Fig. 1.

Illustration of GGAN architecture and its loss functions. We use $(x,y)\in {\mathbb{R}}^{l+t}$ to denote a gene expression profile, where $x\in {\mathbb{R}}^l$ corresponds to the landmark genes and $y\in {\mathbb{R}}^t$ represents the target genes. Our goal is to learn a generator function G which takes x as the input and output $\widehat{\mathbf{y}}$ as the prediction of the target gene expression. To construct an appropriate prediction function G, we consider three loss terms in our model: ${\mathcal{L}}_{cons},{\mathcal{L}}_{adv}$ and ${\mathcal{L}}_1$. ${\mathcal{L}}_{cons}$ measures the consistency of the prediction from G when the input x is perturbed by random noise u and $u\prime$. ${\mathcal{L}}_1$ measures the difference between the prediction vector $\widehat{\mathbf{y}}$ and the ground truth y. For the term ${\mathcal{L}}_{adv}$, we construct a discriminator D which takes both $(x,y)$ and $(x,\widehat{\mathbf{y}})$ as the input. The discriminator D tries to distinguish the real’ sample $(x,y)$ from the ‘fake’ sample $(x,\widehat{\mathbf{y}})$ while the G tries to predict the realistic $\widehat{\mathbf{y}}$ vector to fool the discriminator. ${\mathcal{L}}_{adv}$ measures the adversarial loss in the game between the generator G and discriminator D