  The vast majority of current machine learning algorithms are designed to
predict single responses or a vector of responses, yet many types of response
are more naturally organized as matrices or higher-order tensor objects where
characteristics are shared across modes. We present a new machine learning
algorithm BaTFLED (Bayesian Tensor Factorization Linked to External Data) that
predicts values in a three-dimensional response tensor using input features for
each of the dimensions. BaTFLED uses a probabilistic Bayesian framework to
learn projection matrices mapping input features for each mode into latent
representations that multiply to form the response tensor. By utilizing a
Tucker decomposition, the model can capture weights for interactions between
latent factors for each mode in a small core tensor. Priors that encourage
sparsity in the projection matrices and core tensor allow for feature selection
and model regularization. This method is shown to far outperform elastic net
and neural net models on 'cold start' tasks from data simulated in a three-mode
structure. Additionally, we apply the model to predict dose-response curves in
a panel of breast cancer cell lines treated with drug compounds that was used
as a Dialogue for Reverse Engineering Assessments and Methods (DREAM)
challenge.
