We consider S virtual subjects ( S = 200 ) monitored over D days ( D = 30 ). For each subject s ∈ { 1 , ⋯ , S } and day d ∈ { 1 , ⋯ , D } , we generate a behavioural feature vector

where F denotes the number of behavioural variables (sleep duration, step count, social interactions, screen time, and diurnal phone usage components). In total, F = 7 features per day, comprising: sleep duration (1), step count (1), social interaction count (1), total screen time (1), and three diurnal phone-usage components (morning, afternoon, evening).

Each subject has a binary depression label

with y s = 0 denoting a healthy subject and y s = 1 a depressed subject. Labels are drawn from a Bernoulli distribution

producing approximately 70% healthy and 30% depressed subjects, consistent with the class distribution visualized in Figure 1(A). Although real-world depression prevalence in population-level samples is often lower (5% - 15%), we selected p_dep = 0.3 to ensure sufficient minority representation for stable self-supervised pre-training and downstream classifier evaluation in this proof-of-concept study. Future work should evaluate robustness under more severe imbalance conditions.

2.1.1. PHQ-9 Score Model

For each subject we simulate a PHQ-9 score PHQ 9 s conditional on the label:

with μ 0 < 10 < μ 1 and moderate variances to produce overlapping yet separated distributions (Figure 1(B)). The clinical threshold at score 10 is used to verify label consistency:

This ensures that behavioural labels correspond to standard PHQ-9 definitions of non-depressed versus clinically relevant depressive symptoms [30]-[34].

2.1.2. Behavioural Feature Generation

For each feature f ∈ { 1 , ⋯ , F } and subject s , the baseline daily behaviour is modelled as a Gaussian distribution conditioned on the subject label:

where:

μ f ( y s ) is the label-dependent global mean (e.g., lower step count for depressed subjects). σ f ( y s ) controls inter-day variability. w d ∈ { 0 , ⋯ , 6 } denotes the weekday of day d , with w d = 0 representing Monday. Δ f ( y s ) ( w d ) encodes weekly structure (e.g., increased weekend sleep and screen time in depression).

The label-dependent means and variances were selected to approximate behavioural effect sizes reported in digital phenotyping literature. Prior studies have documented reduced step counts (15% - 30% decrease), increased sleep variability, and elevated late-evening screen engagement in individuals with depressive symptoms. Accordingly, group mean differences in the synthetic generator were calibrated to correspond to moderate standardized effect sizes (Cohen’s d ≈ 0.5 - 0.8), ensuring overlapping but non-trivially separable behavioural distributions.

For diurnal phone usage, we introduce three components morning, afternoon, evening whose daily values are drawn with time-of-day specific means:

Evening phone usage has larger means for depressed subjects, consistent with the bar plots in Figure 2(D) and Figure 4(D).

To enforce non-negativity for count-like variables (steps, interactions), we apply an element-wise rectification:

2.1.3. Behavioural Variability

Subject-level day-to-day variability for feature f is defined as the sample standard deviation:

Healthy subjects are given lower variability for some features (e.g., sleep, steps) relative to depressed subjects; their distributions are compared in Figure 2(E).

To contextualize the synthetic environment, we compute:

Class distribution and PHQ-9 histograms (Figure 1(A) & Figure 1(B)).Temporal trajectories for one representative healthy and one depressed subject (Figures 2(A)-(C)).Diurnal phone usage patterns (Figure 2(D)).Behavioural variability across subjects (Figure 2(E)).Pearson correlation matrix of key features and PHQ-9 scores (Figure 2(F)).

This descriptive layer verifies that depressed subjects exhibit longer sleep, reduced activity, diminished social interactions, increased evening screen time, and altered cross-feature relationships.

2.3.1. Sequence Construction

For each subject we consider the full 30-day behavioural trajectory:

The SSL encoder is trained on the set { X s } s = 1 S without using labels y s .

2.3.2. Data Augmentation

We employ a family T of stochastic augmentations acting on sequences:

1) Time masking: randomly zeroing out contiguous day segments.

2) Additive Gaussian noise:

3) Time warping/interpolation: non-linear rescaling of the time axis followed by interpolation back to length D .

For each subject s we sample two independent transformations T 1 , T 2 ~ T and create two augmented views

2.3.3. Encoder, Projection Head, and Decoder

The SSL model consists of:

A temporal encoder g θ   : ℝ D × F → ℝ K implemented as a 1-D convolutional network with global average pooling and a fully connected layer.A projection head h ϕ   : ℝ K → ℝ K used only during contrastive training.A decoder d ψ   : ℝ K → ℝ D × F used for reconstruction.

