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PersonaX: Multimodal Datasets with LLM-Inferred Behavior Traits

Loka Li, Wong Yu Kang, Minghao Fu, Guangyi Chen, Zhenhao Chen, Gongxu Luo, Yuewen Sun, Salman Khan, Peter Spirtes, Kun Zhang

arXiv:2509.11362v2cs.LGcs.CV

TL;DR

Existing resources are often fragmented or lack unified textual, visual, and biographical information, limiting multimodal study of human behavior traits. PersonaX links LLM-inferred traits with facial and biographical data, analyzes them with dependence tests and causal representation learning, and reports population-specific patterns and interpretable latent structures.

  • Problem

    Existing resources are often fragmented or lack unified textual, visual, and biographical information for studying human behavior traits.

    Source: A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS · p. 21

  • Method

    PersonaX links LLM-inferred behavioral traits with facial and biographical information in two datasets, analyzed using structured dependence tests and multimodal causal representation learning.

    Source: §5 · p. 10

  • Results

    The authors report population-specific patterns and interpretable latent structures in their empirical analyses.

    Source: §5 · p. 10

  • Takeaways & Limitations

    PersonaX provides a foundation for studying invariant causal mechanisms of human behavioral traits.

    Source: §5 · p. 10

    The current release is not universally representative: AthlePersona covers only male athletes, while CelebPersona focuses on high-visibility celebrities.

    Source: A1 ETHICS STATEMENTS AND BROADER IMPACTS · p. 20

Abstract

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Understanding human behavior traits is central to applications in human-computer interaction, computational social science, and personalized AI systems. Such understanding often requires integrating multiple modalities to capture nuanced patterns and relationships. However, existing resources rarely provide datasets that combine behavioral descriptors with complementary modalities such as facial attributes and biographical information. To address this gap, we present PersonaX, a curated collection of multimodal datasets designed to enable comprehensive analysis of public traits across modalities. PersonaX consists of (1) CelebPersona, featuring 9444 public figures from diverse occupations, and (2) AthlePersona, covering 4181 professional athletes across 7 major sports leagues. Each dataset includes behavioral trait assessments inferred by three high-performing large language models, alongside facial imagery and structured biographical features. We analyze PersonaX at two complementary levels. First, we abstract high-level trait scores from text descriptions and apply five statistical independence tests to examine their relationships with other modalities. Second, we introduce a novel causal representation learning (CRL) framework tailored to multimodal and multi-measurement data, providing theoretical identifiability guarantees. Experiments on both synthetic and real-world data demonstrate the effectiveness of our approach. By unifying structured and unstructured analysis, PersonaX establishes a foundation for studying LLM-inferred behavioral traits in conjunction with visual and biographical attributes, advancing multimodal trait analysis and causal reasoning. The code is available at https://github.com/lokali/PersonaX.

1 INTRODUCTION

The introduction frames observable behavior traits as distinct from internal personality and highlights LLMs as a way to assess them at scale. PersonaX’s broader vision is multimodal analysis that can support causal reasoning across populations.

1 INTRODUCTION

  • Behavior traits are observable conduct patterns inferred from public signals, unlike internal personality dispositions measured through self-reports or expert evaluation.The introduction presents these non-intrusive traits as a complement to personality research, not clinical diagnoses.Source: §1 · p. 1
  • LLM assessments aligned with the Big Five can be reliable under carefully designed prompting, enabling automated large-scale analysis while mitigating some self-report biases.The introduction cites prior studies supporting this claim: Serapio-Garc´ıa et al. (2023); Jiang et al. (2023); Tseng et al. (2024); Zou et al. (2024).Source: §1 · p. 1
  • PersonaX’s pipelines collect public data, facial images, and biographical features for AthlePersona and CelebPersona, then use LLMs to infer behavior traits.AthlePersona draws from major sports league rosters; CelebPersona links CelebA identities to Wikidata entities.Source: Figure 1 · p. 2
  • The long-term vision is to use these resources to uncover invariant causal patterns across populations and advance multimodal interpretation and causal reasoning.The stated aim is to advance diversity, equality, and mutual respect.Source: §1 · p. 3

2 PE R S O N AX DATASET

PersonaX combines AthlePersona and CelebPersona to study LLM-inferred behavior traits alongside facial and biographical data. The section describes each dataset, the prompt experiments used to select trait-generating models, and safeguards addressing consent, privacy, bias, and use.

