# SAUSS: Stochastic Approximation with Unbiased Simulated Scores for Limited Dependent Variable Models

arXiv: https://arxiv.org/abs/2608.25304 · HTML: https://mlsanity.com/paper/2608.25304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Fast and Robust Online Inference with Stochastic Gradient Descent via Random Scaling](https://mlsanity.com/paper/2106.03156/) (2021)
- [On Constructing Confidence Region for Model Parameters in Stochastic Gradient Descent via Batch Means](https://mlsanity.com/paper/1911.01483/) (2019)
- [SGMM: Stochastic Approximation to Generalized Method of Moments](https://mlsanity.com/paper/2308.13564/) (2023)
- [Computationally Efficient Estimation of Large Probit Models](https://mlsanity.com/paper/2407.09371/) (2024)
- [SLIM: Stochastic Learning and Inference in Overidentified Models](https://mlsanity.com/paper/2510.20996/) (2025)
- [Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks](https://mlsanity.com/paper/2603.24705/) (2026)

## Abstract (arXiv)

Multinomial choice models allow flexible substitution patterns but become computationally demanding with many alternatives or observations. With a fixed per-observation simulation budget, simulated maximum likelihood introduces simulation bias, while each optimization step requires a full-sample likelihood evaluation. We propose Stochastic Approximation with Unbiased Simulated Scores (SAUSS), an averaged stochastic approximation based on conditionally unbiased mini-batch score estimates. Each iteration uses a fixed mini-batch regardless of sample size. For multinomial probit, accept-reject sampling provides exact conditional draws and unbiased score estimates for any fixed number of accepted draws. Under local conditions, asymptotic theory for the averaged estimator and the partial-sum process of the SAUSS iterates incorporates mini-batch and simulation variability and supports random-scaling and plug-in inference. In simulations and an application, SAUSS gives comparable results in less than 1% of the computation time of simulated maximum likelihood. SAUSS extends to limited dependent variable models with conditional-expectation score representations and exact conditional sampling.