Given an input sequence X ˜ , the encoder outputs a latent vector

The projection head produces a contrastive representation

which is subsequently L 2 -normalized:

The decoder reconstructs the original sequence from z :

We adopt the NT-Xent (normalized temperature-scaled cross-entropy) loss applied to pairs of augmented views. Assume a mini batch of N subjects, resulting in 2 N augmented sequences and corresponding projection vectors { p ^ k } k = 1 2 N . Let ( i , j ) denote the two views of the same subject. Cosine similarity between two vectors is

The contrastive loss for anchor i and its positive pair j is

where τ > 0 is a temperature hyperparameter. The full NT-Xent loss over the batch is

To encourage the latent representation to retain information useful for reconstructing the original sequences, we add a mean-squared reconstruction loss:

where ‖   ⋅   ‖ F denotes the Frobenius norm.

The combined SSL training objective is

with α > 0 controlling the contribution of reconstruction.

In all experiments, α was set to 0.2, placing stronger emphasis on contrastive discrimination while maintaining reconstruction regularization. Preliminary sensitivity analysis across α ∈ { 0.1 , 0.2 , 0.5 } showed stable downstream AUC, with α = 0.2 yielding optimal validation performance.

After SSL pre-training, we discard the projection head and decoder and apply the encoder g θ to the original (non-augmented) sequences to obtain a single latent vector for each subject:

These vectors constitute the SSL feature matrix

For comparison, we construct simple raw features by averaging across days:

The full raw feature matrix is

We then train multiple supervised classifiers f ω   : ℝ p → [ 0 , 1 ] to predict depression label y s from either SSL features ( p = K ) or raw features ( p = F ):

Models considered include Random Forest, XGBoost, SVM, and Logistic Regression [35]-[39].

Given an estimated probability p ^ s , the predicted label is obtained via thresholding:

with default δ = 0.5 .

We compute standard binary classification metrics on held-out data. Let T P , T N , F P , and F N denote the number of true positives, true negatives, false positives, and false negatives.

The F1-score is defined as the harmonic mean of precision and recall:

To quantify ranking performance across thresholds, we compute the area under the ROC curve (AUC):

where t denotes the discrimination threshold and TPR , FPR are the true-positive and false-positive rates.

Figure 1.Class distribution and PHQ-9 score profiles of the synthetic population.

Panel 1A (left): Class distribution of healthy vs. depressed subjects.

Panel 1B (right): PHQ-9 score distributions with clinical threshold marked.

Figure 1(A) (left panel) shows that the dataset contains approximately 70% healthy and 30% depressed subjects, closely mirroring typical prevalence patterns in population-level studies.

Figure 1(B) (right panel) presents the PHQ-9 distributions for both groups. Healthy subjects cluster sharply below the clinical threshold of 10, while depressed subjects span a wide distribution across moderate to severe ranges. The overlap near the threshold reflects real-world diagnostic uncertainty, where behavioural signatures and clinical scores do not always perfectly align. Together, the two panels confirm that label assignment and score distributions are clinically coherent.

Row 1:

Panel 2A (top-left): Sleep duration trajectoriesPanel 2B (top-middle): Physical activity (step count)Panel 2C (top-right): Social interaction patterns

Row 2:

Panel 2D (bottom-left): Diurnal phone usagePanel 2E (bottom-middle): Behavioural variability (standard deviations)Panel 2F (bottom-right): Correlation matrix of behavioural features and PHQ-9

Figure 2. Temporal, diurnal, variability, and correlation patterns in synthetic behavioural data.

Panels 2A-2C (top row) highlight the primary temporal patterns across modalities.

In Panel 2A (top-left), healthy subjects maintain stable sleep durations (8-10 hours), whereas depressed subjects experience longer and more fluctuating sleep, often exceeding 10 hours.

Panel 2B (top-middle) reveals consistently reduced physical activity in the depressed group.

Panel 2C (top-right) shows lower social interaction levels throughout the 30-day period, reflecting reduced social engagement typical of depressive behaviour. Panels 2D-2F (bottom row) provide deeper behavioural insight. Panel 2D (bottom-left) displays diurnal phone usage averaged across subjects. Depressed individuals show a distinctive surge in evening phone use, suggesting late-night wakefulness and circadian disruption [40]-[42]. Panel 2E (bottom-middle) demonstrates that depressed subjects exhibit greater variability across all modalities-sleep, steps, social interactions, and screen time indicating behavioural instability rather than simple mean differences. Finally, Panel 2F (bottom-right) shows the correlation structure of the dataset, including a clear negative relationship between PHQ-9 scores and activity/social features, and strong positive coupling among activity-related behaviours. This confirms that the synthetic generator encodes realistic multivariate behavioural dependencies.

Row 1:

Panel 3A (top-left): AUC comparison across models

Figure 3. Classifier performance using SSL embeddings versus raw behavioural features.

