# PIT-SUN: A Deployable Empirical Marginal Transform Framework with Expectation-Consistent Recovery for Regression in Recommender Systems

arXiv: https://arxiv.org/abs/2607.08202 · HTML: https://mlsanity.com/paper/2607.08202/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Builds on (most cited first, 12 of 12)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Deconfounding Duration Bias in Watch-time Prediction for Video Recommendation](https://mlsanity.com/paper/2206.06003/) (2022)
- [Tree based Progressive Regression Model for Watch-Time Prediction in Short-video Recommendation](https://mlsanity.com/paper/2306.03392/) (2023)
- [Billion-user Customer Lifetime Value Prediction: An Industrial-scale Solution from Kuaishou](https://mlsanity.com/paper/2208.13358/) (2022)
- [CREAD: A Classification-Restoration Framework with Error Adaptive Discretization for Watch Time Prediction in Video Recommender Systems](https://mlsanity.com/paper/2401.07521/) (2024)
- [Generative Regression Based Watch Time Prediction for Short-Video Recommendation](https://mlsanity.com/paper/2412.20211/) (2024)
- [OptDist: Learning Optimal Distribution for Customer Lifetime Value Prediction](https://mlsanity.com/paper/2408.08585/) (2024)
- [Conditional Quantile Estimation for Uncertain Watch Time in Short-Video Recommendation](https://mlsanity.com/paper/2407.12223/) (2024)
- [AlignPxtr: Aligning Predicted Behavior Distributions for Bias-Free Video Recommendations](https://mlsanity.com/paper/2503.06920/) (2025)
- [TranSUN: A Preemptive Paradigm to Eradicate Retransformation Bias Intrinsically from Regression Models in Recommender Systems](https://mlsanity.com/paper/2505.13881/) (2025)
- [Relative Advantage Debiasing for Watch-Time Prediction in Short-Video Recommendation](https://mlsanity.com/paper/2508.11086/) (2025)
- [CC-OR-Net: A Unified Framework for LTV Prediction through Structural Decoupling](https://mlsanity.com/paper/2601.10176/) (2026)

## Abstract (arXiv)

Estimating original-space conditional expectations is central to value-driven recommender systems, including dwell time, GMV, and LTV forecasting. Standard MSE is expectation-consistent in principle, but its gradients become unstable on heavy-tailed, zero-inflated, and multimodal targets, causing mean collapse and tail shrinkage. Target transformation alleviates this scale conflict, yet any useful nonlinear marginal transform loses expectation consistency under direct inversion. This is not an implementation oversight: a direct inverse-transform estimator is universally expectation-consistent only when the inverse transform is affine, which cannot simultaneously provide bounded tail compression. Existing conditionally linear recovery methods restore expectation consistency, but still leave open which coordinate, inverse lookup, recovery base, and deployment monitor should be selected for sparse complex marginals. We propose Probability-Integral-TranSformed Unbiased recovery (PIT-SUN), a deployable empirical marginal recovery framework. PIT-SUN uses one empirical marginal table to define a bounded normal-score coordinate, its inverse-quantile lookup, a variance-controlled recovery base, and drift monitoring, then applies multiplicative SUN recovery to estimate the original-space expectation instead of directly inverting transformed predictions. Experiments on synthetic distributions, public benchmarks, large-scale industrial datasets, and online deployment show robust improvements in point accuracy, calibration, and ranking quality with lightweight deployment overhead.