  We propose an efficient sensitivity analysis method for a wide class of
colored noise-driven interacting particle systems (IPS). Our method is based on
unperturbed simulations and significantly extends the Malliavin weight sampling
method proposed by Szamel (EPL, 117 (2017) 50010) for evaluating sensitivities
such as linear response functions of IPS driven by simple Ornstein-Uhlenbeck
processes. We show that the sensitivity index depends not only on two effective
parameters that characterize the variance and correlation time of the noise,
but also on the noise spectrum. In the case of a single particle in a harmonic
potential, we obtain exact analytical formulas for two types of linear response
functions. By applying our method to a system of many particles interacting via
a repulsive screened Coulomb potential, we compute the mobility and effective
temperature of the system. Our results show that the system dynamics depend, in
a nontrivial way, on the noise spectrum.
