# Connecting Surrogate Safety Measures to Crash Probablity via Causal Probabilistic Time Series Prediction

arXiv: https://arxiv.org/abs/2210.01363 · HTML: https://mlsanity.com/paper/2210.01363/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 66 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 13 of 13)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [INTERACTION Dataset: An INTERnational, Adversarial and Cooperative moTION Dataset in Interactive Driving Scenarios with Semantic Maps](https://mlsanity.com/paper/1910.03088/) (2019)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Learning to Collide: An Adaptive Safety-Critical Scenarios Generating Method](https://mlsanity.com/paper/2003.01197/) (2020)

## Abstract (arXiv)

Surrogate safety measures can provide fast and pro-active safety analysis and give insights on the pre-crash process and crash failure mechanism by studying near misses. However, validating surrogate safety measures by connecting them to crashes is still an open question. This paper proposed a method to connect surrogate safety measures to crash probability using probabilistic time series prediction. The method used sequences of speed, acceleration and time-to-collision to estimate the probability density functions of those variables with transformer masked autoregressive flow (transformer-MAF). The autoregressive structure mimicked the causal relationship between condition, action and crash outcome and the probability density functions are used to calculate the conditional action probability, crash probability and conditional crash probability. The predicted sequence is accurate and the estimated probability is reasonable under both traffic conflict context and normal interaction context and the conditional crash probability shows the effectiveness of evasive action to avoid crashes in a counterfactual experiment.