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Combining Machine Learning and Queueing Theory for Data-Driven Incarceration-Diversion Program Management
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Combines ML outcome prediction (GBT selected) with a queueing-style simulation and a two-stage right-censoring correction to predict program census for an Illinois incarceration-diversion program and support sizing and staffing counterfactuals.
Problem
Predicting census and program outcomes of individuals in incarceration-diversion programs, under varied outcomes and lengths of stay, to support program sizing and staffing decisions, with right-censored termination data.
Approach
Couples an ML outcome classifier and empirical length-of-stay distributions with a queueing-based census simulation, and handles right-censoring with a two-stage sampling scheme that assigns extended LOS to still-in-program individuals, enabling counterfactual analysis of admission criteria and new county launches.
Key results
- GBT achieved the best outcome prediction with ROC AUC 0.718 and weighted F1 0.526, versus LR at 0.590 and 0.389.
- Census simulation MAPE with predicted outcomes was 9.40, 10.05, 7.03, and 21.21 for DuPage, Cook, Will, and Peoria; with actual outcomes it was 3.01, 4.95, 5.51, and 15.78.
- Counterfactual analysis suggested the optimal Will County program size is slightly larger than current admissions, and a web app cut average run time from 8 minutes to 15 seconds.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use gradient boosting tree instead of logistic regression for outcome prediction | Program outcome prediction · Program outcome prediction test set | ROC AUC: 0.590 -> 0.718 | Helped |
| Use gradient boosting tree instead of logistic regression for outcome prediction | Program outcome prediction · Program outcome prediction test set | Weighted F1 score: 0.389 -> 0.526 | Helped |
| Use gradient boosting tree instead of decision tree for outcome prediction | Program outcome prediction · Program outcome prediction test set | ROC AUC: 0.703 -> 0.718 | Helped |
| Use gradient boosting tree instead of decision tree for outcome prediction | Program outcome prediction · Program outcome prediction test set | Weighted F1 score: 0.497 -> 0.526 | Helped |
| Use gradient boosting tree instead of multi-layer perceptron for outcome prediction | Program outcome prediction · Program outcome prediction test set | ROC AUC: 0.691 -> 0.718 | Helped |
| Use gradient boosting tree instead of multi-layer perceptron for outcome prediction | Program outcome prediction · Program outcome prediction test set | Weighted F1 score: 0.454 -> 0.526 | Helped |
| Predict outcomes rather than use actual outcomes in the census simulation | Census simulation · DuPage census | MAPE: 3.01 -> 9.40 | Hurt |
| Predict outcomes rather than use actual outcomes in the census simulation | Census simulation · Cook census | MAPE: 4.95 -> 10.05 | Hurt |
| Predict outcomes rather than use actual outcomes in the census simulation | Census simulation · Will census | MAPE: 5.51 -> 7.03 | Hurt |
| Predict outcomes rather than use actual outcomes in the census simulation | Census simulation · Peoria census | MAPE: 15.78 -> 21.21 | Hurt |
| Address right-censoring with two-stage sampling and extended LOS for censored arrivals | Census simulation · Historical census calibration | Census prediction accuracy | Helped |
| Use empirical LOS distributions instead of machine-learning LOS prediction | Length-of-stay prediction · Diversion program participants | Mean squared error | Helped |
Surprising findings
- Lognormal, normal, and exponential fits to LOS all failed Kolmogorov-Smirnov tests, and ML regressors for LOS gave poor MSE, so empirical sampling was used instead.
Limitations
- Outcome prediction is weak (weighted F1 about 0.53), and it is the main source of census error, especially for later years and small counties.
- Data are from four Illinois counties and the model has not been validated for other jurisdictions.
- Right-censoring correction relies on assumed censoring probabilities and extended LOS assignments.
Experimental setup
Datasets: Illinois incarceration-diversion program records (DuPage, Cook, Will, Peoria counties)
Benchmarks: held-out program outcome test split historical census (weekly) for four counties
Metrics: OVR ROC AUC weighted F1 MAPE
Baselines: logistic regression decision tree multi-layer perceptron
Builds on: queueing network models for jail systems (Usta and Wein 2015) trace-based arrival simulation
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