Behavioral Embeddings and Propensity Neighborhoods

Research on a practical question in energy-program recommendation: when should a recommender trust a more specific local comparison, and when should it keep the broader model?

The primary output is the accessible edition of Behavioral Embeddings and Propensity Neighborhoods for Program Recommendation:

• Read the paper in HTML
• Download the accessible PDF
• Visit the project landing page

Everything else in this repository, including earlier notes, follow-up experiments, scripts, and machine-readable results, is supporting material for that paper.

The story arc

The argument moves through three ideas.

1. Behavior creates a useful geometry. A customer's pre-decision history is compressed into an embedding. Combined with ordinary customer attributes, that embedding improves the estimated probability that the customer will enroll in each eligible program.
2. More specific neighborhoods spend support. Adding matching criteria produces peers who are more alike, but fewer in number. Similarity improves while statistical uncertainty grows.
3. A frontier governs trust. The method prices mismatch against sample size. Local evidence can calibrate a score or support a confidence flag; when the evidence is too thin, the recommender keeps the direct propensity ranking or abstains.

The empirical ending matters: behavioral embeddings deliver the main predictive and ranking gain. Propensity neighborhoods deliver a smaller calibration and reliability benefit, but no confirmed improvement in the winning recommendation.

The formalism, simply

For customer $x$, let $\mathcal A(x)$ be the eligible programs and let

$$ p_a(x)=\Pr(x\text{ enrolls in program }a) $$

be the true enrollment propensity. A fitted model combines static attributes $s(x)$ with a behavioral embedding $z(x)$:

$$ \widetilde p_a(x)=f_a!\left(s(x),z(x)\right). $$

The direct recommender chooses the eligible program with the largest fitted propensity. To test whether local evidence should adjust that score, the method builds nested peer sets

$$ \mathcal N_1(x;r)\supseteq\mathcal N_2(x;r)\supseteq\cdots\supseteq\mathcal N_M(x;r). $$

Each refinement adds detail. The worst mismatch among the remaining peers can only improve, while the peer count $n_m$ can only fall. The central bound makes that tradeoff explicit:

$$ b_m(x)=\varepsilon_m^\rho(x) +B\sqrt{\frac{\log(2K_x/\alpha)}{2n_m}}. $$

Here $\varepsilon_m^\rho$ measures how unlike the peers' remaining model errors are from the target's error; the second term is the uncertainty cost of limited support. The selected program's propensity regret is at most $2b_m(x)$ under the theorem's stated assumptions. The useful neighborhood is therefore not automatically the deepest one—it is the point where a closer match is still worth the peers it costs.

What the evidence says

In the chronological KuaiRec study, adding a behavioral embedding to static features:

• reduced propensity RMSE by 31.9%;
• reduced top-1 regret by 6.4%; and
• increased exact top-1 hit rate by 2.58 percentage points.

The embedding improved RMSE on all ten splits. Neighborhood methods found real calibration information, but the accumulated exploratory and confirmation experiments did not establish a reproducible top-1 ranking improvement. The supported workflow is consequently:

1. filter to eligible programs;
2. construct a behavioral embedding from pre-decision history;
3. fit a propensity for every eligible program;
4. rank directly by fitted propensity; and
5. use neighborhoods as an optional layer for calibration, diagnostics, confidence, fallback, or abstention.

This is a study of enrollment propensity, not incremental enrollment, energy savings, or causal program impact.

Repository map

Path	Role
papers/propensity-neighborhoods-accessible/	Primary accessible paper in HTML, PDF, and LaTeX
papers/propensity-neighborhoods/	Longer technical note and extensions
propensity-neighborhoods-v2/	Supplemental ranking and decision-boundary experiments
scripts/	Reproducible KuaiRec experiments
results/	Metrics, selected parameters, summaries, and experiment reports
data/	Data acquisition and local-layout instructions; raw data are not tracked

For the consolidated experimental interpretation, see propensity-neighborhoods-v2/OVERALL_CONCLUSION.md.

Reproduce the main experiment

The scripts target Python 3 and use the dependencies pinned in requirements.txt.

python -m venv .venv
.venv\Scripts\Activate.ps1
pip install -r requirements.txt

Place KuaiRec at data/kuairec/extracted as described in data/README.md, then run:

python scripts\kuairec_behavior_embedding_test.py

The script writes machine-readable output under results/. Additional experiment commands and their interpretations live beside the relevant scripts and result folders.

Citation

If this work informs your research, cite the paper title and author shown in the accessible edition. A machine-readable citation record will be added when the manuscript receives a permanent identifier.