  We consider the problem of partial identification, the estimation of bounds
on the treatment effects from observational data. Although studied using
discrete treatment variables or in specific causal graphs (e.g., instrumental
variables), partial identification has been recently explored using tools from
deep generative modeling. We propose a new method for partial identification of
average treatment effects(ATEs) in general causal graphs using implicit
generative models comprising continuous and discrete random variables. Since
ATE with continuous treatment is generally non-regular, we leverage the partial
derivatives of response functions to define a regular approximation of ATE, a
quantity we call uniform average treatment derivative (UATD). We prove that our
algorithm converges to tight bounds on ATE in linear structural causal models
(SCMs). For nonlinear SCMs, we empirically show that using UATD leads to
tighter and more stable bounds than methods that directly optimize the ATE.
