Univariate Probability Density Estimation With Partially Monotone Neural Networks: A Case Study on Shopping Activity Durations
Bibliographic record
Abstract
This study introduces a novel univariate probability density (UPD) model leveraging partially monotone neural networks to analyze activity durations, with a specific focus on shopping trips by noncommuters in Shanghai. The proposed method ensures the monotonicity of the cumulative distribution function (CDF) with respect to time while enabling flexible modeling of complex distributions influenced by exogenous variables. Simulation experiments validate the model’s robustness and accuracy in capturing distributional patterns and variable effects. Empirical analysis using the 2019 Shanghai Household Travel Survey data demonstrates the model’s capability to reveal nuanced relationships between shopping durations and demographic, household, and locational factors. The results provide valuable insights into activity‐based modeling and inform urban planning, transportation systems, and policy‐making. By enabling realistic sampling and robust scenario analysis, this approach establishes a flexible, data‐driven framework for studying activity durations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".