Fig. 1

Overview of the VAE-XGBoost method that we used for predicting tumor response to chemotherapy in vivo for five different cancer types. For each tumor t, the encoder’s input vector \({\varvec{x}}_t\) contains the levels of the top 20% of genes by intertumoral gene expression variance. Each network has multiple fully connected dense layers (“VAE model architectures” section). The encoder outputs two vectors of configurable latent variable dimension \(h \ll m\): a vector of means \(\varvec{\mu }\) and a vector of standard deviations \(\varvec{\sigma }\) that parameterize the multivariate normal latent-space vector \({\varvec{Z}}|{\varvec{x}}_t\) (“Variational autoencoder (VAE)” section). The sampled encoding \({\varvec{Z}}|{\varvec{x}}_t={\varvec{\boldsymbol z}}_t\) is passed to the decoding neural network (decoder), whose architecture is identical to (with inversion) that of the encoder network. The sampled latent-space vector \({\varvec{\boldsymbol z}}_t\) is passed to XGBoost for supervised classification to predict response to chemotherapy (training label \({\varvec{y}}\), prediction \(\widetilde{{\varvec{y}}}\))