2 PE R S O N AX DATASET

  • 9444 public figures populate CelebPersona, which builds on CelebA and retains 10 stable, inherent appearance attributes while adding WikiData biographies and physical characteristics.Short-term-variable attributes such as Heavy Makeup were discarded.Source: §2 · p. 3
  • Each record combines LLM-inferred textual behavior descriptions and Big Five scores, facial images or embeddings with attributes, and structured biographical metadata.Full feature lists and distributions are provided in the paper’s appendices.Source: §2 · p. 3

2.1 LLM SELECTION AND PROMPT DESIGN

  • Numeric 3-level scoring minimized variability, while 5-level scales increased inconsistency; the selected generators were ChatGPT-4o-Latest, Gemini-2.5-Pro, and Llama-4-Maverick.Ten state-of-the-art LLMs were evaluated across both datasets, with controlled trials varying output format, scoring scale, and ordering direction.Source: §2.1 · pp. 3–4, Figure 2 · p. 4

2.2 ETHICAL CONSIDERATIONS: CONSENT, PRIVACY, BIAS, AND USAGE

  • Both datasets use legally accessible, consent-based sources and restrict use to non-commercial, non-high-stakes contexts; released facial and text embeddings are obfuscated.Facial images are replaced with 1024-dimensional embeddings and text descriptions with 3584-dimensional embeddings, both further obfuscated through an invertible transformation. AthlePersona contains only male athletes and CelebPersona focuses on wealthy, high-visibility individuals, so findings should be interpreted as population-specific; sports diversity offers opportunities to study invariant causal patterns.Source: §2.2 · pp. 4–5

3 ANALYSIS LEVEL I: INFERRING STATISTICAL DEPENDENCE FROM STRUCTURED DATA

Structured-data analysis finds different dependence patterns across persona types: celebrity trait scores relate strongly to demographics and facial appearance, while athlete scores relate more to birth year and organizational affiliation.

3 ANALYSIS LEVEL I: INFERRING STATISTICAL DEPENDENCE FROM STRUCTURED DATA

  • Trait scores exclude zero values and combine three LLM assessments through median-based voting; CelebPersona facial attributes are aggregated across images by majority vote.Zero scores denote insufficient information, and median voting reduces sensitivity to outliers.Source: §3 · p. 5
  • The analysis uses five independence tests—KCI, RCIT, HSIC, Chi-square, and G-square—and treats dependence as significant when p < 0.05.Figure 3 summarizes counts of tests finding significant dependence and score distributions; complete p-values appear in Tables A3 and A4.Source: §3 · p. 5
  • CelebPersona shows strong dependence of nearly all traits on gender and occupation, while AthlePersona is more dependent on birth year and league affiliation.Celebrities also show significant facial-feature associations; athletes show more moderate height and weight associations, while latitude and longitude effects are comparably moderate across datasets.Source: §3 · pp. 5–6

4 ANALYSIS LEVEL II: LEARNING CAUSAL RELATIONS FROM UNSTRUCTURED DATA

PersonaX’s multimodal and multi-measurement causal representation learning framework is designed to recover latent variables and their causal relations from unstructured data, with theoretical identifiability guarantees. Synthetic experiments show stronger results than the reported baselines, while PersonaX analysis reveals interpretable causal structures across traits and images.

4.1 CAUSAL MODEL FORMULATION

  • The causal model links modality-specific latent variables within and across modalities while allowing shared latent factors and mutually independent exogenous noise.Its differentiable causal function has a Jacobian that can be permuted into a strictly triangular matrix.Source: Figure 4 · p. 6, §4.1 · p. 6

4.4 SYNTHETIC EXPERIMENTS ON VARIANT MNIST

  • R2 of 0.96 and MCC of 0.92 outperform MMCRL’s R2 of 0.90 and MCC of 0.85, while also surpassing BetaVAE and MCL on synthetic data.The experiments use Colored MNIST and Fashion MNIST with explicitly designed cross-modal causal dependencies and multiple measurements.Source: Figure 5 · p. 7, §4.4 · p. 9

