Real distance data rarely cooperate: measurements are noisy, observations are missing, and the numbers that result seldom satisfy the triangle inequality. A family of methods exists to correct them, and every one of those methods rests on the same hope — that analysis run on the corrected data is a more faithful surrogate for the truth than analysis run on the raw data. We are not aware of anyone having tested that hope. We test it through the problem of Metric Repair, which asks for the fewest edges whose reweighting restores the triangle inequality. We implement a suite of algorithms, covering the literature and new methods, both with theoretical guarantees and heuristics, and evaluate their performance on real and synthetic data, both inherently non metric and corrupted. We demonstrate that the algorithms' performance is determined predominantly by the type and fraction of corruption, rather than the corruption's magnitude or graph size. We further test the effect of repair on downstream tasks, namely MDS and kNN, and ask if the repair got the result closer to the truth compared to a corrupted instance. In most cases it did not, and we identify the culprit. A small set of edges is not enough. Finding the correct set of edges, be it an injected corruption or a natural non-metricity, is critical. Moreover, deciding on a weight rule impacts performance: on data instances with available metric ground truth, a metric repair algorithm can pull the graph further from the truth, while an oracle access to the true weights helps. Surprisingly, the opposite can be true as well. Setting the weights is not an implementation detail; it is half the problem.

Graph machine learning has enjoyed a meteoric rise in popularity since the introduction of deep learning in graph contexts. This is no surprise due to the ubiquity of graph data in large scale industrial settings. Tacitly assumed in all graph learning tasks is the separation of the graph structure and node features: node features strictly encode individual data while the graph structure consists only of pairwise interactions. The driving belief is that node features are (by themselves) insufficient for these tasks, so benchmark performance accurately reflects improvements in graph learning. In our paper, we challenge this orthodoxy by showing that, surprisingly, node features are oftentimes more-than-sufficient for many common graph benchmarks, breaking this critical assumption. When comparing against a well-tuned feature-only MLP baseline on seven of the most commonly used graph learning datasets, one gains little benefit from using graph structure on five datasets. We posit that these datasets do not benefit considerably from graph learning because the features themselves already contain enough graph information to obviate or substantially reduce the need for the graph. To illustrate this point, we perform a feature study on these datasets and show how the features are responsible for closing the gap between MLP and graph-method performance. Further, in service of introducing better empirical measures of progress for graph neural networks, we present a challenging parametric family of principled synthetic datasets that necessitate graph information for nontrivial performance. Lastly, we section out a subset of real-world datasets that are not trivially solved by an MLP and hence serve as reasonable benchmarks for graph neural networks.

The success of algorithms in the analysis of high-dimensional data is often attributed to the manifold hypothesis, which supposes that this data lie on or near a manifold of much lower dimension. It is often useful to determine or estimate the dimension of this manifold before performing dimension reduction, for instance. Existing methods for dimension estimation are calibrated using a flat unit ball. In this paper, we develop CA-PCA, a version of local PCA based instead on a calibration of a quadratic embedding, acknowledging the curvature of the underlying manifold. Numerous careful experiments show that this adaptation improves the estimator in a wide range of settings.

Optimal transport (OT) and the related Wasserstein metric (W) are powerful and ubiquitous tools for comparing distributions. However, computing pairwise Wasserstein distances rapidly becomes intractable as cohort size grows. An attractive alternative would be to find an embedding space in which pairwise Euclidean distances map to OT distances, akin to standard multidimensional scaling (MDS). We present Wasserstein Wormhole, a transformer-based autoencoder that embeds empirical distributions into a latent space wherein Euclidean distances approximate OT distances. Extending MDS theory, we show that our objective function implies a bound on the error incurred when embedding non-Euclidean distances. Empirically, distances between Wormhole embeddings closely match Wasserstein distances, enabling linear time computation of OT distances. Along with an encoder that maps distributions to embeddings, Wasserstein Wormhole includes a decoder that maps embeddings back to distributions, allowing for operations in the embedding space to generalize to OT spaces, such as Wasserstein barycenter estimation and OT interpolation. By lending scalability and interpretability to OT approaches, Wasserstein Wormhole unlocks new avenues for data analysis in the fields of computational geometry and single-cell biology.

