Weighted Constrained CP-nets: an Extension of Constrained CP-nets with Weighted Constraints
Bibliographic record
Abstract
A Conditional Preference Network (CP-net) is a graphical model widely used to represent qualitative preferences in many real-world applications. Preference elicitation, representation, and reasoning plays an essential role in e-commerce and other applications relying on users’ preferences and desires. However, managing preferences often comes with dealing with hard and soft constraints. While hard constraints are requirements that can either be satisfied or violated, this two-level of satisfiability can be generalized to multiple levels through soft constraints. In this context, our main objective is to manage conditional and qualitative preferences together with hard and soft constraints, within a unique model. The constrained CP-net graphical model has been proposed to manage both conditional preferences and hard constraints. In order to include soft constraints, we extend the underlying constraint network of the constrained CP-net to a Weighted Constraint Satisfaction Problem (WCSP). A WCSP is a CSP where (soft) constraints can be violated or satisfied with associated costs. More precisely, a cost function is associated to each constraint. We call the Weighted Constrained CP-nets (WCCP-net) the new model we propose. Like for CP-nets and Constrained CP-nets, there are two queries to consider for WCCP-nets: outcome optimization and outcome comparison. The outcome optimization query in the case of a constrained CP-net consists in finding the set of feasible solutions that are not dominated by any other solutions. This set is called the Pareto optimal set. In the case of the WCCP-net, this task consists of finding those solutions, from the Pareto optimal set, that maximize the total cost function of the underlying WCSP. This is a NP-hard problem that we tackle using a variant of the branch and bound algorithm that has been proposed to solve the outcome optimization in the case of constrained CP-nets.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".