Interpretable factorization of clinical questionnaires to identify latent factors of psychopathology
Psychiatry research seeks to understand the manifestations of psychopathology in behavior, as measured in questionnaire data, by identifying a small number of latent factors that explain them. While factor analysis is the traditional tool for this purpose, the resulting factors may not be interpretable, and may also be subject to confounding variables. Moreover, missing data are common, and explicit imputation is often required. To overcome these limitations, we introduce interpretability constrained questionnaire factorization (ICQF), a non-negative matrix factorization method with regularization tailored for questionnaire data. Our method aims to promote factor interpretability and solution stability. We provide an optimization procedure with theoretical convergence guarantees, and an automated procedure to detect latent dimensionality accurately. We validate these procedures using realistic synthetic data. We demonstrate the effectiveness of our method in a widely used general-purpose questionnaire, in two independent datasets (the Healthy Brain Network and Adolescent Brain Cognitive Development studies). Specifically, we show that ICQF improves interpretability, as defined by domain experts, while preserving diagnostic information across a range of disorders, and outperforms competing methods for smaller dataset sizes. This suggests that the regularization in our method matches domain characteristics. The python implementation for ICQF is available at \url{//github.com/jefferykclam/ICQF}.
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Gene set analysis, a popular approach for analysing high-throughput gene expression data, aims to identify sets of genes that show enriched expression patterns between two conditions. In addition to the multitude of methods available for this task, users are typically left with many options when creating the required input and specifying the internal parameters of the chosen method. This flexibility can lead to uncertainty about the 'right' choice, further reinforced by a lack of evidence-based guidance. Especially when their statistical experience is scarce, this uncertainty might entice users to produce preferable results using a 'trial-and-error' approach. While it may seem unproblematic at first glance, this practice can be viewed as a form of 'cherry-picking' and cause an optimistic bias, rendering the results non-replicable on independent data. After this problem has attracted a lot of attention in the context of classical hypothesis testing, we now aim to raise awareness of such over-optimism in the different and more complex context of gene set analyses. We mimic a hypothetical researcher who systematically selects the analysis variants yielding their preferred results, thereby considering three distinct goals they might pursue. Using a selection of popular gene set analysis methods, we tweak the results in this way for two frequently used benchmark gene expression data sets. Our study indicates that the potential for over-optimism is particularly high for a group of methods frequently used despite being commonly criticised. We conclude by providing practical recommendations to counter over-optimism in research findings in gene set analysis and beyond.
This article presents factor copula approaches to model temporal dependency of non- Gaussian (continuous/discrete) longitudinal data. Factor copula models are canonical vine copulas which explain the underlying dependence structure of a multivariate data through latent variables, and therefore can be easily interpreted and implemented to unbalanced longitudinal data. We develop regression models for continuous, binary and ordinal longitudinal data including covariates, by using factor copula constructions with subject-specific latent variables. Considering homogeneous within-subject dependence, our proposed models allow for feasible parametric inference in moderate to high dimensional situations, using two-stage (IFM) estimation method. We assess the finite sample performance of the proposed models with extensive simulation studies. In the empirical analysis, the proposed models are applied for analysing different longitudinal responses of two real world data sets. Moreover, we compare the performances of these models with some widely used random effect models using standard model selection techniques and find substantial improvements. Our studies suggest that factor copula models can be good alternatives to random effect models and can provide better insights to temporal dependency of longitudinal data of arbitrary nature.
Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts. In particular, we introduce a surrogate model where yield surfaces are expressed in terms of a set of single-variable feature mappings obtained from supervised learning. A post-processing step is then used to re-interpret the set of single-variable neural network mapping functions into mathematical form through symbolic regression. This divide-and-conquer approach provides several important advantages. First, it enables us to overcome the scaling issue of symbolic regression algorithms. From a practical perspective, it enhances the portability of learned models for partial differential equation solvers written in different programming languages. Finally, it enables us to have a concrete understanding of the attributes of the materials, such as convexity and symmetries of models, through automated derivations and reasoning. Numerical examples have been provided, along with an open-source code to enable third-party validation.
Coronary artery disease (CAD) remains the leading cause of death globally and invasive coronary angiography (ICA) is considered the gold standard of anatomical imaging evaluation when CAD is suspected. However, risk evaluation based on ICA has several limitations, such as visual assessment of stenosis severity, which has significant interobserver variability. This motivates to development of a lesion classification system that can support specialists in their clinical procedures. Although deep learning classification methods are well-developed in other areas of medical imaging, ICA image classification is still at an early stage. One of the most important reasons is the lack of available and high-quality open-access datasets. In this paper, we reported a new annotated ICA images dataset, CADICA, to provide the research community with a comprehensive and rigorous dataset of coronary angiography consisting of a set of acquired patient videos and associated disease-related metadata. This dataset can be used by clinicians to train their skills in angiographic assessment of CAD severity and by computer scientists to create computer-aided diagnostic systems to help in such assessment. In addition, baseline classification methods are proposed and analyzed, validating the functionality of CADICA and giving the scientific community a starting point to improve CAD detection.
