# Variogram Preservation on Synthetic Bivariate Relationships Variable X - Spherical

Source: [Variogram Preservation on Synthetic Bivariate Relationships Variable X - Spherical](<https://www.sota2.com/research/sota/variogram-preservation-on-synthetic-bivariate-relationships-variable-x-spherical>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-03-20T08:13:49.361Z

Evaluation of model performance on preserving specific structural components (Step, Gaussian Mix, Sinusoidal, etc.) when modeling the Synthetic Bivariate Relationships Variable X - Spherical dataset.

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 | Variogram Preservation |
| Dataset (including any stated split) | Synthetic Bivariate Relationships Variable X - Spherical |
| Metric | Step Preservation |
| Unit | PERCENT |
| 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

- [Step Preservation](<https://www.sota2.com/research/sota/variogram-preservation-on-synthetic-bivariate-relationships-variable-x-spherical.md?metric=Step%20Preservation>): Higher is better; unit: PERCENT.

- [Gaussian Mix Preservation](<https://www.sota2.com/research/sota/variogram-preservation-on-synthetic-bivariate-relationships-variable-x-spherical.md?metric=Gaussian%20Mix%20Preservation>): Higher is better; unit: PERCENT.

- [Sinusoidal Preservation](<https://www.sota2.com/research/sota/variogram-preservation-on-synthetic-bivariate-relationships-variable-x-spherical.md?metric=Sinusoidal%20Preservation>): Higher is better; unit: PERCENT.

- [Step Random Preservation](<https://www.sota2.com/research/sota/variogram-preservation-on-synthetic-bivariate-relationships-variable-x-spherical.md?metric=Step%20Random%20Preservation>): Higher is better; unit: PERCENT.

- [Heteroscedastic Preservation](<https://www.sota2.com/research/sota/variogram-preservation-on-synthetic-bivariate-relationships-variable-x-spherical.md?metric=Heteroscedastic%20Preservation>): Higher is better; unit: PERCENT.

- [Wins Count](<https://www.sota2.com/research/sota/variogram-preservation-on-synthetic-bivariate-relationships-variable-x-spherical.md?metric=Wins%20Count>): Higher is better; unit: SCALAR.

## Recorded results

| Method | Step Preservation | Result date | Report paper |
| --- | --- | --- | --- |
| LU | 99.8 | Not recorded | 69bcd4880636e5bf4afc29be |
| MST-Direct | 99.5 | Not recorded | 69bcd4880636e5bf4afc29be |
| Copula | 93.4 | Not recorded | 69bcd4880636e5bf4afc29be |

### LU

Step Preservation: 99.8. Result ID: 69bd01b347f34ce924a6f0f1.

[Reporting paper](<https://www.sota2.com/research/paper/69bcd4880636e5bf4afc29be.md>)

Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction.

### MST-Direct

Step Preservation: 99.5. Result ID: 69bd01b347f34ce924a6f0ef.

[Reporting paper](<https://www.sota2.com/research/paper/69bcd4880636e5bf4afc29be.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69bcd4880636e5bf4afc29be.md>)

Recorded evaluation configuration: {"k":"8","beta":"35.0","lambda":"2.2"}. This record does not assert independent reproduction.

### Copula

Step Preservation: 93.4. Result ID: 69bd01b347f34ce924a6f0f0.

[Reporting paper](<https://www.sota2.com/research/paper/69bcd4880636e5bf4afc29be.md>)

Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction.

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