# Boundary Density Likelihood for Direct Event-Time Supervision

arXiv: https://arxiv.org/abs/2408.12792 · HTML: https://mlsanity.com/paper/2408.12792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 23 Aug 2024.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [Simple Baselines for Human Pose Estimation and Tracking](https://mlsanity.com/paper/1804.06208/) (2018)
- [BMN: Boundary-Matching Network for Temporal Action Proposal Generation](https://mlsanity.com/paper/1907.09702/) (2019)
- [BSN: Boundary Sensitive Network for Temporal Action Proposal Generation](https://mlsanity.com/paper/1806.02964/) (2018)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [TURN TAP: Temporal Unit Regression Network for Temporal Action Proposals](https://mlsanity.com/paper/1703.06189/) (2017)
- [SeqSleepNet: End-to-End Hierarchical Recurrent Neural Network for Sequence-to-Sequence Automatic Sleep Staging](https://mlsanity.com/paper/1809.10932/) (2018)
- [U-Time: A Fully Convolutional Network for Time Series Segmentation Applied to Sleep Staging](https://mlsanity.com/paper/1910.11162/) (2019)
- [Rethinking the Heatmap Regression for Bottom-up Human Pose Estimation](https://mlsanity.com/paper/2012.15175/) (2020)
- [Precision and Recall for Time Series](https://mlsanity.com/paper/1803.03639/) (2018)
- [Heatmap Regression via Randomized Rounding](https://mlsanity.com/paper/2009.00225/) (2020)

## Abstract (arXiv)

Event detection turns long recordings into a sparse set of ranked timestamps. Yet many sequence models are trained for samplewise segmentation and only convert predicted states into events after training. We ask whether training directly for the evaluated output improves detection. Boundary Density Likelihood (BDL) assigns one unit of target mass to each annotated event, preserves that mass through smoothing and temporal downsampling, and uses a Poisson objective to estimate expected event mass in each output bin; local peaks become ranked detections. In a prespecified five-fold nested sleep study, BDL-Hard raises pooled out-of-fold mAP from 0.586 to 0.705 over interval segmentation (+11.9 percentage points; 95% interval [10.8, 13.0]) and strict one-minute AP from 0.071 to 0.286 (4.0x; +21.5 points), improving on every outer fold. A separate held-out rerun reproduces the direction of the effect. A matched boundary-BCE detector reaches 0.702 mAP, showing that direct boundary supervision and event decoding account for most of the gain, with a smaller contribution from the Poisson objective. The same trend appears with an offline convolutional model; causal, Transformer, and patient-grouped seizure experiments leave broader generalization unresolved. Our results support training on event times when timestamps define the evaluated output.