Kaplan–Meier Markov network: Learning the distribution of market price by censored data in online advertising

With the rapid development of real-time bidding (RTB) in online advertising, learning the distribution of market price has attracted wide attention, since it plays a critical role in designing bidding strategies. One important problem is the right-censored issue in which the true market price can only be observed by the winner of the auction. To address this, existing studies often use Kaplan–Meier estimation (KM), which is one of the best options for survival analysis. However, these approaches depend on counting sample segments and cannot provide accurate predictions for each individual bid request. To enhance the prediction ability, we propose an original method to build the KM for each bid request by predicting (1) the probability of winning an auction at a specific market price, and (2) the probability of losing an auction at a certain bid price. To deal with the high-dimensional sample data common in RTB scenarios, we design a Markov network to calculate these two probabilities. Extensive experiments on two public datasets demonstrate that the proposed approach significantly outperforms state-of-the-art baselines in terms of various metrics, including Wasserstein distance, KL-divergence, average negative log probability and mean squared error.