4.2 IDENTIFIABILITY THEORY

  • Theorems establish identifiability of modality-specific and shared subspaces, and component-wise latent variables, under stated model conditions.For three measurements from one modality, the identified modality and shared subspaces are related by invertible differentiable maps; component-wise identifiability additionally requires sufficient variability and sparsity regularization.Source: §4.2 · pp. 7–8

4.3 NETWORK TRAINING

  • Training combines per-measurement reconstruction, latent-independence, and sparse causal-graph objectives to recover interpretable latent variables across modalities.The losses use mean squared error for reconstruction, KL divergence to an isotropic Gaussian prior for independence, and an L1 penalty on the learned adjacency matrix.Source: §4.3 · pp. 8–9

4.5 REAL-WORLD TRAIT ANALYSIS ON PE R S O N AX

  • AthlePersona analysis identifies two shared, five image-based, and five trait-based latents, with interpretable links between behavioral traits and facial attributes.Examples include confidence affecting facial expressions and emotional stability impacting grooming; the discovered trait latents may correlate with, but are not necessarily identical to, Big Five traits.Source: Figure 6 · p. 9, §4.5 · p. 9

5 DISCUSSIONS AND CONCLUSION

PersonaX links LLM-inferred behavioral traits with facial and biographical information in two datasets and combines dependence tests with causal representation learning. The authors note cohort and temporal limitations and identify broader data collection and temporally rich datasets as future work.

Discussions

  • The cohorts are restricted—AthlePersona covers only male athletes and CelebPersona wealthy, high-visibility celebrities—so they are not universally representative, though they enable controlled domain comparisons.The authors plan to expand PersonaX by continually collecting data from additional sources to broaden coverage and inclusivity.Source: §5 · p. 9
  • Traits are subjective and dynamic, but PersonaX infers them from static public data without longitudinal tracking, complicating validation.The authors identify temporally rich datasets as future work.Source: §5 · p. 10

Conclusion

  • PersonaX links LLM-inferred behavioral traits to facial and biographical data in two datasets and combines dependence tests with multimodal, multi-measurement causal representation learning.The framework proposes identifiability theory tailored to this setting; experiments demonstrate population-specific patterns and interpretable latent structures. The datasets provide a foundation for studying invariant causal mechanisms of human behavioral traits.Source: §5 · p. 10

Appendix for · A1 ETHICS STATEMENTS AND BROADER IMPACTS

PersonaX pairs publicly accessible multimodal datasets with causal analysis to support research on behavioral traits while foregrounding ethical safeguards and limits to representativeness. The authors discourage high-stakes individual use and call for broader, more inclusive extensions.

A1 ETHICS STATEMENTS AND BROADER IMPACTS

  • PersonaX provides two publicly accessible datasets and a two-level causal analysis framework for studying behavioral traits alongside facial and biographical features.The work also aims to advance methodological research in multimodal causal representation learning.Source: A1 ETHICS STATEMENTS AND BROADER IMPACTS · p. 20
  • Because trait inference from public data could reinforce stereotypes or enable misuse in sensitive domains, the release uses obfuscated embeddings, restricts commercial use, and follows consent-based, legally accessible sourcing.Raw images and texts are not released; a detailed usage-guidelines file accompanies the restrictions.Source: A1 ETHICS STATEMENTS AND BROADER IMPACTS · p. 20
  • AthlePersona covers only male athletes and CelebPersona focuses on high-visibility celebrities, so findings are population-specific rather than universally representative.The selected cohorts were intended to provide public records and visibility sufficient for reliable LLM inference.Source: A1 ETHICS STATEMENTS AND BROADER IMPACTS · p. 20
  • The cohort choices reflect accessible, consistent public attention for male professional leagues and CelebPersona’s basis in the established CelebA benchmark.The authors selected cohorts with sufficient public visibility to support high-quality behavioral-trait inference.Source: A1 ETHICS STATEMENTS AND BROADER IMPACTS · p. 20
  • Future extensions should broaden demographic coverage to female athletes, less visible public figures, and longitudinal data; the authors also plan iterative updates guided by community feedback, inclusivity, and transparency.The paper presents these extensions as crucial to addressing the release’s demographic limits.Source: A1 ETHICS STATEMENTS AND BROADER IMPACTS · p. 20
  • The authors frame PersonaX as a resource for population-level patterns, not deterministic individual inference, and discourage high-stakes decision-making.They encourage methodological work on causal discovery under selection bias and multimodal integration, as well as fairness and robustness analyses across social contexts.Source: A1 ETHICS STATEMENTS AND BROADER IMPACTS · p. 20

A2 DETAILS ABOUT RELATED WORK · A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS

Prior behavior-trait work spans observable-signal inference and multimodal datasets, but existing resources remain fragmented. PersonaX addresses this gap with two datasets linking LLM-inferred Big Five behavior traits to facial, physical, and occupational features.

