  This study introduces an innovative method for analyzing the impact of
various interventions on customer churn, using the potential outcomes
framework. We present a new causal model, the tensorized latent factor block
hazard model, which incorporates tensor completion methods for a principled
causal analysis of customer churn. A crucial element of our approach is the
formulation of a 1-bit tensor completion for the parameter tensor. This
captures hidden customer characteristics and temporal elements from churn
records, effectively addressing the binary nature of churn data and its
time-monotonic trends. Our model also uniquely categorizes interventions by
their similar impacts, enhancing the precision and practicality of implementing
customer retention strategies. For computational efficiency, we apply a
projected gradient descent algorithm combined with spectral clustering. We lay
down the theoretical groundwork for our model, including its non-asymptotic
properties. The efficacy and superiority of our model are further validated
through comprehensive experiments on both simulated and real-world
applications.
