumatic stress disorder data. In addition, we discuss the effect of the hyperparameter that needs to be manually set by the researcher, how to handle non-normal data, how to determine the required sample size for a network analysis, and provide a checklist with potential solutions for problems that can arise when estimating regularized partial correlation networks.

/pdf/a-tutorial-on-regularized-partial-correlation-networks-4vtbhqb1xk.pdf

A Tutorial on Regularized Partial Correlation Networks

The usage of psychological networks that conceptualize psychological behavior as a complex interplay of psychological and other components has gained increasing popularity in various fields of psychology. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online.

Estimating Psychological Networks and their Accuracy: A Tutorial Paper

Age-frequency distributions of dead skeletal material on the landscape or seabed—information on the time that has elapsed since the death of individuals—provide decadal- to millennial-scale perspectives both on the history of production and on the processes that lead to skeletal disintegration and burial. So far, however, models quantifying the dynamics of skeletal loss have assumed that skeletal production is constant during time-averaged accumulation. Here, to improve inferences in conservation paleobiology and historical ecology, we evaluate the joint effects of temporally variable production and skeletal loss on postmortem age-frequency distributions (AFDs) to determine how to detect fluctuations in production over the recent past from AFDs. We show that, relative to the true timing of past production pulses, the modes of AFDs will be shifted to younger age cohorts, causing the true age of past pulses to be underestimated. This shift in the apparent timing of a past pulse in production will be stronger where loss rates are high and/or the rate of decline in production is slow; also, a single pulse coupled with a declining loss rate can, under some circumstances, generate a bimodal distribution. We apply these models to death assemblages of the bivalve Nuculana taphria from the Southern California continental shelf, finding that: (1) an onshore-offshore gradient in time averaging is dominated by a gradient in the timing of production, reflecting the tracking of shallow-water habitats under a sea-level rise, rather than by a gradient in disintegration and sequestration rates, which remain constant with water depth; and (2) loss-corrected model-based estimates of the timing of past production are in good agreement with likely past changes in local production based on an independent sea-level curve.

https://bioone.org/journals/Paleobiology/volume-42/issue-1/pab.2015.30/Inferring-skeletal-production-from-time-averaged-assemblages--skeletal-loss/10.1017/pab.2015.30.pdf

Inferring skeletal production from time-averaged assemblages: skeletal loss pulls the timing of production pulses towards the modern period

We propose the group knockoff filter, a method for false discovery rate control in a linear regression setting where the features are grouped, and we would like to select a set of relevant groups which have a nonzero effect on the response. By considering the set of true and false discoveries at the group level, this method gains power relative to sparse regression methods. We also apply our method to the multitask regression problem where multiple response variables share similar sparsity patterns across the set of possible features. Empirically, the group knockoff filter successfully controls false discoveries at the group level in both settings, with substantially more discoveries made by leveraging the group structure.

The knockoff filter for FDR control in group-sparse and multitask regression

Summary
 In many practical applications of multiple testing, there are natural ways to partition the hypotheses into groups by using the structural, spatial or temporal relatedness of the hypotheses, and this prior knowledge is not used in the classical Benjamini–Hochberg procedure for controlling the false discovery rate (FDR). When one can define (possibly several) such partitions, it may be desirable to control the group FDR simultaneously for all partitions (as special cases, the ‘finest’ partition divides the n hypotheses into n groups of one hypothesis each, and this corresponds to controlling the usual notion of FDR, whereas the ‘coarsest’ partition puts all n hypotheses into a single group, and this corresponds to testing the global null hypothesis). We introduce the p-filter, which takes as input a list of n p-values and M⩾1 partitions of hypotheses, and produces as output a list of n or fewer discoveries such that the group FDR is provably simultaneously controlled for all partitions. Importantly, since the partitions are arbitrary, our procedure can also handle multiple partitions which are non-hierarchical. The p-filter generalizes two classical procedures—when M=1, choosing the finest partition into n singletons, we exactly recover the Benjamini–Hochberg procedure, whereas, choosing instead the coarsest partition with a single group of size n, we exactly recover the Simes test for the global null hypothesis. We verify our findings with simulations that show how this technique can not only lead to the aforementioned multilayer FDR control but also lead to improved precision of rejected hypotheses. We present some illustrative results from an application to a neuroscience problem with functional magnetic resonance imaging data, where hypotheses are explicitly grouped according to predefined regions of interest in the brain, thus allowing the scientist to employ field-specific prior knowledge explicitly and flexibly.

The p‐filter: multilayer false discovery rate control for grouped hypotheses

Iterative thresholding algorithms seek to optimize a differentiable objective function over a sparsity or rank constraint by alternating between gradient steps that reduce the objective, and thresholding steps that enforce the constraint. This work examines the choice of the thresholding operator, and asks whether it is possible to achieve stronger guarantees than what is possible with hard thresholding. We develop the notion of relative concavity of a thresholding operator, a quantity that characterizes the worst-case convergence performance of any thresholding operator on the target optimization problem. Surprisingly, we find that commonly used thresholding operators, such as hard thresholding and soft thresholding, are suboptimal in terms of worst-case convergence guarantees. Instead, a general class of thresholding operators, lying between hard thresholding and soft thresholding, is shown to be optimal with the strongest possible convergence guarantee among all thresholding operators. Examples of this general class includes $\ell_q$ thresholding with appropriate choices of $q$, and a newly defined {\em reciprocal thresholding} operator. We also investigate the implications of the improved optimization guarantee in the statistical setting of sparse linear regression, and show that this new class of thresholding operators attain the optimal rate for computationally efficient estimators, matching the Lasso.

Between hard and soft thresholding: optimal iterative thresholding algorithms

We present a new methodology for simultaneous variable selection and parameter estimation in function-on-scalar regression with an ultra-high dimensional predictor vector. We extend the LASSO to functional data in both the $\textit{dense}$ functional setting and the $\textit{sparse}$ functional setting. We provide theoretical guarantees which allow for an exponential number of predictor variables. Simulations are carried out which illustrate the methodology and compare the sparse/functional methods. Using the Framingham Heart Study, we demonstrate how our tools can be used in genome-wide association studies, finding a number of genetic mutations which affect blood pressure and are therefore important for cardiovascular health.

Rina Foygel Barber

Papers

Inferring skeletal production from time-averaged assemblages: skeletal loss pulls the timing of production pulses towards the modern period

The knockoff filter for FDR control in group-sparse and multitask regression

The p‐filter: multilayer false discovery rate control for grouped hypotheses

Between hard and soft thresholding: optimal iterative thresholding algorithms

The Function-on-Scalar LASSO with Applications to Longitudinal GWAS