Bayesian active learning is based on information theoretical approaches that
focus on maximising the information that new observations provide to the model
parameters. This is commonly done by maximising the Bayesian Active Learning by
Disagreement (BALD) acquisitions function. However, we highlight that it is
challenging to estimate BALD when the new data points are subject to
censorship, where only clipped values of the targets are observed. To address
this, we derive the entropy and the mutual information for censored
distributions and derive the BALD objective for active learning in censored
regression ($\mathcal{C}$-BALD). We propose a novel modelling approach to
estimate the $\mathcal{C}$-BALD objective and use it for active learning in the
censored setting. Across a wide range of datasets and models, we demonstrate
that $\mathcal{C}$-BALD outperforms other Bayesian active learning methods in
censored regression.

提出了一种新的建模方法来估计在剪辑回归中的主动学习目标，并证明其在各种数据集和模型中优于其他贝叶斯主动学习方法。

贝叶斯主动学习用于被审查回归

Bayesian Active Learning for Censored Regression

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.

本文提出了一个基于未完全观测数据的 heteroscedastic fully parametric censored regression 方法和混合密度 censored 网络，用于估计广告拍卖中的赢价分布，并在实验上证明了该方法的有效性。