In recent years, advertisers have increasingly shifted their ad expenditures online. One of the most effective platforms for online advertising is search engine result pages. Given a user query, the search engine allocates a few ad slots (e.g., above or below its organic search results) and runs an auction among advertisers who are bidding and competing for these slots. Quantifying the effectiveness of ad placement is vital not only to the experience of the user, but also revenue of the advertiser and the search engine. Click yield is a common metric used in this regard. Often, statistical and flexible machine learning models are used to predict the click behavior of users by estimating the likelihood of receiving a click in a given slot using logged data. A rich literature is devoted to click prediction in sponsored search advertising (Shaparenko et al., 2009; Cheng and Cantú-Paz, 2010; Cheng et al., 2012; Xiong et al., 2012; Zhang et al., 2014; Nabi-Abdolyousefi, 2015; Effendi and Ali, 2017; Bisht and Susan, 2021). For a survey on click prediction in online advertising please refer to Wang (2020). However, a comprehensive understanding of click behavior requires causal, rather than associative, reasoning (Bottou et al., 2013; Yin et al., 2014; Hill et al., 2015; Zeng et al., 2021).

Causal inference is central to making data-driven decisions. Inferring valid cause-effect relations, even with granular data and large sample sizes, is complicated by confounding induced by common causes of observed exposures and outcomes. In classical causal inference, it is assumed that samples are independent and identically distributed (iid). However, a causal view of ad placement under the iid assumption is implausible as ads interfere with one another from the beginning of the auction until the end when clicks on impressed ads are recorded. In non-iid settings, confounding arises due to not only the individual ad-level covariates but also the exposures and covariates of other ads in the system. This is commonly referred to as interference (Hudgens and Halloran, 2008). Incorporating knowledge of interference into the statistical models used to compute rank scores for each ad can help optimize the final layout of each search page. Moreover, a proper understanding of the interference issue in relation to causal inference directly impacts engineering of more purposeful interventions and design of more effective A/B testing for ad placement. Alternatively, randomized experiments via bipartite graphs offer a useful formalism to study two-sided market experiments under violation of iid assumption (Pouget-Abadie et al., 2018, 2019; Bajari et al., 2021; Harshaw et al., 2021; Johari et al., 2022). This stands in contrast with interference that occurs on networks where all units are of the same type (e.g., ads in a block)—in bipartite experiments, there is a distinction between units that can be subject to an intervention and units whose responses are of interest to the experimenter. Hence, modeling what we are after in the context of sponsored search advertising is closer to the causal framework for modeling interference in social networks.

In this paper, we formalize the problem of interference among ads using the language of causal inference. To the best of our knowledge, this is the first analyis of ads under the plausible and realistic setting of interference. We hope our proposed framework serves as a benchmark for future work in search advertising that go beyond the classical iid assumption. Throughout the paper, we discuss mechanisms that give rise to interference in ad placement. Using graphical models, we assume a causal structure that encodes the various sources of interference. We formulate our causal questions and discuss the identification and estimation of relevant effects. Our experiments find statistically significant interference effects among ads. We further adapt the constraint-based structure learning algorithm Fast Causal Inference (Spirtes et al., 2000) to verify the correctness of our presumed causal structure and learn the underlying mechanisms that give rise to interference. Finally, we incorporate the knowledge of interference to improve the performance of the statistical models used during the course of the auction. We demonstrate this improvement in performance by running experiments that closely resemble the framework in the Genie model—an offline counterfactual policy estimation framework for optimizing Sponsored Search Marketplace in Bing ads (Bayir et al., 2019).

In causal inference, we are interested in quantifying the cause-effect relationships between a treatment variable A and an outcome Y using experimental or observational data. A common setting assumes that the treatment received by one unit does not affect the outcomes of other units—this is known as the stable unit treatment value assumption or SUTVA Rubin (1980) and is informally referred to as the “no-interference” assumption. In this setting, the average causal effect (ACE) of a binary treatment A on Y is defined as ACE: = 𝔼[Y(1)] − 𝔼[Y(0)], where Y(a) denotes the counterfactual/potential outcome Y had treatment A been assigned to a, possibly contrary to the fact.

