Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-rank structures in the tensor additive regression. We formulate the parameter estimation as a non-convex optimization problem, and propose an efficient penalized alternating minimization algorithm. We establish a non-asymptotic error bound for the estimator obtained from each iteration of the proposed algorithm, which reveals an interplay between the optimization error and the statistical rate of convergence. We demonstrate the efficacy of STAR through extensive comparative simulation studies, and an application to the click-through-rate prediction in online advertising.

Modern search engines aggregate results from different verticals : webpages, news, images, video, shopping, knowledge cards, local maps, and so on. Unlike “ten blue links,” these search results are heterogeneous in nature and not even arranged in a list on the page. This revolution directly challenges the conventional “ranked list” formulation in ad hoc search. Therefore, finding proper presentation for a gallery of heterogeneous results is critical for modern search engines. We propose a novel framework that learns the optimal page presentation to render heterogeneous results onto search result page (SERP). Page presentation is broadly defined as the strategy to present a set of items on SERP, much more expressive than a ranked list. It can specify item positions, image sizes, text fonts, and any other styles as long as variations are within business and design constraints. The learned presentation is content aware, i.e., tailored to specific queries and returned results. Simulation experiments show that the framework automatically learns eye-catchy presentations for relevant results. Experiments on real data show that simple instantiations of the framework already outperform leading algorithm in federated search result presentation. It means the framework can learn its own result presentation strategy purely from data, without even knowing the “probability ranking principle.”

Tensor factorization is a powerful tool to analyse multi-way data. Recently proposed nonlinear factorization methods, although capable of capturing complex relationships, are computationally quite expensive and may suffer a severe learning bias in case of extreme data sparsity. Therefore, we propose a distributed, flexible nonlinear tensor factorization model, which avoids the expensive computations and structural restrictions of the Kronecker-product in the existing TGP formulations, allowing an arbitrary subset of tensor entries to be selected for training. Meanwhile, we derive a tractable and tight variational evidence lower bound (ELBO) that enables highly decoupled, parallel computations and high-quality inference. Based on the new bound, we develop a distributed, key-value-free inference algorithm in the MapReduce framework, which can fully exploit the memory cache mechanism in fast MapReduce systems such as Spark. Experiments demonstrate the advantages of our method over several state-of-the-art approaches, in terms of both predictive performance and computational efficiency.

Modern search engines aggregate results from different verticals: webpages, news, images, video, shopping, knowledge cards, local maps, etc. Unlike "ten blue links", these search results are heterogeneous in nature and not even arranged in a list on the page. This revolution directly challenges the conventional "ranked list" formulation in ad hoc search. Therefore, finding proper presentation for a gallery of heterogeneous results is critical for modern search engines.

Advertising effectiveness measurement is a fundamental problem in online advertising. Various causal inference methods have been employed to measure the causal effects of ad treatments. However, existing methods mainly focus on linear logistic regression for univariate and binary treatments and are not well suited for complex ad treatments of multi-dimensions, where each dimension could be discrete or continuous. In this paper we propose a novel two-stage causal inference framework for assessing the impact of complex ad treatments. In the first stage, we estimate the propensity parameter via a sparse additive model; in the second stage, a propensity-adjusted regression model is applied for measuring the treatment effect. Our approach is shown to provide an unbiased estimation of the ad effectiveness under regularity conditions. To demonstrate the efficacy of our approach, we apply it to a real online advertising campaign to evaluate the impact of three ad treatments: ad frequency, ad channel, and ad size. We show that the ad frequency usually has a treatment effect cap when ads are showing on mobile device. In addition, the strategies for choosing best ad size are completely different for mobile ads and online ads.

As the online advertising industry has evolved into an age of diverse ad formats and delivery channels, users are exposed to complex ad treatments involving various ad characteristics. The diversity and generality of ad treatments call for accurate and causal measurement of ad effectiveness, i.e., how the ad treatment causes the changes in outcomes without the confounding effect by user characteristics. Various causal inference approaches have been proposed to measure the causal effect of ad treatments. However, most existing causal inference methods focus on univariate and binary treatment and are not well suited for complex ad treatments. Moreover, to be practical in the data-rich online environment, the measurement needs to be highly general and efficient, which is not addressed in conventional causal inference approaches. In this paper we propose a novel causal inference framework for assessing the impact of general advertising treatments. Our new framework enables analysis on uni- or multi-dimensional ad treatments, where each dimension (ad treatment factor) could be discrete or continuous. We prove that our approach is able to provide an unbiased estimation of the ad effectiveness by controlling the confounding effect of user characteristics. The framework is computationally efficient by employing a tree structure that specifies the relationship between user characteristics and the corresponding ad treatment. This tree-based framework is robust to model misspecification and highly flexible with minimal manual tuning. To demonstrate the efficacy of our approach, we apply it to two advertising campaigns. In the first campaign we evaluate the impact of different ad frequencies, and in the second one we consider the synthetic ad effectiveness across TV and online platforms. Our framework successfully provides the causal impact of ads with different frequencies in both campaigns. Moreover, it shows that the ad frequency usually has a treatment effect cap, which is usually over-estimated by naive estimation.

In online advertising market it is crucial to provide advertisers with a reliable measurement of advertising effectiveness to make better marketing campaign planning. The basic idea for ad effectiveness measurement is to compare the performance (e.g., success rate) among users who were and who were not exposed to a certain treatment of ads. When a randomized experiment is not available, a naive comparison can be biased because exposed and unexposed populations typically have different features. One solid methodology for a fair comparison is to apply inverse propensity weighting with doubly robust estimation to the observational data. However the existing methods were not designed for the online advertising campaign, which usually suffers from huge volume of users, high dimensionality, high sparsity and imbalance. We propose an efficient framework to address these challenges in a real campaign circumstance. We utilize gradient boosting stumps for feature selection and gradient boosting trees for model fitting, and propose a subsampling-and-backscaling procedure that enables analysis on extremely sparse conversion data. The choice of features, models and feature selection scheme are validated with irrelevant conversion test. We further propose a parallel computing strategy, combined with the subsampling-and-backscaling procedure to reach computational efficiency. Our framework is applied to an online campaign involving millions of unique users, which shows substantially better model fitting and efficiency. Our framework can be further generalized to comparison of multiple treatments and more general treatment regimes, as sketched in the paper. Our framework is not limited to online advertising, but also applicable to other circumstances (e.g., social science) where a 'fair' comparison is needed with observational data.