A Heterogeneous Domain Adversarial Neural Network for Trans-Domain Behavioral Targeting

Abstract

To realize trans-domain behavioral targeting, which targets interested potential users of a source domain (e.g. E-Commerce) based on their behaviors in a target domain (e.g. Ad-Network), heterogeneous transfer learning (HeTL) is a promising technique for modeling behavior linkage between domains. It is required for HeTL to learn three functionalities: representation alignment, distribution alignment, and classification. In our previous work, we prototyped and evaluated two typical transfer learning algorithms, but neither of them jointly learns the three desired functionalities. Recent advances in transfer learning include a domain-adversarial neural network (DANN), which jointly learns distribution alignment and classification. In this paper, we extended DANN to be able to learn representation alignment by simply replacing its shared encoder with domain-specific types, so that it jointly learns the three desired functionalities. We evaluated the effectiveness of the joint learning of the three functionalities using real-world data of two domains: E-Commerce, which is set as the source domain, and Ad Network, which is set as the target domain.

Appendix

• PM1: HeMap + HEGS + Xgboost

Modeling Behavior Linkage.

HeMap learns a common latent space from the source and target features. The optimization objective related to the common latent space is as follows (the same equation appears in [7]):

$$ \mathop{\min}\nolimits_{{{\text{B}}_{{\rm T}}^{\text{T}} {{\rm B}}_{\text{T}} = {{\rm I}}, {\text{B}}_{{\rm S}}^{\text{T}} {{\rm B}}_{\text{S}} = {\rm {I}}}} \left\| {{\text{X}}_{{\rm S}} - {\text{B}}_{{\rm S}} {\text{P}}_{{\rm S}} } \right\|^{2} + \left\| {{\text{X}}_{{\rm T}} - {\text{B}}_{{\rm T}} {\text{P}}_{{\rm T}} } \right\|^{2} + \beta \left( {\frac{1}{2}\left\| {{{\rm X}}_{\text{T}} - {{\rm B}}_{\text{S}} {{\rm P}}_{\text{T}} } \right\|^{2} + \frac{1}{2}\left\| {{{\rm X}}_{\text{S}} - {{\rm B}}_{\text{T}} {{\rm P}}_{\text{S}} } \right\|^{2} } \right) $$

(2)

where, ${\text{B}}_{\text{S}}$, ${\text{B}}_{\text{T}}$ are the projected source and target instances onto the common latent space respectively, and ${\text{P}}_{\text{S}}$, ${\text{P}}_{\text{T}}$ are the projection matrices from the common latent space onto the source and target space, respectively.

Then, HEGS selects the source instances in ${\text{B}}_{\text{S}}$ similar to the target instances in ${\text{B}}_{\text{T}}$. Since HEGS is originally a domain adaptation method for regression, we modified HEGS by hiring logistic regression to unify the labels in both domains. Finally, Xgboost learns the binary classification model $F_{Xgb} \left( \cdot \right)$ using the selected instances and labels. Hyper-parameters of HeMap, HEGS, and Xgboost are tuned using cross validation. The resulting behavior linkage model ${\mathbf{\mathcal{M}}} = \left( {{\text{P'}}_{\text{T}} ,F_{Xgb} } \right)$, where ${\text{P'}}_{\text{T}}$ is a pseudo-inverse of the projection matrix ${\text{P}}_{\text{T}}$ obtained by HeMap.

Applying Behavior Linkage Model.

We compute the predictive probability of conversion ${\text{P}}\left( {y_{j} |\varvec{x}_{j}^{{\left( {\text{T}} \right)}} } \right) = F_{Xgb} \left( {{\text{P'}}_{\text{T}} \varvec{ x}_{j}^{{\left( {\text{T}} \right)}} } \right)$ for each user $j$ in the target domain. The resulting target users are defined by $\left\{ {j; {\text{P}}\left( {y_{j} |\varvec{x}_{j}^{{\left( {\text{T}} \right)}} } \right) > \theta } \right\}$ with an arbitrary threshold $0 < \theta < 1$.

• PM2: HFA

Modeling Behavior Linkage.

HFA learns a multiple kernel classifier $F_{HFA} \left( \cdot \right)$ on a common latent space using the source and target features and the labels. The projection matrices ${\text{P}}, {\text{Q}}$ from the source and target space onto the common latent space are coupled as ${\text{H}} = \left[ {{\text{P}}, {\text{Q}}} \right] '\left[ {{\text{P}}, {\text{Q}}} \right]$, and then kernel matrices are computed and optimized based on ${\text{H}}$. Hyper-parameters of HFA are tuned using cross validation. The resulting behavior linkage model ${\mathbf{\mathcal{M}}} = \left( {F_{HFA} } \right)$.

Applying Behavior Linkage Model.

Similar to PM1, we compute the predictive probability of conversion ${\text{P}}\left( {y_{j} |\varvec{x}_{j}^{{\left( {\text{T}} \right)}} } \right) = F_{HFA} \left( {\varvec{ x}_{j}^{{\left( {\text{T}} \right)}} } \right)$ for each user $j$ in the target domain. The resulting target users are defined by $\left\{ {j; {\text{P}}\left( {y_{j} |\varvec{x}_{j}^{{\left( {\text{T}} \right)}} } \right) > \theta } \right\}$ with an arbitrary threshold $0 < \theta < 1$.