Turbulence in two-phase flows drives many important natural and engineering processes, from geophysical flows to nuclear power generation. Strong interphase coupling between the carrier fluid and disperse phase precludes the use of classical turbulence models developed for single-phase flows. In recent years, there has been an explosion of machine learning techniques for turbulence closure modeling, though many rely on augmenting existing models. In this work, we propose an approach that blends sparse regression and gene expression programming (GEP) to generate closed-form algebraic models from simulation data. Sparse regression is used to determine a minimum set of functional groups required to capture the physics, and GEP is used to automate the formulation of the coefficients and dependencies on operating conditions. The framework is demonstrated on homogeneous turbulent gas-particle flows in which two-way coupling generates and sustains carrier-phase turbulence.