The problem of measuring the true incremental effectiveness of a digital advertising campaign is of increasing importance to marketers. With a large and increasing percentage of digital advertising delivered via Demand-Side-Platforms (DSPs) executing campaigns via Real-Time-Bidding (RTB) auctions and programmatic approaches, a measurement solution that satisfies both advertiser concerns and the constraints of a DSP is of particular interest. MediaMath (a DSP) has developed the first practical, statistically sound randomization-based methodology for causal ad effectiveness (or Ad Lift) measurement by a DSP (or similar digital advertising execution system that may not have full control over the advertising transaction mechanisms). We describe our solution and establish its soundness within the causal framework of counterfactuals and potential outcomes, and present a Gibbs-sampling procedure for estimating confidence intervals around the estimated Ad Lift. We also address practical complications (unique to the digital advertising setting) that stem from the fact that digital advertising is targeted and measured via identifiers (e.g., cookies, mobile advertising IDs) that may not be stable over time. One such complication is the repeated occurrence of identifiers, leading to interference among observations. Another is due to the possibility of multiple identifiers being associated with the same consumer, leading to "contamination" with some of their identifiers being assigned to the Treatment group and others to the Control group. Complications such as these have severely impaired previous efforts to derive accurate measurements of lift in practice. In contrast to a few other papers on the subject, this paper has an expository aim as well, and provides a rigorous, self-contained, and readily-implementable treatment of all relevant concepts.
We note that in the category of observational approaches, there has been recent interest in applying Machine Learning techniques to estimate the @math (or Individual Treatment Effect, @math ) as a function of covariates (or features) of an individual entity. For example, @cite_2 @cite_8 present a decision-tree based approach to estimate the @math ; @cite_20 show how counterfactuals can be estimated by learning representations (using linear models or deep neural networks) that encourage similarity (or balance) between Test and Control populations; @cite_9 introduce the concept of "Deep Instrumental Variables Networks" which are able to predict the counterfactual and hence estimate causal effects.
@cite_8 @cite_9 @cite_20 @cite_2
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Machine learning is now being used to make crucial decisions about people's lives. For nearly all of these decisions there is a risk that individuals of a certain race, gender, sexual orientation, or any other subpopulation are unfairly discriminated against. Our recent method has demonstrated how to use techniques from counterfactual inference to make predictions fair across different subpopulations. This method requires that one provides the causal model that generated the data at hand. In general, validating all causal implications of the model is not possible without further assumptions. Hence, it is desirable to integrate competing causal models to provide counterfactually fair decisions, regardless of which causal "world" is the correct one. In this paper, we show how it is possible to make predictions that are approximately fair with respect to multiple possible causal models at once, thus mitigating the problem of exact causal specification. We frame the goal of learning a fair classifier as an optimization problem with fairness constraints entailed by competing causal explanations. We show how this optimization problem can be efficiently solved using gradient-based methods. We demonstrate the flexibility of our model on two real-world fair classification problems. We show that our model can seamlessly balance fairness in multiple worlds with prediction accuracy. Learning representations for counterfactual inference from observational data is of high practical relevance for many domains, such as healthcare, public policy and economics. Counterfactual inference enables one to answer "What if...?" questions, such as "What would be the outcome if we gave this patient treatment @math ?". However, current methods for training neural networks for counterfactual inference on observational data are either overly complex, limited to settings with only two available treatment options, or both. Here, we present Perfect Match (PM), a method for training neural networks for counterfactual inference that is easy to implement, compatible with any architecture, does not add computational complexity or hyperparameters, and extends to any number of treatments. PM is based on the idea of augmenting samples within a minibatch with their propensity-matched nearest neighbours. Our experiments demonstrate that PM outperforms a number of more complex state-of-the-art methods in inferring counterfactual outcomes across several real-world and semi-synthetic datasets. Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregionalization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes. We conduct experiments on observational datasets for an interventional social program applied to premature infants, and a left ventricular assist device applied to cardiac patients wait-listed for a heart transplant. In both experiments, we show that our method significantly outperforms the state-of-the-art. Motivated by online recommendation and advertising systems, we consider a causal model for stochastic contextual bandits with a latent low-dimensional confounder. In our model, there are @math observed contexts and @math arms of the bandit. The observed context influences the reward obtained through a latent confounder variable with cardinality @math ( @math ). The arm choice and the latent confounder causally determines the reward while the observed context is correlated with the confounder. Under this model, the @math mean reward matrix @math (for each context in @math and each arm in @math ) factorizes into non-negative factors @math ( @math ) and @math ( @math ). This insight enables us to propose an @math -greedy NMF-Bandit algorithm that designs a sequence of interventions (selecting specific arms), that achieves a balance between learning this low-dimensional structure and selecting the best arm to minimize regret. Our algorithm achieves a regret of @math at time @math , as compared to @math for conventional contextual bandits, assuming a constant gap between the best arm and the rest for each context. These guarantees are obtained under mild sufficiency conditions on the factors that are weaker versions of the well-known Statistical RIP condition. We further propose a class of generative models that satisfy our sufficient conditions, and derive a lower bound of @math . These are the first regret guarantees for online matrix completion with bandit feedback, when the rank is greater than one. We further compare the performance of our algorithm with the state of the art, on synthetic and real world data-sets.