A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS

  • Traditional personality instruments include Cattell’s 16PF, the Eysenck Personality Questionnaire, and the Myers–Briggs Type Indicator; the Big Five became prevailing, though self-reports face bias and scalability limits.Behavior traits concern outwardly observable patterns, unlike personality assessments focused on internal dispositions.Source: A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS · p. 20
  • Computational approaches infer traits from observable signals rather than introspection, including language, handwriting, speech, facial expressions, and online profiles (Pennebaker et al., 1999; Asra & Shubhangi, 2015; Mohammadi et al., 2010; G¨uc¸l¨ut¨urk et al., 2018; Youyou et al., 2015; Celli et al., 2014).Related work also links traits to driving, smart-home activity, and long-term lifelogging, where questionnaires may be impractical.Source: A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS · pp. 20–21
  • Facebook Likes predicted sensitive traits, including personality and demographics, with accuracies comparable to psychometric tests.The study illustrates behavioral-data inference in settings where traditional questionnaires may be impractical.Source: A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS · p. 21
  • Existing multimodal resources are often small or lack textual trait descriptions and unified cross-modal analysis, while large facial datasets generally omit trait annotations.The cited examples include SALSA; YouTube-Vlogs, FI-V2, MuPTA, MDPE, and Amigos; and facial datasets CelebA, FFHQ, and FairFace.Source: A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS · p. 21
  • Cross-modal evidence links facial morphology to health and aggression, body images to personality judgments, and Big Five traits to facial behavior, activity, sensor, and physiological signals.The cited findings include the “kernel of truth” hypothesis and machine-learning prediction from facial behavior (Zebrowitz, 2018; Kramer & Ward, 2010; Carr´e & McCormick, 2008; Naumann et al., 2009; Cai & Liu, 2022; Youyou et al., 2015; Kachur et al., 2020; Wilson & Dishman, 2015; Dotti et al., 2018; Gao et al., 2019).Source: A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS · p. 21
  • PersonaX introduces CelebPersona and AthlePersona, linking facial, physical, and occupational features with LLM-inferred Big Five behavior traits for cross-modal predictive and causal analyses.The paper presents the datasets as enabling systematic exploration of cross-modal relationships at scale.Source: A2.1 HUMAN BEHAVIOR TRAIT ANALYSIS · p. 21

A2.2 CAUSAL DISCOVERY AND CAUSAL REPRESENTATION LEARNING

Prior work spans constraint- and score-based causal discovery and CRL methods that use functional, environmental, or multimodal assumptions for identifiability. This work combines theory and application through identifiability conditions and an estimation framework for multimodal, multi-measurement human trait analysis.

A2.2 CAUSAL DISCOVERY AND CAUSAL REPRESENTATION LEARNING

  • Causal discovery includes constraint-based methods using conditional independence tests and score-based approaches ranging from greedy or exact search to continuous optimization.Examples include PC and FCI, GES, NOTEARS, GOLEM, and neural-network extensions such as DAG-GNN and DAG-NoCurl.Source: A2.2 CAUSAL DISCOVERY AND CAUSAL… · pp. 21–22
  • CRL recovers high-level causal variables from low-level observations, with identifiability methods relying on functional constraints, distribution shifts, or aligned multimodal observations.Recent work unifies these approaches through broader invariance principles (Ahuja et al., 2023).Source: A2.2 CAUSAL DISCOVERY AND CAUSAL… · p. 22
  • The paper derives formal identifiability conditions for multimodal, multi-measurement settings and uses them in a practical framework for human trait analysis.This aims to combine theoretical guarantees with practical CRL estimation.Source: A2.2 CAUSAL DISCOVERY AND CAUSAL… · p. 22

A2.3 MULTIMODALITY AND REPRESENTATION LEARNING

The section situates PersonaX against multimodal representation learning and contrastive methods, then distinguishes its focus on uncovering shared causal structure across modalities to generate personality insights.

