# Shape Preservation on Synthetic Bivariate Dataset Step Relationship Source: [Shape Preservation on Synthetic Bivariate Dataset Step Relationship]() Collection index: [llms.txt]() Data updated: 2026-03-20T08:13:49.384Z Evaluation of shape preservation capabilities using the Synthetic Bivariate Dataset Step Relationship, measured via Histogram 2D Similarity. A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. | Scope | Recorded value | | --- | --- | | Task | Shape Preservation | | Dataset (including any stated split) | Synthetic Bivariate Dataset Step Relationship | | Metric | Histogram 2D Similarity | | Unit | SCALAR | | Direction | Higher is better | | Results loaded | 3 of 3 | | Coverage | All results currently returned for this benchmark | Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol. ## Metrics - [Histogram 2D Similarity](): Higher is better; unit: SCALAR. ## Recorded results | Method | Histogram 2D Similarity | Result date | Report paper | | --- | --- | --- | --- | | MST-Direct | 1 | Not recorded | 69bcd4880636e5bf4afc29be | | LU Decomposition | 0.678 | Not recorded | 69bcd4880636e5bf4afc29be | | Gaussian Copula | 0.657 | Not recorded | 69bcd4880636e5bf4afc29be | ### MST-Direct Histogram 2D Similarity: 1. Result ID: 69bd01b347f34ce924a6f0f2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"k":"8","beta":"35.0","lambda":"2.2"}. This record does not assert independent reproduction. ### LU Decomposition Histogram 2D Similarity: 0.678. Result ID: 69bd01b347f34ce924a6f0f4. [Reporting paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### Gaussian Copula Histogram 2D Similarity: 0.657. Result ID: 69bd01b347f34ce924a6f0f3. [Reporting paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.