Causal inference uses assumptions in causal models to link the observed data distribution to the distribution over counterfactual random variables. A simple example of a causal model is the conditionally ignorable model which encodes three main assumptions: (i) Consistency assumes the mechanism that determines the value of the outcome does not distinguish the method by which the treatment was assigned, as long as the treatment value assigned was invariant, (ii) Conditional ignorability assumes Y(a) ⊥ A ∣ X, where X acts as a set of observed confounders, such that adjusting for their influence suffices to remove all non-causal dependence between A and Y, and (iii) Positivity of p(A = a ∣ X = x), ∀ a, x. Under these assumptions, p[Y(a)] is identified as the following function of the observed data: ∑Xp(Y∣A=a,X)×p(X), known as backdoor adjustment or g-formula (Robins, 1986; Pearl, 2009). For a general identification theory of causal effects in the presence of unmeasured confounders see (Huang and Valtorta, 2006; Shpitser and Pearl, 2006; Bhattacharya et al., 2020a). Alternative causal quantities of interest include conditional causal effects (effects within subpopulations defined by covariates) (Shpitser and Pearl, 2012), mediation quantities (which decompose effects into components along different mechanisms) (Shpitser, 2013), and the effects of decision rules in sequential settings (such as dynamic treatment regimes in personalized medicine) (Nabi et al., 2018, 2019).

In this paper, we relax the implausible assumption of no-interference in ad placement. Interference among ads across different pageviews creates the most extreme scenario of full interference, as this allows for user interaction with the system over multiple time frames. Following the convention in Sobel (2006), Hudgens and Halloran (2008), Tchetgen and VanderWeele (2012), and Ogburn and VanderWeele (2014), we model only interference within pageviews and restrict any cross-pageview interference among ads. In other words, we restrict the interference to spatial constraints and exclude temporal dependence across pageviews. This is known as partial interference and could be justified by the fact that pageviews are query specific and are separated by time and space. In presence of interference, the counterfactual Y(a) is no longer well-defined as we need to distinguish ads by a proper indexing scheme and consider the treatment assignments of other ads simultaneously.

Suppose we have N pageviews, indexed by n = 1, …, N, with each containing m impressed ads. We index the ads on each pageview by i = 1, …, m based on the order in which they appear on the page. The i-th ad on the n-th pageview is represented by the tuple (X_ni, A_ni, Y_ni), where X_ni denotes the vector that collects all the ad-specific features such as geometric features (e.g., line width, pixel height), decorative features (e.g., rating information, twitter followers), and other textual features extracted from the ad. A_ni denotes the treatment and is predefined by the analyst. An example of a treatment is the block membership of the ad: an indicator that specifies whether the ad is placed on top of the page (Top) or bottom of the page (Bottom). Ads can also appear elsewhere such as the sidebars. In this paper, without loss of generality, we assume we only have two distinct blocks of ads on each pageview: Top and Bottom. Y_ni denotes a binary indicator of receiving a click by the user. We denote the state space of a random variable V by 𝔛_V.

Let X_n: = (X_n1, …, X_nm), A_n: = (A_n1, …, A_nm), and Y_n: = (Y_n1, …, Y_nm) collect the features, treatment assignments, and outcomes of all the ads on the n-th pageview, respectively. We define the counterfactual Y_ni(a_n) to be the click response of the i-th ad on the n-th pageview where every ad on the same pageview is relocated according to the treatment assignment rule a_n, which is a vector of size m and the i-th element a_i denotes the treatment value of the i-th ad. This notation makes the interference among ads on the same pageview more explicit as the potential outcome of a single ad now depends on the entire treatment assignment a_n, rather than just a_ni. The causal effect of interventions in the presence of interference can be quantified by comparing such counterfactuals under different interventions; for instance Y_ni(a_n) vs. Yni(a′n), where a_n and a′n denote two plausible interventions.