Panels 3B-3D (top-middle to top-right): Confusion matrices for Random Forest, SVM, and Logistic Regression

Row 2:

Panel 3E (bottom panel): ROC curves for all classifiers trained on SSL embeddings

Panel 3A (top-left) compares ROC-AUC scores across multiple classifiers trained on either raw aggregated behavioural features or SSL-derived latent embeddings [43]-[46]. Across all models including Random Forest, XGBoost, Logistic Regression, and SVM the SSL embeddings provide substantial performance gains, often improving AUC by 0.20 - 0.35. This indicates that the self-supervised encoder captures temporal and cross-feature structure that simple daily averages fail to represent. Panels 3B-3D (top-middle to top-right) show confusion matrices for the held-out subjects. Random Forest and SVM demonstrate strong balanced discrimination between healthy and depressed subjects, while Logistic Regression performs more modestly, reflecting the inherently non-linear class separation present in the latent space [47]-[51]. Most misclassifications occur among subjects with intermediate PHQ-9 scores or behaviour patterns that do not clearly signal depression or health, highlighting the subtlety of behavioural indicators in borderline cases. Panel 3E (bottom) presents multi-model ROC curves for SSL-trained classifiers. All curves rise well above the diagonal, confirming meaningful discriminative power [52]-[54]. The SVM curve exhibits the steepest early rise, suggesting high sensitivity at lower false-positive rates. This behaviour allows clinicians or system designers to adjust thresholds to prioritize either sensitivity (recall) for safety-focused screening or specificity for resource-limited settings.

Figure 4. Weekly and diurnal behavioural patterns across healthy and depressed subjects.

Row 1:

Panel 4A (top-left): Weekly sleep durationPanel 4B (top-right): Weekly physical activity

Row 2:

Panel 4C (bottom-left): Weekly social interactionsPanel 4D (bottom-right): Diurnal phone usage patterns

Figure 4 provides a structured analysis of weekly and diurnal rhythms.

In Panel 4A (top-left), healthy individuals maintain consistent sleep duration across the week, while depressed individuals show markedly increased weekend sleep, suggesting circadian irregularity and potential “catch-up” behaviour following weekday dysregulation. Panel 4B (top-right) shows that step counts for depressed subjects remain consistently lower than those of healthy individuals, with only minor weekday variation. This reflects a stable behavioural signature of reduced physical activity in depressive states. Panel 4C (bottom-left) demonstrates higher social engagement throughout the week for healthy subjects, whereas depressed individuals experience more pronounced mid-week declines, aligning with motivational and social withdrawal patterns commonly reported in clinical literature. Finally, Panel 4D (bottom-right) shows that depressed subjects exhibit significantly elevated evening phone usage, a behaviour absent in the healthy group. This diurnal asymmetry reflects disrupted sleep hygiene and increased evening rumination, reinforcing the importance of time-of-day analysis in behavioural mental-health modelling [55]-[59]. These weekly and diurnal patterns together highlight the value of modelling rhythmic structure when interpreting digital phenotyping data for mental-health assessment [60]-[62].

Figure 5. Cluster-level behavioural archetypes derived from SSL latent embeddings.

Row 1:

Panel 5A (top-left): Sleep patterns by clusterPanel 5B (top-right): Step-count patterns by cluster

Row 2:

Panel 5C (bottom-left): Social interaction patterns by clusterPanel 5D (bottom-right): Screen-time patterns by cluster

To investigate how the self-supervised encoder organizes subjects in latent space, we apply k-means clustering to the latent embeddings { z s } . Figures 5(A)-(D) show cluster-level averages across key behavioural dimensions.

Cluster 0 displays high activity, moderate sleep, and frequent social interactions, forming a profile predominantly aligned with healthy subjects.Cluster 1 demonstrates low activity and low social engagement, but with relatively normal sleep patterns indicative of milder depressive expressions or subthreshold symptoms.Cluster 2 exhibits moderate activity but disproportionately high evening screen time, consistent with digitally engaged yet behaviourally withdrawn individuals.

Panels 5A-5D (top-left to bottom-right) visually highlight these archetypes across sleep, steps, social interactions, and screen time. The emergence of such structured clusters without using depression labels during SSL training demonstrates that the encoder effectively identifies meaningful inter-subject behavioural variability beyond the binary classification boundary.

Figure 6.UMAP projection of SSL latent embeddings for healthy and depressed subjects.

Figure 6Figure 6 presents a two-dimensional UMAP projection of the SSL-derived embeddings, with healthy subjects shown in blue and depressed subjects in red. Although the distributions overlap consistent with the subtle behavioural differences between groups the embeddings form partially distinct regions. Depressed subjects gravitate toward areas associated with longer sleep, lower activity, and increased screen time, reflecting the behavioural patterns seen in Figure 2 and Figure 4.

This geometric structure explains why downstream classifiers trained on SSL features achieve above-chance performance: the SSL encoder reshapes the high-dimensional behavioural trajectories into a more linearly separable manifold, enabling traditional classifiers to detect depression-related structure that is not clearly visible in raw feature space.