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Predictive Modeling of Homeless Service Assignment: A Representation Learning Approach
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Proposes REPLETE, a representation-learning model that factorizes service-time, service-transition and individual-clustering matrices with ADMM-optimized NMF-style updates, then feeds the derived features into a feed-forward network to predict the next homeless service assignment.
Problem
Predicting the next service assignment for chronically homeless individuals from categorical administrative data, where one-hot encoding misses feature and service relationships.
Approach
Jointly learns latent service and feature representations via a single objective with temporal (NMF with smoothness), functional (symmetric NMF on transition matrix) and individual (soft clustering with L2,1 norms and cosine-similarity regularizer) contexts, and uses the resulting representations and interaction features as input to an FFNN instead of one-hot encodings.
Key results
- REPLETE reaches 0.832 accuracy and 0.567 F1 on next-service prediction (N=3), versus 0.745 accuracy and 0.435 F1 for PREVISE and 0.802 accuracy and 0.513 F1 for LSTM.
- Ablation shows service and feature representations drive most of the gain: rep alone gives 0.825 accuracy, while inst-only gives 0.625 and feat-only gives 0.614.
- Bias analysis shows REPLETE has more balanced demographic parity and equal opportunity than PREVISE, which fails to predict some services for some groups, though low-frequency services remain biased.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace one-hot baseline inputs with REPLETE's learned representations and interaction features | Service assignment prediction · CARES of NY service assignment test set (N=3) | accuracy: 0.802 -> 0.832 | Helped |
| Replace one-hot baseline inputs with REPLETE's learned representations and interaction features | Service assignment prediction · CARES of NY service assignment test set (N=3) | F1 score: 0.513 -> 0.567 | Helped |
| Use service and feature representations instead of omitting representations (ablation) | REPLETE derived features · CARES of NY service assignment test set | accuracy: 0.717 -> 0.832 | Helped |
| Add instance interactions to representations and feature interactions (ablation) | REPLETE derived features · CARES of NY service assignment test set | accuracy: 0.829 -> 0.832 | Helped |
| Add feature interactions to representations and instance interactions (ablation) | REPLETE derived features · CARES of NY service assignment test set | F1 score: 0.543 -> 0.567 | Helped |
| Add individual context to temporal and functional contexts in optimization (ablation) | REPLETE representation learning · CARES of NY service assignment test set | accuracy: 0.801 -> 0.832 | Helped |
| Add temporal context to individual and functional contexts in optimization (ablation) | REPLETE representation learning · CARES of NY service assignment test set | F1 score: 0.534 -> 0.567 | Helped |
| Add functional context to individual and temporal contexts in optimization (ablation) | REPLETE representation learning · CARES of NY service assignment test set | accuracy: 0.827 -> 0.832 | Helped |
| Set service-history length to 2 rather than 3 (ablation) | REPLETE · CARES of NY service assignment test set | accuracy: 0.832 -> 0.828 | Hurt |
| Set service-history length to 4 rather than 3 (ablation) | REPLETE · CARES of NY service assignment test set | accuracy: 0.832 -> 0.809 | Hurt |
| Set service-history length to 5 rather than 3 (ablation) | REPLETE · CARES of NY service assignment test set | accuracy: 0.832 -> 0.805 | Hurt |
| Set service-history length to 6 rather than 3 (ablation) | REPLETE · CARES of NY service assignment test set | F1 score: 0.567 -> 0.561 | Hurt |
Surprising findings
- Feature interactions alone perform poorly (accuracy 0.614, F1 0.144), and adding them to instance interactions only partially helps, indicating the learned service/feature representations carry most of the benefit.
- A plain FFNN on one-hot features (0.714 accuracy) beats TRACE and LR but is well below the learned-representation model.
Limitations
- Dataset is geographically limited to the Capital Region of New York and cannot be shared due to privacy.
- Dataset does not record service availability or capacity, so predictions cannot account for it.
- Bias is not explicitly modeled; low-frequency services still show bias.
Experimental setup
Datasets: CARES of NY administrative data (anonymized)
Benchmarks: CARES of NY homeless service dataset
Metrics: accuracy recall precision F1 score demographic parity equal opportunity
Baselines: TRACE PREVISE Transformer LR FFNN_1 RF RNN LSTM
Builds on: non-negative matrix factorization symmetric NMF ADMM TRACE PREVISE
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