In the next section, we discuss various sources that give rise to interference among ads and propose a causal graphical model that captures such interactions in a reasonable way. In what follows, we discuss various ways of quantifying the interference effect among ads and provide sufficient conditions for identification of such effects along with estimation strategies. In general, we observe fewer pageviews that would have m > 5 impressed ads. This may affect the finite sample performances of our effect estimations for such pageviews, discussed in Section 4.3. The number of impressed ads does not affect any of our identification claims in Section 4.2. We do consider pageviews with up to m = 8 impressed ads in our experiments in Section 5.

We describe ad placement in the presence of interference by a system of nonparametric structural equation models with independent errors (Pearl, 2009). The key characteristic of structural models is that they represent each variable as deterministic functions of their direct causes together with an unobserved exogenous noise term, which itself represents all causes outside of the model. Let U denote a variable capturing user intention which is unknown and hidden to the analyst. Given such intent, the user types a query, denoted by C, which is expressed as an unrestricted function of the intent U and a noise term ϵ_c, denoted by f_c(.). Upon observing the query, a set of ads are selected from the inventory, then online auction is run to determine winner ads to be displayed on the page. The i-th displayed ad is denoted by X_i. The relation between X_i and C is captured by an unrestricted function f_xi(.) and the perturbation term ϵ_xi. The block allocation of i-th ad is denoted by A_i. The set of all impressed ads and the allocations are denoted by X and A, respectively (we suppress the indexing of pageviews for clarity). The information on U, X, A, along with the noise term ϵ_yi, determines whether the i-th ad is clicked or not which is captured by Y_i. The structural equation models are summarized as follows.

Note that in the above display, when allocating the i-th ad to Top or Bottom, we are not only considering the corresponding features of the ad itself, but also features of other ads on the page, hence the entire array of X is acting as causes of A_i. Similarly, we allow for the entire vector of A and array of X to influence Y_i. These equation capture the interference mechanism in ad placement. In the absence of interference, the above equations simplify by replacing the allocation structural equation with A_i ← f_ai(X_i, ϵ_ai) and the click indication structural equation with Y_i ← f_yi(U, X_i, A_i, ϵ_yi).

Causal relationships are often represented by graphical causal models (Spirtes et al., 2000; Pearl, 2009). Such models generalize independence models on directed acyclic graphs (DAGs) to also encode conditional independencies on counterfactual variables (Richardson and Robins, 2013). A DAG G(V) consists of a set of nodes V connected through directed edges such that there are no directed cycles. We will abbreviate G(V) as simply G, when the vertex set is clear from the given context. Statistical models of a DAG G are sets of distributions that factorize as p(V) = ∏ _{Vi ∈ V} p[V_i ∣pa _G(V_i)], where pa_G(V_i) are the parents of V_i in G. The absence of edges between variables in G, relative to a complete DAG entails conditional independence facts in p(V). These can be directly read off from the DAG G by the well-known d-separation criterion (Pearl, 2009). That is, for disjoint sets X, Y, Z, the following global Markov property holds: (X_{⊥⊥d-sepY ∣ Z)G} ⇒ (X ⊥⊥Y ∣ Z)_p(V). When the context is clear, we will simply use X ⊥⊥ Y ∣ Z to denote the conditional independence between X and Y given Z. The DAG representation of the structural (Equation 1) for a pageview with three impressed ads is shown in Figure 1A. For simplicity and to avoid cluttering the graph, we only depict the outcome of the i-th ad on the DAG and marginalize out all the other outcomes (since all the outcomes share the same set of parents). The statistical model of the DAG in Figure 1A, assuming all outcomes are included on the DAG, can be written as,

As we mentioned earlier, the user intent is unmeasured. We further restrict our attention to ad-specific features and leave the query-specific features aside. In other words U and C are both treated as latent. We highlight this in Figure 1A by coloring both vertices and the relevant edges in gray. In this case, the joint distribution over observed variables X, A, Y and latent variables U, C is said to be Markov relative to a hidden variable DAG. There may be infinitely many hidden variable DAGs that imply the same set of conditional independencies on the observed margin, i.e., p(X, A, Y). It is typical to use a single acyclic directed mixed graph that entails the same set of equality constraints as this infinite class; see Verma and Pearl (1990) and Richardson et al. (2017) for more details.

