Thermal conductivity and power factor are key factors in evaluating heat transfer performance and designing thermoelectric conversion devices. To search for materials with ultralow thermal conductivity and a high power factor, we proposed a set of universal statistical interaction descriptors (SIDs) and developed accurate machine learning models for the prediction of thermoelectric properties. For lattice thermal conductivity prediction, the SID-based model achieved the state-of-the-art results with an average absolute error of 1.76W m-1 K-1. The well-performing models predicted that hypervalent triiodides XI3 (X = Rb, Cs) have ultralow thermal conductivities and high power factors. Combining first-principles calculations, the self-consistent phonon theory, and the Boltzmann transport equation, we obtained the anharmonic lattice thermal conductivities of 0.10 and 0.13W m-1 K-1 for CsI3 and RbI3 in the c-axis direction at 300K, respectively. Further studies show that the ultralow thermal conductivity of XI3 arises from the competition of vibrations between alkali metal atoms and halogen atoms. In addition, at 700K, the thermoelectric figure of merit ZT values of CsI3 and RbI3 are 4.10 and 1.52, respectively, at the optimal hole doping level, which indicates hypervalent triiodides are potential high performance thermoelectric materials.