  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.
