# Density Estimation on Pumsb-star Twenty Datasets (test)

Source: [Density Estimation on Pumsb-star Twenty Datasets (test)](<https://www.sota2.com/research/sota/density-estimation-on-pumsb-star-twenty-datasets-test>)

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

Data updated: 2026-02-26T05:48:42.873Z

Evaluation of Density Estimation performance on the test split of the Pumsb-star Twenty Datasets, typically measured using Log-Likelihood (Log-LH).

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 | Density Estimation |
| Dataset (including any stated split) | Pumsb-star Twenty Datasets (test) |
| Metric | Log-Likelihood |
| Unit | SCALAR |
| Direction | Higher is better |
| Results loaded | 4 of 4 |
| 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

- [Log-Likelihood](<https://www.sota2.com/research/sota/density-estimation-on-pumsb-star-twenty-datasets-test.md?metric=Log-Likelihood>): Higher is better; unit: SCALAR.

## Recorded results

| Method | Log-Likelihood | Result date | Report paper |
| --- | --- | --- | --- |
| HyperSPN | -31.07 | Not recorded | 68fa6b621e209131cea2de8f |
| SPN + Weight Decay | -31.08 | Not recorded | 68fa6b621e209131cea2de8f |
| RAT-SPN | -32.53 | Not recorded | 68fa6b621e209131cea2de8f |
| EiNETs | -39.23 | Not recorded | 68fa6b621e209131cea2de8f |

### HyperSPN

Log-Likelihood: -31.07. Result ID: 698e8414ffc3901de09e41ce.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6b621e209131cea2de8f.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6b621e209131cea2de8f.md>)

[Implementation](<https://github.com/AndyShih12/HyperSPN>)

Recorded evaluation configuration: {"Optimizer":"Adam","Regularization Strategy":"HyperSPN","Architecture":"SPN","# Params":"82615"}. This record does not assert independent reproduction.

### SPN + Weight Decay

Log-Likelihood: -31.08. Result ID: 698e8414ffc3901de09e41cd.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6b621e209131cea2de8f.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6a281e209131cea2670f.md>)

Recorded evaluation configuration: {"Optimizer":"Adam","Regularization Strategy":"Weight Decay","Architecture":"SPN","# Params":"407550"}. This record does not assert independent reproduction.

### RAT-SPN

Log-Likelihood: -32.53. Result ID: 698e8414ffc3901de09e41d0.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6b621e209131cea2de8f.md>)

Recorded evaluation configuration: {"Optimizer":"sEM†","Architecture":"RAT-SPN"}. This record does not assert independent reproduction.

### EiNETs

Log-Likelihood: -39.23. Result ID: 698e8414ffc3901de09e41cf.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6b621e209131cea2de8f.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa675d1e209131cea15e1f.md>)

Recorded evaluation configuration: {"Optimizer":"Adam\*","Architecture":"EiNETs"}. This record does not assert independent reproduction.

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