In programmatic advertising, ad slots are usually sold using second-price (SP) auctions in real-time. The highest bidding advertiser wins but pays only the second-highest bid (known as the winning price). In SP, for a single item, the dominant strategy of each bidder is to bid the true value from the bidder's perspective. However, in a practical setting, with budget constraints, bidding the true value is a sub-optimal strategy. Hence, to devise an optimal bidding strategy, it is of utmost importance to learn the winning price distribution accurately. Moreover, a demand-side platform (DSP), which bids on behalf of advertisers, observes the winning price if it wins the auction. For losing auctions, DSPs can only treat its bidding price as the lower bound for the unknown winning price. In literature, typically censored regression is used to model such partially observed data. A common assumption in censored regression is that the winning price is drawn from a fixed variance (homoscedastic) uni-modal distribution (most often Gaussian). However, in reality, these assumptions are often violated. We relax these assumptions and propose a heteroscedastic fully parametric censored regression approach, as well as a mixture density censored network. Our approach not only generalizes censored regression but also provides flexibility to model arbitrarily distributed real-world data. Experimental evaluation on the publicly available dataset for winning price estimation demonstrates the effectiveness of our method. Furthermore, we evaluate our algorithm on one of the largest demand-side platforms and significant improvement has been achieved in comparison with the baseline solutions.

中文翻译：

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实时竞价中的可扩展竞价前景预测

在程序化广告中，广告位通常使用第二价格 (SP) 实时拍卖进行销售。出价最高的广告商获胜，但只支付第二高的出价（称为中标价格）。在SP中，对于单个项目，每个投标人的优势策略是从投标人的角度投标真实价值。然而，在实际环境中，由于预算有限，出价真实价值是次优策略。因此，要设计出最优的竞价策略，准确了解中标价格分布至关重要。此外，代表广告商出价的需求方平台 (DSP) 会在赢得拍卖后观察中标价格。对于失败的拍卖，DSP 只能将其投标价格视为未知中标价格的下限。在文学中，通常，删失回归用于对这种部分观察到的数据进行建模。删失回归中的一个常见假设是获胜价格来自固定方差（同方差）单峰分布（最常见的是高斯分布）。然而，在现实中，这些假设经常被违反。我们放宽了这些假设，并提出了异方差全参数删失回归方法，以及混合密度删失网络。我们的方法不仅概括了删失回归，而且还提供了对任意分布的现实世界数据进行建模的灵活性。对用于获胜价格估计的公开可用数据集的实验评估证明了我们方法的有效性。此外，