A Data-Driven State Aggregation Approach for Dynamic Discrete Choice Models

We study dynamic discrete choice models, where a commonly studied problem involves estimating parameters of agent reward functions (also known as "structural" parameters), using agent behavioral data. Maximum likelihood estimation for such models requires dynamic programming, which is limited by the curse of dimensionality. In this work, we present a novel algorithm that provides a data-driven method for selecting and aggregating states, which lowers the computational and sample complexity of estimation. Our method works in two stages. In the first stage, we use a flexible inverse reinforcement learning approach to estimate agent Q-functions. We use these estimated Q-functions, along with a clustering algorithm, to select a subset of states that are the most pivotal for driving changes in Q-functions. In the second stage, with these selected "aggregated" states, we conduct maximum likelihood estimation using a commonly used nested fixed-point algorithm. The proposed two-stage approach mitigates the curse of dimensionality by reducing the problem dimension. Theoretically, we derive finite-sample bounds on the associated estimation error, which also characterize the trade-off of computational complexity, estimation error, and sample complexity. We demonstrate the empirical performance of the algorithm in two classic dynamic discrete choice estimation applications

Dynamics of diffusive rough interfaces in inhomogeneous systems

We investigate the dynamics of interfaces growth in inhomogeneous systems. The description of the kinetics is based on the mean field master equation in terms of lattice gas model. The existence of repulsive interactions between nearest-neighbour particles creates an order in the system. We show that the order extension has an influence on the localisation of the diffusive interface called "the diffusion front" which delimits disordered region from ordered one. We analyze the time evolution of diffusion fronts by dynamic scaling approach and we find that the scaling behavior of these interfaces is characterized by anomalously large exponents which agree with the experimental and theoretical results.We investigate the dynamics of interfaces growth in inhomogeneous systems. The description of the kinetics is based on the mean field master equation in terms of lattice gas model. The existence of repulsive interactions between nearest-neighbour particles creates an order in the system. We show that the order extension has an influence on the localisation of the diffusive interface called "the diffusion front" which delimits disordered region from ordered one. We analyze the time evolution of diffusion fronts by dynamic scaling approach and we find that the scaling behavior of these interfaces is characterized by anomalously large exponents which agree with the experimental and theoretical results

Study of adatoms diffusion through current density fluctuation functions

In this work, we investigate the diffusion process by using a mean field lattice gas dynamical model. The temporal correlation function of the current density is calculated in a probe area of radius R. The latter is considered to test if the developed formulation can be applied to reproduce STM experiments. The obtained results concerning the effective diffusion coefficient exhibit clearly the order disorder transition effect translated by two minima appearing respectively at p=1/3 and p=2/3. The effect of the ordering phase at p=1/3 requires a threshold size more precisely, the minimum size system where, the ordering phase effect begins, to appear here is R=5.In this work, we investigate the diffusion process by using a mean field lattice gas dynamical model. The temporal correlation function of the current density is calculated in a probe area of radius R. The latter is considered to test if the developed formulation can be applied to reproduce STM experiments. The obtained results concerning the effective diffusion coefficient exhibit clearly the order disorder transition effect translated by two minima appearing respectively at p=1/3 and p=2/3. The effect of the ordering phase at p=1/3 requires a threshold size more precisely, the minimum size system where, the ordering phase effect begins, to appear here is R=5