A2.3 MULTIMODALITY AND REPRESENTATION LEARNING

A2.4 LLM REASONING AND INFERENCE

Prior work uses LLMs to infer, simulate, and annotate personality traits; PersonaX combines multimodal trait datasets with multiple model-generated assessments and prompts models to assess public Big Five personas from reliable public information.

A2.4 LLM REASONING AND INFERENCE

  • The prompt asks models to analyze each Big Five trait using public information, such as interviews, observed behavior, career patterns, and biography, while avoiding gossip and diagnosis.It directs assessments toward the individual’s public persona rather than a definitive psychological or clinical evaluation.Source: A2.4 LLM REASONING AND INFERENCE · p. 23
  • For each trait, the prompt requires a concise analysis, a 0–3 score, and an evidence-linked justification, then a hyphen-separated summary of all five scores.The scale distinguishes insufficient information (0) from mixed or non-prominent evidence (2), with 1 for contradictory evidence and 3 for supporting evidence.Source: A2.4 LLM REASONING AND INFERENCE · p. 23
  • Prior studies report LLM Big Five inference from user text, consistent prompted profiles, personality control and emulation, and trait annotation or assessment.Examples include moderate accuracy in zero-shot settings and alignment with standardized psychometric assessments (Peters et al., 2024; Serapio-Garc´ıa et al., 2023), methods to elicit traits (Jiang et al., 2023), personality emulation, and annotation or assessment.Source: A2.4 LLM REASONING AND INFERENCE · p. 24
  • PersonaX unites visual, physical, demographic, and personality dimensions with assessments generated by multiple models.The authors describe this as enabling systematic evaluation.Source: A2.4 LLM REASONING AND INFERENCE · p. 24

A3 DETAILS ABOUT AT H L EPERSONA AND CELEBPERSONA DATASETS … A9.3 RESULTS AND ANALYSIS OF BASELINE MMCRL

This section documents PersonaX’s datasets and LLM-generated trait assessments, including their features, distributions, missingness, terms of use, scoring formats, and statistical analyses. It develops and evaluates the causal representation framework, detailing its identifiability and training constraints and analyzing PersonaX causal pathways and trait–latent dependencies alongside baseline graph comparisons.

A3.1 FULL FEATURE LISTS

  • CelebPersona combines demographic and geographic data, facial attributes, occupation and gender labels, and personality analyses and Big Five scores from ChatGPT, Gemini, and LLaMA.Its Final OCEAN scores aggregate the three models’ scores by voting, and its 10 selected facial attributes are aggregated across multiple images by majority vote; AthlePersona instead has one image per athlete, no facial annotations or occupation labels, and league information.Source: A3.1 FULL FEATURE LISTS · pp. 24–27

A3.2 DISTRIBUTION PLOTS

  • AthlePersona skews toward North American athletes in NFL, NHL, and NBA, while CelebPersona skews toward North America and Europe and toward Entertainment, Music, and Sports occupations.AthlePersona is concentrated among people born from 1985–2005; CelebPersona birth years peak in 1990–1999, females slightly outnumber males, and most facial attributes are absent.Source: A3.2 DISTRIBUTION PLOTS · pp. 27–28, Figure A1 · p. 27, Figure A2 · p. 28

A3.3 MISSING VALUES

  • CelebPersona had 71.5% missing Height and 87% missing Weight, whereas AthlePersona was cleaned to contain no missing values.CelebPersona also had missing Birthday and Birthmonth values in 2% of records each, Birthyear in 0.6%, Latitude and Longitude in 0.2%, Occupation Num in 0.05%, and Gender Num in 0.2%.Source: A3.3 MISSING VALUES · pp. 28–29

A3.4 DETAILS ABOUT CONSENT: TERMS-OF-USE COMPLIANCE

  • CelebA images are restricted to non-commercial research use and may not be redistributed, while Wikidata data is licensed CC0 for the public domain.The appendix also points to a summary of sports-league terms-of-use compliance.Source: A3.4 DETAILS ABOUT CONSENT:… · p. 29

