Interpretable factorization of clinical questionnaires to identify latent factors of psychopathology

The study of representations is widespread across fields, including neuroscience, psychology, and artificial intelligence. While representations are often studied and compared through similarities between stimuli, current methods provide only limited access to the dimensions that shape these representations and are often limited in interpretability. To overcome these challenges, here we introduce Similarity-Based Representation Factorization (SRF), a general computational method for recovering low-dimensional, non-negative, interpretable embeddings from similarity matrices derived from measured data. Across simulations and many neural, behavioral, and computational datasets, SRF recovers interpretable dimensions from diverse forms of representational data, even for very sparsely sampled, incomplete data. The dimensions derived from these datasets match those obtained by task-specific models, predict independent behavioral properties, improve exploratory analysis, and offer higher power for confirmatory hypothesis testing than comparing similarity matrices. Together, these results establish SRF as a general-purpose method with broad applications for uncovering, understanding, and using the dimensions underlying representations.

The common factor analytic model is related to Helmholtz and Boltzmann machines, can be conceived as a linear autoencoder, or can be thought of as a single-hidden-layer generative neural network. We thus consider it a basal generative representation learner that can be used as a minimal model for studying the foundational characteristics of (deep) generative model architectures. We focus on the fundamental problem of indeterminacy in latent factor projections. This indeterminacy implies that, even when the intrinsic dimension of the latent vector is known, regularity conditions are met, and rotational indeterminacy is resolved, an inherent indefiniteness in the retrieval of causative latent sources remains: they will be uncertain, distributionally deviant, and non-unique. This can have major implications for data representation but remains an elusive issue, even to practitioners and theorists well-versed in the factor model. Moreover, this classic psychometric problem is intricately related to the modern issue of latent variable collapse in the variational autoencoder framework for deep generative modeling. Here, we assess this indeterminacy from various perspectives and show how these are mathematically and conceptually related and we discuss subsequent implications for the Psychometrics, Statistics, and Artificial Intelligence communities. We show that one has latent factor determinacy across all its facets when the feature-dimension grows to infinity. This feeds into an essentially distribution-free estimation approach in the sample case when the number of features grows very large. We conclude, as these are emergent properties at scale, that the factor model is suited for representation learning of very-high-dimensional data.

Psychometric questionnaires contain rich item-level information, yet it remains unclear whether different representation learning objectives recover the same latent organization. We investigated this question using 757 matched teacher-child pairs from the baseline assessment of the Cyprus ProW preschool trial. Behavioral structure was characterized from child SDQ, ASBI, and CBRS item responses using principal component analysis and clustering, yielding four behavioral phenotypes. A contrastive objective substantially improved teacher-child retrieval relative to PCA-based representations, increasing Top-1 accuracy from 0.13% to 7.27% and Top-10 accuracy from 1.98% to 56.14%. However, contrastive representations preserved behavioral phenotype structure less effectively than PCA-based representations. A multi-task objective jointly optimizing alignment and behavioral prediction partially restored behavioral organization but reduced retrieval performance. These findings indicate that teacher-child correspondence and behavioral phenotypes represent distinct forms of latent organization and demonstrate that the latent structure recovered from linked psychometric data depends on the representation learning objective.