# Arbitrary Distribution Modeling with Censorship in Real-Time Bidding Advertising

arXiv: https://arxiv.org/abs/2110.13587 · HTML: https://mlsanity.com/paper/2110.13587/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 20 of 20)

- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Pay Attention to MLPs](https://mlsanity.com/paper/2105.08050/) (2021)
- [DCN V2: Improved Deep & Cross Network and Practical Lessons for Web-scale Learning to Rank Systems](https://mlsanity.com/paper/2008.13535/) (2020)
- [AutoInt: Automatic Feature Interaction Learning via Self-Attentive Neural Networks](https://mlsanity.com/paper/1810.11921/) (2018)
- [xDeepFM: Combining Explicit and Implicit Feature Interactions for Recommender Systems](https://mlsanity.com/paper/1803.05170/) (2018)
- [Neural Factorization Machines for Sparse Predictive Analytics](https://mlsanity.com/paper/1708.05027/) (2017)
- [Product-based Neural Networks for User Response Prediction](https://mlsanity.com/paper/1611.00144/) (2016)
- [Attentional Factorization Machines: Learning the Weight of Feature Interactions via Attention Networks](https://mlsanity.com/paper/1708.04617/) (2017)
- [Do You Even Need Attention? A Stack of Feed-Forward Layers Does Surprisingly Well on ImageNet](https://mlsanity.com/paper/2105.02723/) (2021)
- [Display Advertising with Real-Time Bidding (RTB) and Behavioural Targeting](https://mlsanity.com/paper/1610.03013/) (2016)
- [RepMLP: Re-parameterizing Convolutions into Fully-connected Layers for Image Recognition](https://mlsanity.com/paper/2105.01883/) (2021)
- [Modeling the Sequential Dependence among Audience Multi-step Conversions with Multi-task Learning in Targeted Display Advertising](https://mlsanity.com/paper/2105.08489/) (2021)
- [Real-time Bidding for Online Advertising: Measurement and Analysis](https://mlsanity.com/paper/1306.6542/) (2013)
- [Neural Auction: End-to-End Learning of Auction Mechanisms for E-Commerce Advertising](https://mlsanity.com/paper/2106.03593/) (2021)
- [Bidding Machine: Learning to Bid for Directly Optimizing Profits in Display Advertising](https://mlsanity.com/paper/1803.02194/) (2018)
- [Real-Time Bidding Benchmarking with iPinYou Dataset](https://mlsanity.com/paper/1407.7073/) (2014)
- [An Efficient Deep Distribution Network for Bid Shading in First-Price Auctions](https://mlsanity.com/paper/2107.06650/) (2021)
- [Deep Landscape Forecasting for Real-time Bidding Advertising](https://mlsanity.com/paper/1905.03028/) (2019)
- [A Deep Recurrent Survival Model for Unbiased Ranking](https://mlsanity.com/paper/2004.14714/) (2020)

## Built on by (most cited first, 3 of 3)

- [Breaking Determinism: Stochastic Modeling for Reliable Off-Policy Evaluation in Ad Auctions](https://mlsanity.com/paper/2512.03354/) (2025)
- [Generative Bid Shading in Real-Time Bidding Advertising](https://mlsanity.com/paper/2508.06550/) (2025)
- [Bid2X: Revealing Dynamics of Bidding Environment in Online Advertising from A Foundation Model Lens](https://mlsanity.com/paper/2510.23410/) (2025)

## Abstract (arXiv)

The purpose of Inventory Pricing is to bid the right prices to online ad opportunities, which is crucial for a Demand-Side Platform (DSP) to win advertising auctions in Real-Time Bidding (RTB). In the planning stage, advertisers need the forecast of probabilistic models to make bidding decisions. However, most of the previous works made strong assumptions on the distribution form of the winning price, which reduced their accuracy and weakened their ability to make generalizations. Though some works recently tried to fit the distribution directly, their complex structure lacked efficiency on online inference. In this paper, we devise a novel loss function, Neighborhood Likelihood Loss (NLL), collaborating with a proposed framework, Arbitrary Distribution Modeling (ADM), to predict the winning price distribution under censorship with no pre-assumption required. We conducted experiments on two real-world experimental datasets and one large-scale, non-simulated production dataset in our system. Experiments showed that ADM outperformed the baselines both on algorithm and business metrics. By replaying historical data of the production environment, this method was shown to lead to good yield in our system. Without any pre-assumed specific distribution form, ADM showed significant advantages in effectiveness and efficiency, demonstrating its great capability in modeling sophisticated price landscapes.