Algorithm 1.

Learning and Prediction Procedures

INPUT: Train data collection 𝒟 = {< Yl, xl >}, where l = 1, ···, N. DVI sampling frequency r. Number of hidden states in LDS d. Current observations Yu for patient u who is being predicted. An arbitrary future time stamp t* (t* > Tu).

PROCEDURE: // Stage1: Learning the population model. {Ỹl} = DV I({Yl}, {xl}, r). Ω = LearnLDS({Ỹl}). // Stage2: Learning the multivariate interaction model. Compute residual time series Ru. Λu = LearnMT GP (Ru). // Adaptive Prediction: Predicting ${\widehat{\mathbf{y}}}_{t\ast }^u$ by Ω and Λu. Trend prediction: ${\widehat{\mathbf{y}}}_{t\ast }^u(\mathrm{\Omega })=\mathit{PredictLDS}(\mathrm{\Omega },t\ast )$. Variability prediction: ${\widehat{\mathbf{y}}}_{t\ast }^u({\mathrm{\Lambda }}^u)=\mathit{PredictMTGP}({\mathrm{\Lambda }}^u,t\ast )$. ${\widehat{\mathbf{y}}}_{t\ast }^u={\widehat{\mathbf{y}}}_{t\ast }^u(\mathrm{\Omega })+{\widehat{\mathbf{y}}}_{t\ast }^u({\mathrm{\Lambda }}^u)$.

OUTPUT: Prediction at time stamp $t_{\ast }:{\widehat{\mathbf{y}}}_{t\ast }^u$.