# Network Weight Estimation for Binary-Valued Observation Models

## TL;DR

This paper introduces a recursive estimation algorithm for network weights in systems with binary, quantized observations, addressing challenges posed by unknown quantization and system coupling, with proven consistency and applicability to real-time tasks.

## Contribution

It presents a novel recursive estimation method using stochastic approximation for systems with binary observations, ensuring strong consistency and handling unknown quantization effects.

## Key findings

- The proposed algorithm is strongly consistent.
- The objective function is strictly concave with a unique maximum.
- Applicable to online real-time decision-making and surveillance.

## Abstract

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.