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link prediction included. Claims have also been made about the geometric suitability of particular hierarchical graph datasets to representation in hyperbolic space. Despite these claims, our work makes a surprising discovery: when simple Euclidean models with comparable numbers of parameters are properly trained in the same environment, in most cases, they perform as well, if not better, than all introduced hyperbolic graph representation learning models, even on graph datasets previously claimed to be the most hyperbolic as measured by Gromov δ-hyperbolicity (i.e., perfect trees). This observation gives rise to a simple question: how can this be? We answer this question by taking a careful look at the field of hyperbolic graph representation learning as it stands today, and find that a number of papers fail to diligently present baselines, make faulty modelling assumptions when constructing algorithms, and use misleading metrics to quantify geometry of graph datasets. We take a closer look at each of these three problems, elucidate the issues, perform an analysis of methods, and introduce a parametric family of benchmark datasets to ascertain the applicability of (hyperbolic) graph neural networks.

This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared in (Adler et al, 2018) as a theoretical model for a generic manifold in high dimensions. In particular, we take the covariance function of the Gaussian process to be the heat kernel, and computing the embedding amounts to sketching a matrix representing the heat kernel. The Karhunen-Lo\`eve expansion reveals that the straight-line distances in the embedding approximate the diffusion distance in a probabilistic sense, avoiding the need for sharp cutoffs and maintaining some of the smaller-scale structure. Our method demonstrates further advantage in its robustness to outliers. We justify the approach with both theory and experiments.

Graph machine learning has enjoyed a meteoric rise in popularity since the introduction of deep learning in graph contexts. This is no surprise due to the ubiquity of graph data in large scale industrial settings. Tacitly assumed in all graph learning tasks is the separation of the graph structure and node features: node features strictly encode individual data while the graph structure consists only of pairwise interactions. The driving belief is that node features are (by themselves) insufficient for these tasks, so benchmark performance accurately reflects improvements in graph learning. In our paper, we challenge this orthodoxy by showing that, surprisingly, node features are oftentimes more-than-sufficient for many common graph benchmarks, breaking this critical assumption. When comparing against a well-tuned feature-only MLP baseline on seven of the most commonly used graph learning datasets, one gains little benefit from using graph structure on five datasets. We posit that these datasets do not benefit considerably from graph learning because the features themselves already contain enough graph information to obviate or substantially reduce the need for the graph. To illustrate this point, we perform a feature study on these datasets and show how the features are responsible for closing the gap between MLP and graph-method performance. Further, in service of introducing better empirical measures of progress for graph neural networks, we present a challenging parametric family of principled synthetic datasets that necessitate graph information for nontrivial performance. Lastly, we section out a subset of real-world datasets that are not trivially solved by an MLP and hence serve as reasonable benchmarks for graph neural networks.

Introduction: People who identify as sexual minorities are at increased risk for suicide. Non-suicidal self-injury (NSSI) is also a risk factor for suicide and NSSI severity may contribute to development of capability for lethal self-injury. Further research is needed to understand how NSSI severity increases suicide risk, specifically in high-risk populations like sexual minorities. The current study seeks to examine whether sexual minority adults exhibit greater NSSI severity and suicide risk than heterosexuals, and if NSSI severity moderates the relationship between sexual orientation and suicide risk. Methods: Undergraduate students (N = 1,994) who reported five or more acts of NSSI in their lifetime completed online self-report questionnaires including sexual orientation, NSSI severity, and suicide risk. Results: A factorial ANOVA demonstrated main effects of sexual orientation and NSSI severity on suicide risk. Discussion: The lack of significant interaction effect indicates NSSI severity does not amplify the effect of on sexual orientation on suicide risk; rather, it predicts the same level of increased risk across orientations. Therefore, suicidality related to both sexual orientation and NSSI severity are equally important treatment targets.

Complex materials science problems such as glass formation must consider large system sizes that are many orders of magnitude too large to be solved by first-principles calculations. The successful application of machine learning (ML) in various other fields suggests that ML could be useful to address complex problems in materials science. To test its efficacy, we attempt to predict bulk metallic glass formation using ML. Surprisingly, we find that a recently developed ML model based on 201 alloy features constructed using simple combinations of 31 elemental features is indistinguishable from models that are based on unphysical features. The 201ML-model performs better than the unphysical model only when significant separation of training and testing data is achieved. However, it performs significantly worse than a human-learning based three-feature model. The limited performance of the 201ML-model originates from the inability to accurately represent alloy features through elemental features, showing that physical insights about mixing behavior are required to develop predictable ML models.

