Latent Similarity Gaussian Processes: A Theory-Grounded Approach to Personalized Suicide-Risk Forecasting for Clinical Decision-Support

Yaniv Yacoby; Weiwei Pan; Hope Neveux; Taylor C. McGuire; Franchesca Castro-Ramirez; Anushka R. Patel; Matthew K. Nock

stat.MLOct 5, 2026

Latent Similarity Gaussian Processes: A Theory-Grounded Approach to Personalized Suicide-Risk Forecasting for Clinical Decision-Support

Authors: Yaniv Yacoby, Weiwei Pan, Hope Neveux, Taylor C. McGuire, Franchesca Castro-Ramirez, Anushka R. Patel, Matthew K. Nock

Organizations: Wellesley College · Harvard University · Harvard University Harvard Medical School Massachusetts General Hospital

Abstract

Forecasting suicide risk is difficult due to the high heterogeneity of patients and the low base rate of suicide-related events (SREs). We present Latent Similarity Gaussian Processes (LSGPs), which embed patients in a continuous latent space to jointly model similarity and forecast risk. By selectively drawing information from latent peers, LSGPs better capture individualized risk trajectories, generalizing nomothetic (pooled), idiographic (per-patient), and hierarchical frameworks. Our contributions are: (1) an identifiable two-channel Similarity Kernel; (2) proof that the standard model-fitting algorithm, mean-field variational inference, collapses LSGPs to nomothetic models, along with a fix; and (3) empirical results on intensive longitudinal suicide data showing LSGPs outperform nomothetic, idiographic, and hierarchical models for next-week risk forecasting, with the largest gains in forecasting first-occurrence SREs.

Figures & tables

Figure 1: Structured Outperforms Factorized PG-LSGP by Learning Patient Similarity. Top row: structured. Bottom row: factorized. $\mathrm{MODS}$ is the mean off-diagonal similarity ( Eq. 118 ); cells labeled PC denote personalization collapse ( $\mathrm{MODS}(A^{\mathrm{comb}})=1.00$ to two decimals); cells labeled Undefined represent rank correlations that are undefined because the learned similarity matrix is constant off the diagonal. Recovery is the Spearman rank correlation between the learned and true similarity. Details in Secs. 5 and F .

Figure 2: Paired per-patient comparison: PG-LSGP outperforms baselines on per-patient AP. Markers denote mean patient-level differences (LSGP minus reference); bars denote

\pm 1

and

\pm 2

paired standard errors, for

n

patients. Pooled AP (non-decomposable) is shown without bars, while the MODS panel confirms the LSGP avoids collapse across all

h

. The LSGP gains concentrate in test-only event cases (top-right panel).

Figure 3: Learned combined similarity ( $A^{\mathrm{comb}}$ ) for patients with an SRE anywhere in their record. Each panel shows the variant with the highest validation per-patient AP, at the restart selected on validation LL, for its $h$ . Patients are ordered by the first principal component of their inferred latent codes $z_{n}$ , with annotation strips displaying demographic categories, total survey counts, and numbers of SRE episodes. Full cohort in Fig. 6 .

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Synthetic Hemisphere dataset with ground-truth similarity. Top left: Patient directions $v_{n}$ on the upper unit semicircle ( $D_{s}=2$ ). Top right: True similarity matrix $-\lVert v_{n}-v_{n^{\prime}}\rVert$ (monotonically equivalent to $v_{n}^{\intercal}v_{n^{\prime}}$ ), ordered along the manifold. Bottom row: Observed feature space for three representative patients, showing patient-specific decision boundaries and survey outcomes.

Figure 5: Paired comparison of the structured PG-LSGP against the factorized and SV variants on the EMA data. This plot is similar to Fig. 2 : each marker is the mean paired per-patient difference (best-validated structured PG-LSGP minus the best-validated member of each reference family at each

h

), with thick and thin bars spanning

\pm 1

and

\pm 2

paired standard errors; the MODS panel shows each method’s own similarity. Within the PG bound, adopting the structured over the factorized variational family improves per-patient LL by more than two paired standard errors at every

h

, reflecting superior predictive calibration, while per-patient AP differences remain largely within noise; the within-SV contrast is mixed. In the MODS panel, the factorized PG variant sits closer to collapse than the structured one at every

h

, yet the selected structured SV variant itself collapses at

h=0.8

—neither class of models consistently exhibits personalization collapse ( Apx. G ). Still, employing the structured family provides critical theoretical safeguards: it eliminates the optimization penalty against non-nomothetic fits, guaranteeing that any collapse is likelihood-driven rather than an artifact of the variational family.

Figure 6: Combined similarity ( $A^{\mathrm{comb}}$ ) across the full cohort ( $N=497$ ). Extending Fig. 3 to every patient, across all training fractions $h$ . Patients with training-window SREs exhibit distinct, well-defined similarity structures, while the remaining patients display less differentiated similarity, as the absence of positive training labels limits the model’s ability to resolve fine-grained boundaries among lower-risk trajectories.

Figure 7: Patient similarity graphs for the training-event cohort: demographic information does not explain patient similarity. Nodes represent patients who experienced an SRE during their training window. Edge thickness reflects the learned combined similarity

A^{\mathrm{comb}}_{nm}

. For legibility, only the strongest edges are drawn: a single similarity threshold, shared across all panels so that an edge means the same similarity everywhere, is chosen so that each panel shows about six edges per patient. Graph modularity

Q

and permutation

p

-values are computed on the complete similarity matrix

A^{\mathrm{comb}}

before this pruning. Rows correspond to training fractions

h\in\{0.3,0.5,0.8\}

, each showing the variant with the highest validation per-patient AP at the restart selected on validation log-likelihood; columns correspond to demographic attributes (node colors).

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Improving Forecasts of Suicide Attempts for Patients with Little Data

Genesis Hang, Annie Chen, Hope Neveux, Matthew K. Nock+1

Wellesley College · Harvard University

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Ecological Momentary Assessment (EMA) studies provide real-time data on suicidal thoughts and behaviors, but forecasting suicide attempts remains challenging: attempts are rare, and the pathways patients take to them are heterogeneous. Here, we investigate a cohort of patients from an EMA study with recorded suicide-related events. We show that a single model fit to all patients forecasts poorly, while idiographic (per-patient) models show improvement but overfit for those with little data. Based on this result, one may hypothesize that patients should be partitioned into subgroups---this way, similar patients' data can be pooled together to improve forecasts. However, we show that grouping patients at random already improves forecasts, with performance increasing monotonically with the number of groups. Moreover, we show that grouping patients by demographics yields worse forecasts than random groupings. From these results, we hypothesize that patient similarity is continuous, rather than discrete, and must be inferred from the data. This motivated us to use Latent Variable Multiple Output Gaussian Processes (LVMOGPs), adapted to our data. Preliminary results show that, even without careful kernel design, LVMOGPs already match the strongest baseline models on most metrics, and their latent spaces yield a similarity between patients that we can inspect directly. Because the cohort is conditioned on the outcome and the splits are not temporal, we read these results as evidence that idiographic structure exists and can be recovered, not as deployable forecasting performance---an area for future work.

Abstract

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