Predicting the long-term success of endovascular interventions in the clinical management of cerebral aneurysms requires detailed insight into the patient-specific physiological conditions. In this work, we not only propose numerical representations of endovascular medical devices such as coils, flow diverters or Woven EndoBridge but also outline numerical models for the prediction of blood flow patterns in the aneurysm cavity right after a surgical intervention. Detailed knowledge about the post-surgical state then lays the basis to assess the chances of a stable occlusion of the aneurysm required for a long-term treatment success. To this end, we propose mathematical and mechanical models of endovascular medical devices made out of thin metal wires. These can then be used for fully resolved flow simulations of the post-surgical blood flow, which in this work will be performed by means of a Lattice Boltzmann method applied to the incompressible Navier-Stokes equations and patient-specific geometries. To probe the suitability of homogenized models, we also investigate poro-elastic models to represent such medical devices. In particular, we examine the validity of this modeling approach for flow diverter placement across the opening of the aneurysm cavity. For both approaches, physiologically meaningful boundary conditions are provided from reduced-order models of the vascular system. The present study demonstrates our capabilities to predict the post-surgical state and lays a solid foundation to tackle the prediction of thrombus formation and, thus, the aneurysm occlusion in a next step.
Despite substantial efforts, neural network interpretability remains an elusive goal, with previous research failing to provide succinct explanations of most single neurons' impact on the network output. This limitation is due to the polysemantic nature of most neurons, whereby a given neuron is involved in multiple unrelated network states, complicating the interpretation of that neuron. In this paper, we apply tools developed in neuroscience and information theory to propose both a novel practical approach to network interpretability and theoretical insights into polysemanticity and the density of codes. We infer levels of redundancy in the network's code by inspecting the eigenspectrum of the activation's covariance matrix. Furthermore, we show how random projections can reveal whether a network exhibits a smooth or non-differentiable code and hence how interpretable the code is. This same framework explains the advantages of polysemantic neurons to learning performance and explains trends found in recent results by Elhage et al.~(2022). Our approach advances the pursuit of interpretability in neural networks, providing insights into their underlying structure and suggesting new avenues for circuit-level interpretability.
Data generation remains a bottleneck in training surrogate models to predict molecular properties. We demonstrate that multitask Gaussian process regression overcomes this limitation by leveraging both expensive and cheap data sources. In particular, we consider training sets constructed from coupled-cluster (CC) and density function theory (DFT) data. We report that multitask surrogates can predict at CC level accuracy with a reduction to data generation cost by over an order of magnitude. Of note, our approach allows the training set to include DFT data generated by a heterogeneous mix of exchange-correlation functionals without imposing any artificial hierarchy on functional accuracy. More generally, the multitask framework can accommodate a wider range of training set structures -- including full disparity between the different levels of fidelity -- than existing kernel approaches based on $\Delta$-learning, though we show that the accuracy of the two approaches can be similar. Consequently, multitask regression can be a tool for reducing data generation costs even further by opportunistically exploiting existing data sources.
Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networks
We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data, learning an undirected graph we call the unconditional dependence graph. We show that unconditional dependence graphs of Bayesian networks correspond to the graphs having equal independence and intersection numbers. Using this observation, a Gr\"obner basis for a toric ideal associated to unconditional dependence graphs of Bayesian networks is given and then extended by additional binomial relations to connect the space of all such graphs. An MCMC method, called GrUES (Gr\"obner-based Unconditional Equivalence Search), is implemented based on the resulting moves and applied to synthetic Gaussian data. GrUES recovers the true marginal independence structure via a penalized maximum likelihood or MAP estimate at a higher rate than simple independence tests while also yielding an estimate of the posterior, for which the $20\%$ HPD credible sets include the true structure at a high rate for data-generating graphs with density at least $0.5$.
In statistical inference, retrodiction is the act of inferring potential causes in the past based on knowledge of the effects in the present and the dynamics leading to the present. Retrodiction is applicable even when the dynamics is not reversible, and it agrees with the reverse dynamics when it exists, so that retrodiction may be viewed as an extension of inversion, i.e., time-reversal. Recently, an axiomatic definition of retrodiction has been made in a way that is applicable to both classical and quantum probability using ideas from category theory. Almost simultaneously, a framework for information flow in in terms of semicartesian categories has been proposed in the setting of categorical probability theory. Here, we formulate a general definition of retrodiction to add to the information flow axioms in semicartesian categories, thus providing an abstract framework for retrodiction beyond classical and quantum probability theory. More precisely, we extend Bayesian inference, and more generally Jeffrey's probability kinematics, to arbitrary semicartesian categories.
Human movement studies and analyses have been fundamental in many scientific domains, ranging from neuroscience to education, pattern recognition to robotics, health care to sports, and beyond. Previous speech motor models were proposed to understand how speech movement is produced and how the resulting speech varies when some parameters are changed. However, the inverse approach, in which the muscular response parameters and the subject's age are derived from real continuous speech, is not possible with such models. Instead, in the handwriting field, the kinematic theory of rapid human movements and its associated Sigma-lognormal model have been applied successfully to obtain the muscular response parameters. This work presents a speech kinematics based model that can be used to study, analyze, and reconstruct complex speech kinematics in a simplified manner. A method based on the kinematic theory of rapid human movements and its associated Sigma lognormal model are applied to describe and to parameterize the asymptotic impulse response of the neuromuscular networks involved in speech as a response to a neuromotor command. The method used to carry out transformations from formants to a movement observation is also presented. Experiments carried out with the (English) VTR TIMIT database and the (German) Saarbrucken Voice Database, including people of different ages, with and without laryngeal pathologies, corroborate the link between the extracted parameters and aging, on the one hand, and the proportion between the first and second formants required in applying the kinematic theory of rapid human movements, on the other. The results should drive innovative developments in the modeling and understanding of speech kinematics.
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