A4.1 DETAILS ABOUT HOW TO SELECT LLMS (REGARDING TABLE 1)

  • The authors considered 10 LLMs after screening candidates, including excluding GPT-4.5-Preview for cost and Gemini-2.0-Pro-Exp-02-05 for inaccessibility, and evaluated 100 sampled individuals per dataset using eight metrics.The authors motivate LLM-based assessments by the availability of online information about public figures and prior work on validity and reliability under specific prompting configurations.Source: A4 DETAILS ABOUT LLM SELECTION AND… · p. 29, A4.1 DETAILS ABOUT HOW TO SELECT LLMS… · pp. 29–30
  • ChatGPT-4o-Latest and Gemini-2.5-Pro had the highest overall scores; performance was stronger on CelebPersona, while Indecisive Rate ranged from 0.46 for Qwen-Plus to 0.11 for DeepSeek-R1.The analysis notes higher Missing Rate on AthlePersona, possibly because younger or less prominent athletes have less public information.Source: A4.1 DETAILS ABOUT HOW TO SELECT LLMS… · p. 31

A4.2 DETAILS ABOUT THE IMPACT OF SCORING SCALE (REGARDING FIGURE 2)

  • Llama-4-Maverick’s standard deviations stayed below 0.2 across prompt formats and traits; “Number-L3-Inc” had the lowest variance, while Qwen2.5-Max was most variable and Level-5 textual scales increased variability.Five top-performing LLMs were tested over 100 trials per prompt format on each dataset, with temperature set to 0; consistency was measured by score standard deviation.Source: A4.2 DETAILS ABOUT THE IMPACT OF… · p. 33
  • Number-L3-Inc consistently yields the lowest variance across models and datasets; textual five-level formats show standard deviations often above 0.5, Manhattan distances above 2.0, and altered distributions versus numerical formats.The authors selected Number-L3-Inc and Llama-4-Maverick, ChatGPT-4o-Latest, and Gemini-2.5-Pro, excluding Grok-3-Beta and Qwen2.5-Max for instability. AthlePersona generally shows higher standard deviations and inter-prompt distances than CelebPersona.Source: A4.2 DETAILS ABOUT THE IMPACT OF… · p. 34

A5 DETAILS ABOUT INDEPENDENT TEST (IT) RESULTS

  • The independence analysis uses five tests suited to categorical, continuous, and mixed variables, and treats p < 0.05 as significant.Chi-square and G-square tests cover discrete variables; HSIC, RCIT, and KCI provide kernel-based tests for continuous and mixed data.Source: A5 DETAILS ABOUT INDEPENDENT TEST (IT)… · p. 35

A5.1 DETAILS ON VOTING AND AGGREGATION

  • Trait scores exclude zero-valued insufficient-information outputs and use the rounded-up median, while celebrity facial attributes use majority voting across images.An exact tie in facial-attribute votes is coded 0; absent and present are coded −1 and +1, respectively.Source: A5.1 DETAILS ON VOTING AND AGGREGATION · p. 35

A5.3 DETAILS ABOUT IT RESULTS OF CELEBPERSONA

  • CelebPersona shows trait associations with birth timing and selected facial and demographic features, with kernel tests detecting patterns that classical tests often miss.Aggregated results show consensus for birth day (3–4/5 methods), bushy eyebrows (3–4/5), and weight (2–3/5); birth day, birth month, facial features, and weight have trait-specific associations.Source: Figure A4 · p. 37, A5.3 DETAILS ABOUT IT RESULTS OF… · pp. 38–39

A6 THEOREMS AND PROOFS

  • The theorem sequence establishes recovery of modality-specific subspaces, then shared latent variables across modalities, and finally modality-specific variables given the shared latent.The final recovery is identifiable up to component-wise indeterminacies, including an inner-modality permutation.Source: A6 THEOREMS AND PROOFS · p. 39

