In our previous post on bid optimisation, we concluded with a cliched cliffhanger. Better with something Bayesian, until next time. Click bait from an era before clicks. It was not all just wishful thinking though. Back then we were already working on a Bayesian win price prediction model and having now put it into production, we are in a position to share why we strongly believe it is worth adopting a Bayesian approach for win price prediction in ad auctions.
Generally speaking, Bayesian approaches refer to updating prior beliefs, expressed as some distributions, based on observed evidence to infer current beliefs, expressed as some posterior distributions. Kind of an incremental model update, you’d say? Yes, but the key word here was not updating, it was distributions. Namely, when performing Bayesian win price prediction, one does not predict a single number, or a point estimate, based on the input features, but a probability distribution for the prediction.
This enables us to do something more than just predicting the win price. It allows us to evaluate the winning probability for any bid for the current auction. To understand how this comes about, it is helpful to revisit the distinction between a normal and Bayesian regression problem (see also this blog post about the relationship between linear and Bayesian regression).
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