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.


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