A6.1 PROOF OF THEOREM 1

  • Under its assumptions, Theorem 1 recovers the latent subspace from three measurements within a modality up to an invertible differentiable transformation.When a modality has fewer than three measurements, additional modalities can supply complementary information if the required assumptions hold.Source: A6.1 PROOF OF THEOREM 1 · pp. 39–40
  • Theorem 1 establishes modality-specific latent variables as block-identifiable, with its proof resolving scaling and permutation indeterminacies under normalization and distinct-density assumptions.Source: A6.1 PROOF OF THEOREM 1 · pp. 41–42, A6.2 PROOF OF THEOREM 2 · p. 42

A6.2 PROOF OF THEOREM 2

  • Theorem 2 identifies the shared latent component up to an invertible function and modality-specific components up to bijections, without requiring each measurement process to be invertible.The framework uses the shared component as a common cause of modality-specific variables.Source: A6.2 PROOF OF THEOREM 2 · pp. 42–43

A6.3 PROOF OF THEOREM 3

  • Under sufficient-variability and sparsity assumptions, components are identifiable up to invertible differentiable transforms, and Proposition 1 resolves permutations within modality blocks.The discussion says conditioning on the shared confounder enables recovery of the causal graph under milder assumptions.Source: A6.3 PROOF OF THEOREM 3 · pp. 43, 45

A7 DETAILS ABOUT NETWORK TRAINING FOR CAUSAL REPRESENTATION LEARNING

  • Training uses 3-layer MLPs over 1024-dimensional ImageBind image embeddings and 3584-dimensional gte-Qwen2-7B-instruct text embeddings, with independence and sparse-graph constraints.The constraints include conditional independence among measurements given modality-specific latents and an L1 penalty on the learned adjacency matrix.Source: A7 DETAILS ABOUT NETWORK TRAINING FOR… · p. 46

A8 DETAILS ABOUT SYNTHETIC EXPERIMENTS ON VARIANT MNIST

A8.1 DETAILS ABOUT EXPERIMENTAL SETUP

  • The synthetic setup links colored-MNIST horizontal position to transparency and fashion-MNIST vertical position, with three colored-MNIST measurements but one fashion-MNIST measurement per sample.Horizontal position also causes fashion-MNIST vertical position, which determines clothing grayscale intensity.Source: A8.1 DETAILS ABOUT EXPERIMENTAL SETUP · p. 47

A8.2 DETAILS ABOUT RESULTS AND ANALYSIS

A9.1 DETAILS ABOUT EXPERIMENTAL SETUP

  • CelebPersona causal discovery identifies three shared latents, 10 facial-image latents, and five behavior-trait latents, each grounded in interpretable features.The passage also points to the AthlePersona causal graph in Figure 6 and the CelebPersona graph in Figure A6.Source: A9.1 DETAILS ABOUT EXPERIMENTAL SETUP · p. 48

A9.2 DETAILS ABOUT RESULTS AND ANALYSIS

  • In the interpreted causal graph, shared latents represent education, cultural background, and growing environment, while expressiveness influences approachability and visual context and lighting influence hairstyle and appearance.Cultural background affects language use, and growing environment affects positive language use; hairstyle then influences face visibility, overall style, and perceived good looks.Source: A9.2 DETAILS ABOUT RESULTS AND ANALYSIS · p. 48
  • In AthlePersona, confidence is statistically dependent on Openness, Extraversion, and Agreeableness, while Self-awareness is associated only with Extraversion.The passage attributes the latter association as likely related to expressiveness, social engagement, and sensitivity.Source: A9.2 DETAILS ABOUT RESULTS AND ANALYSIS · p. 49, Figure A7 · p. 49
  • In CelebPersona, positive language use depends significantly on Agreeableness, expressiveness shows high p-values across Big Five traits, and facial attributes are linked to appearance latents.Big Nose, Pointy Nose, and Oval Face are tightly linked to hairstyle and good-looking; clothing style, lighting, and event context also influence facial attributes.Source: A9.2 DETAILS ABOUT RESULTS AND ANALYSIS · p. 49, Figure A7 · p. 49

A9.3 RESULTS AND ANALYSIS OF BASELINE MMCRL

  • MMCRL produces denser, less interpretable causal graphs than the proposed CRL, whose real-world structures more clearly separate visual and behavioral factors.The proposed method also achieves higher causal alignment metrics such as MCC and R2 in the synthetic results reported in Section 4.4.Source: A9.3 RESULTS AND ANALYSIS OF BASELINE… · p. 50
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