ABSTRACT We aimed to examine whether the trajectories of ecologically derived guilt differ among a transdiagnostic sample of youth with and without recent suicidal ideation and whether sex and age moderated this association. We assessed guilt 3 times a day over a 2-week period via ecological momentary assessment (EMA) technology in 102 children recruited from the community, outpatient, and inpatient settings. The average age of children was 10.95 y.o. (SD = 2.26, range 8–16) and the majority were male (54.9%) and White (76.5%). We found that the real-world guilt during a two-week EMA period was higher among youth with greater suicidal ideation severity in the past six months. Moreover, there was a significant moderating effect of sex and age on this association, such that the association between suicidal ideation severity and guilt was particularly strong among females compared to males and youth who were 10 years old or older. The findings were maintained when we adjusted for the relevant demographic and clinical characteristics, including age, minority status, parental income, EMA response rate, and current internalising symptoms. These preliminary findings highlight the clinical relevance of assessing and targeting feelings of guilt in the day-to-day lives of youth, particularly for females and older youth.

Modern methods in dimensionality reduction are dominated by nonlinear attraction-repulsion force-based methods (this includes t-SNE, UMAP, ForceAtlas2, LargeVis, and many more). The purpose of this paper is to demonstrate that all such methods, by design, come with an additional feature that is being automatically computed along the way, namely the vector field associated with these forces. We show how this vector field gives additional high-quality information and propose a general refinement strategy based on ideas from Morse theory. The efficiency of these ideas is illustrated specifically using t-SNE on synthetic and real-life data sets.

OBJECTIVE:Self-injurious behavior (SIB) is a significant public health concern in the United States, especially among adolescents with histories of maltreatment. This study compared maltreatment characteristics and reasons for SIB between three homogenous samples of adolescents with either: (1) non-suicidal self-injury (NSSI); (2) suicide attempt/s (SA), and (3) typically developing controls (TDC).METHOD:Participants (N = 124) aged 13-17 years completed questionnaires about their maltreatment and SIB histories.RESULTS:Maltreatment rates were as follows: 90% NSSI group, 76% SA group, and 40% TDC group. Adolescents in the NSSI group reported significantly higher rates of emotional neglect compared to the SA group. Maltreated adolescents in the NSSI and SA groups reported the same top three SIB reasons: (1) get rid of bad feelings, (2) mental state at the time, and (3) problems with family. However, maltreated NSSI participants were significantly more likely to engage in SIB for emotion regulation reasons than maltreated SA participants, who were more likely to engage in SIB for interpersonal reasons. Physical neglect and physical abuse also arose as significant predictors of specific SIB reasons.CONCLUSIONS:Our findings help elucidate the maltreatment profiles and reasons for SIB among adolescents engaged in NSSI or SA. Specific maltreatment experiences may also influence the reasons why adolescents engaged in SIB.

Multi-view learning tasks typically seek an aggregate synthesis of multiple views or perspectives of a single data set. The current approach assumes that there is an ambient space X in which the views are images of X under certain functions and attempts to learn these functions via a neural network. Unfortunately, such an approach neglects to consider the geometry of the ambient space. Hierarchically hyperbolic spaces (HHSes) do, however, provide a natural multi-view arrangement of data; they provide geometric tools for the assembly of different views of a single data set into a coherent global space, a CAT(0) cube complex. In this work, we provide the first step toward theoretically justifiable methods for learning embeddings of multi-view data sets into CAT(0) cube complexes. We present an algorithm which, given a finite set of finite metric spaces (views) on a finite set of points (the objects), produces the key components of an HHS structure. From this structure, we can produce a CAT(0) cube complex that encodes the hyperbolic geometry in the data while simultaneously allowing for Euclidean features given by the detected relations among the views.

Pooled testing for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) detection is instrumental for increasing test capacity while decreasing test cost. Pooled testing programs permit sustainable, long-term surveillance measures, which are essential for the early detection of virus resurgence in communities or the emergence of variants of concern. While numerous pooled approaches have been proposed to increase test capacity, uptake by laboratories has been limited. On 9 December 2020, we invited 362 U.S. laboratories that inquired about the Yale School of Public Health SalivaDirect test to participate in a survey to evaluate testing constraints and pooling strategies for SARS-CoV-2 testing. The survey was distributed using Qualtrics, and three reminders were sent. The survey closed on 21 January 2021. Of 93 responses received (25.7% response rate), 90 were from Clinical Laboratory Improvement Amendments (CLIA)-certified laboratories conducting SARS-CoV-2 testing. The remaining three were excluded from the analyses. Responses indicated that the major barriers to the uptake of pooled testing in the United States may not simply be the number of tests a laboratory can process per day, but rather the lack of clear protocols and adequate resources; laboratories are working with fixed physical and human capital constraints. Importantly, laboratories across the country are heterogeneous in infrastructure and workflow. The need for SARS-CoV-2 testing will remain for years to come. Testing programs can be maintained through pooled PCR testing strategies, and while statisticians, operations researchers, and others with expertise in sampling design have important value to add, laboratories require support on how to transition from traditional diagnostic testing to pooled surveillance. IMPORTANCE While numerous pooled SARS-CoV-2 testing approaches have been described in an effort to increase testing capacity and decrease test prices, uptake by laboratories has been limited. Responses to our survey of United States-based laboratories highlight the importance of consulting end-users-those that solutions are being designed for-so challenges can be addressed in a manner tailored to meet the specific needs out in the field. It may be surprising to those designing pooled testing strategies to learn that laboratories view pooling as more time-consuming than testing samples individually, and therefore that it is thought to create delays in test reporting.

