Under mild regularity conditions on the densities (see Hyvärinen, 2005; Sriperumbudur et al., 2017, and below), the score can be rewritten
J(p0||pT ) =E [ d∑
i=1 ∂2i Tx(y) +
1 2(∂iTx(y))
2 ]
+E [ d∑
i=1 ∂iTx(y)∂i log q0(y)
] + J(p0||q0)
where J(p0||q0) is a constant term for the optimization…