# ProbSAINT: Probabilistic Tabular Regression for Used Car Pricing

arXiv: https://arxiv.org/abs/2403.03812 · HTML: https://mlsanity.com/paper/2403.03812/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [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)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [DeepFM: A Factorization-Machine based Neural Network for CTR Prediction](https://mlsanity.com/paper/1703.04247/) (2017)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [TabTransformer: Tabular Data Modeling Using Contextual Embeddings](https://mlsanity.com/paper/2012.06678/) (2020)
- [SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training](https://mlsanity.com/paper/2106.01342/) (2021)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Noise Flow: Noise Modeling with Conditional Normalizing Flows](https://mlsanity.com/paper/1908.08453/) (2019)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Uncertainty in Gradient Boosting via Ensembles](https://mlsanity.com/paper/2006.10562/) (2020)
- [Probabilistic Gradient Boosting Machines for Large-Scale Probabilistic Regression](https://mlsanity.com/paper/2106.01682/) (2021)

## Built on by (most cited first, 1 of 1)

- [TabResFlow: A Normalizing Spline Flow Model for Probabilistic Univariate Tabular Regression](https://mlsanity.com/paper/2508.17056/) (2025)

## Abstract (arXiv)

Used car pricing is a critical aspect of the automotive industry, influenced by many economic factors and market dynamics. With the recent surge in online marketplaces and increased demand for used cars, accurate pricing would benefit both buyers and sellers by ensuring fair transactions. However, the transition towards automated pricing algorithms using machine learning necessitates the comprehension of model uncertainties, specifically the ability to flag predictions that the model is unsure about. Although recent literature proposes the use of boosting algorithms or nearest neighbor-based approaches for swift and precise price predictions, encapsulating model uncertainties with such algorithms presents a complex challenge. We introduce ProbSAINT, a model that offers a principled approach for uncertainty quantification of its price predictions, along with accurate point predictions that are comparable to state-of-the-art boosting techniques. Furthermore, acknowledging that the business prefers pricing used cars based on the number of days the vehicle was listed for sale, we show how ProbSAINT can be used as a dynamic forecasting model for predicting price probabilities for different expected offer duration. Our experiments further indicate that ProbSAINT is especially accurate on instances where it is highly certain. This proves the applicability of its probabilistic predictions in real-world scenarios where trustworthiness is crucial.