Facial emotion recognition deficits are common in bipolar disorder (BD) and associated with impairment. However, the relationship between facial emotion recognition and mood course is not well understood. This study examined facial emotion recognition and subsequent mood symptoms in young adults with childhood-onset BD versus typically developing controls (TDCs). The sample included 116 young adults (ages 18–30, 58% male, 78% White) with prospectively verified childhood-onset BD ( n = 52) and TDCs ( n = 64). At baseline, participants completed a facial emotion recognition task (Diagnostic Analysis of Non-Verbal Accuracy-2) and clinical measures. Then, participants with BD completed mood symptom assessments every 6 months ( M = 8.7 ± 5.2 months) over two years. Analyses included independent-samples t tests and mixed-effects regression models. Participants with BD made significantly more recognition errors for child expressions than TDCs. There were no significant between-group differences for recognition errors for adult expressions, or errors for specific child or adult emotional expressions. Participants had moderate baseline mood symptoms. Significant time-by-facial emotion recognition interactions revealed more recognition errors for child emotional expressions predicted lower baseline mania and stable/consistent trajectory; fewer recognition errors for child expressions predicted higher baseline mania and decreasing trajectory. In addition, more recognition errors for adult sad expressions predicted stable/consistent depression trajectory and decreasing mania; fewer recognition errors for adult sad expressions predicted decreasing depression trajectory and stable/consistent mania. Effects remained when controlling for baseline demographics and clinical variables. Facial emotion recognition may be an important brain/behavior mechanism, prognostic indicator, and intervention target for childhood-onset BD, which endures into young adulthood and is associated with mood trajectory.

Given a matrix $D$ describing the pairwise dissimilarities of a data set, a common task is to embed the data points into Euclidean space. The classical multidimensional scaling (cMDS) algorithm is a widespread method to do this. However, theoretical analysis of the robustness of the algorithm and an in-depth analysis of its performance on non-Euclidean metrics is lacking. In this paper, we derive a formula, based on the eigenvalues of a matrix obtained from $D$, for the Frobenius norm of the difference between $D$ and the metric $D_{\text{cmds}}$ returned by cMDS. This error analysis leads us to the conclusion that when the derived matrix has a significant number of negative eigenvalues, then $\|D-D_{\text{cmds}}\|_F$, after initially decreasing, will eventually increase as we increase the dimension. Hence, counterintuitively, the quality of the embedding degrades as we increase the dimension. We empirically verify that the Frobenius norm increases as we increase the dimension for a variety of non-Euclidean metrics. We also show on several benchmark datasets that this degradation in the embedding results in the classification accuracy of both simple (e.g., 1-nearest neighbor) and complex (e.g., multi-layer neural nets) classifiers decreasing as we increase the embedding dimension. Finally, our analysis leads us to a new efficiently computable algorithm that returns a matrix $D_l$ that is at least as close to the original distances as $D_t$ (the Euclidean metric closest in $\ell_2$ distance). While $D_l$ is not metric, when given as input to cMDS instead of $D$, it empirically results in solutions whose distance to $D$ does not increase when we increase the dimension and the classification accuracy degrades less than the cMDS solution.

Irritability is a common reason why children and adolescents are brought for psychiatric care. Although research is advancing what is known about the underlying brain and behavior mechanisms of irritability, clinicians often are shut out of that research. This article explains some of these research methods, providing brief summaries of what is known about brain/behavior mechanisms in disorders involving irritability, including bipolar disorder, disruptive mood dysregulation disorder, attention-deficit/hyperactivity disorder, and autism spectrum disorder. Greater access to these methods may help clinicians now and in the future, with such mechanisms translated into improved care, as occurs in the treatment of childhood leukemia.

The original article was published with incorrect funding information.