Network Weight Estimation for Binary-Valued Observation Models
This work addresses the challenging problem of network weight estimation under binary-valued observations with unknown quantization, offering a theoretically grounded recursive solution for online applications.
The paper proposes a recursive algorithm for estimating network weights in systems with binary-valued observations, where states are coupled with observations and quantization is unknown. The algorithm achieves strong consistency and is suitable for online tasks like real-time decision-making.
This paper studies the estimation of network weights for a class of systems with binary-valued observations. In these systems only quantized observations are available for the network estimation. Furthermore, system states are coupled with observations, and the quantization parts are unknown inherent components, which hinder the design of inputs and quantizers. To fulfill the estimation, we propose a recursive algorithm based on stochastic approximation techniques. More precisely, to deal with the temporal dependency of observations and achieve the recursive estimation of network weights, a deterministic objective function is constructed based on the likelihood function by extending the dimension of observations and applying ergodic properties of Markov chains. It is shown that this function is strictly concave and has unique maximum identical to the true parameter vector. Finally, the strong consistency of the algorithm is established. Our recursive algorithm can be applied to online tasks like real-time decision-making and surveillance for networked systems. This work also provides a new scheme for the identification of systems with quantized observations.