Ridge regression for a personally calibrated pressure model AI
A linear regression predicts pressure from a weighted sum of features and an intercept. Ridge regression adds a penalty on the squared weights, reducing sensitivity to noisy or strongly correlated inputs. It generally shrinks weights rather than selecting a small set of exactly nonzero ones. See the scikit-learn linear-model documentation.
For standardized inputs, the objective combines squared prediction errors with a term proportional to the sum of squared coefficients. The penalty parameter alpha controls their tradeoff. Larger alpha pulls the fit toward its intercept; smaller alpha allows more feature influence.
Personal model in this report
Each person has separate systolic and diastolic coefficients. Training-only median imputation handles missing inputs; features are centered and divided by their training SD. All-missing or constant columns are inactive. Scaling matters because otherwise a penalty on coefficients would act differently just because a feature is measured in milliseconds rather than volts.
The report uses the same alpha across people: 10 for SBP and 100 for DBP. Coefficients and preprocessing remain personal. These are the modal calibration-selected penalties across the original 46-feature fits: 12 participants selected 10 for SBP and nine selected 100 for DBP. Each person’s choice minimized validation MAE over candidates 0.1, 1, 10, 100, 1,000 and 10,000 in the chronological calibration splits.
The retained 42-feature panel is refitted at these shared penalties. Reusing a penalty is different from sharing regression slopes. The latter is the cohort-sharing model.
With correlated inputs, individual coefficients need not identify independent physiological effects. Good fit during calibration also does not guarantee accuracy on later waveforms outside that range.