Structural equation models, such as the one in display (1), enable us to determine the response of variables to interventions through incorporating knowledge of the functional dependencies between variables. For instance, intervening on the block allocation of the i-th ad would fix the value of A_i to a_i, and would transform descendants of A_i to counterfactual variables of the form V(a_i). Under an intervention that sets A to a, the structural (Equation 1) are modified as follows:

Interventions can be directly applied to the causal graph through a node-splitting operation where random variables in A are split into two parts: a random part that takes all the incoming edges and a fixed part that takes all the outgoing edges. The resulting graph is called a single-world intervention graph (SWIG) which encodes counterfactual independencies associated with the intervention (Richardson and Robins, 2013). Given the causal model in Figure 1A, we obtain the corresponding SWIG in Figure 1B after performing the intervention described in display (Equation 1).

In this section, we illustrate the utility of our formalization of the ad interference problem through four separate experiments using Bing PC traffic: (i) estimating the counterfactual mean under interference as described in Section 4, (ii) identifying causally relevant features through structure learning, (iii) comparing click prediction models with and without accounting for interference, and (iv) evaluating the performance of models with interfernece on layouts that do not appear in the training data. For training and validation purposes, we used data from the first 2 weeks of June in 2020. The test data comes from the first 2 weeks of July in the same year. We use random forest classifiers for fitting the propensity score and the outcome regression models.

We focused on two types of pageviews: positive pageviews, i.e., pageviews with at least one observed click (corresponding to users with an “ad frame of mind" who are more likely to click on an ad), and balanced pageviews, i.e., pageviews with positive and zero-clicked views. This scenario captures a more realistic view. We used AIPW to estimate the counterfactual mean 𝔼[Y_i(a)] and ran our experiments on pageviews with 3, 4, and 5 number of impressed ads.

Despite the intuition that ads should not be scrutinized independently of one another, to the best of our knowledge, there has not been a formal analysis of interference in advertisement placement and sponsored search marketing. In this paper, we formalized the interference problem among ads using the language of causal inference and counterfactual reasoning. We proposed a framework to quantify the interference effects by posing a graphical causal model that accounts for potential underlying interference mechanisms. We described several causal effects that might be of interest in ad placement systems and discussed identification assumptions and estimation strategies for computing these effects. We further adapted the FCI procedure to learn the underlying mechanisms that give rise to interference and verify the correctness of our presumed causal structures.

In the partial interference framework, it is often assumed that the iid units are of the same size. The equivalent assumption we made is that pageviews have a fixed number of impressed ads. If sample size is not of concern, we can analyze each pageview of size m in isolation. However, in scenarios where data is scarce, we need alternatives to relax this restrictive assumption. One approach is through feature engineering where we first assume that only k nearest neighbors are interacting with the ad itself, a Markov order of k assumption if you will. We further need to assume the neighboring ads influence one another in the exact similar ways, a parameter sharing assumptions, if you will. Investigating such alternatives and exploring other approaches opens up an interesting direction for future work.

In this paper, we focused on the impressed ads on the search result page, and marginalized out the ads involved in the search engine auction. Incorporating the knowledge on how exactly the auction optimizer works on the entire set of candidate ads is important in determining the optimal layouts in presence of interference. We further restricted our attention to auctions that only yield two blocks on the final pageview. This can be simply relaxed by allowing for the allocation treatment to have a discrete state space. We can further group the ads that were not impressed and treat them as a separate block, and investigate their impact on the click yields of the other ads on the page.

The aggregated data supporting the conclusions of this article will be made available upon request. Further requests will be assessed on a case-by-case basis to ensure compliance with privacy agreements and other requirements. Requests to access the datasets should be directed to the corresponding author.

RN, DC, and EK contributed to conception and design of the framework. JP organized the database. RN performed the statistical analysis and wrote the first draft of the manuscript. All authors contributed to manuscript revision, read, and approved the submitted version.

JP, DC, and EK were employed by Microsoft Corporation. The research was conducted while RN was an intern at Microsoft Research.

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