# Estimating conditional expectation using SVR

I have an estimation problem: $$X_t=f(S_t)=E(X_T\mid S_t)$$ given the observations $$(X^i_{T},S^i_{t})$$ for all $$i$$'s. I used support vector regression (SVR) to run a regression of $$X_T$$ on $$S_t$$. Here $$S_t$$ represents the Markovian state variable at time t, and $$X_T$$ the terminal realization of a martingale process $$X_t=f(t,S_t)$$. However, the SVR estimation (in sample) of $$X$$ does not form a martingale, in that $$E(X_t)\neq E(X_T)$$ from the sample means.

Is this a problem with SVR or I have made a mistake somewhere? What would be a good estimator for conditional expectation that would preserve the tower property? The $$S_t$$ paths are simulated. $$X_T=f(T,S_T)$$ with $$f(T,\cdot)$$ known.