  We study generalized special cycles on Hermitian locally symmetric spaces
$\Gamma \backslash D$ associated to the groups $G=\mathrm{U}(p,q)$,
$\mathrm{Sp}(2n,\mathbb{R}) $ and $\mathrm{O}^*(2n)$. These cycles are (covered
by) locally symmetric spaces associated to subgroups of $G$ which are of the
same type. Using oscillator representation and a construction which essentially
comes from the thesis of Greg Anderson, we show that Poincar\'e duals of these
generalized special cycles can be viewed as Fourier coefficients of a theta
series. This gives new cases of theta lifts from the cohomology of Hermtian
locally symmetric manifolds associated to $G$ to vector valued automorphic
forms associated to the groups $G'=\mathrm{U}(m,m)$, $\mathrm{O}(m,m)$ or
$\mathrm{Sp}(m,m)$ which forms a reductive dual pair with $G$ in the sense of
Howe.
