# Convex Programming for Estimation in Nonlinear Recurrent Models

arXiv: https://arxiv.org/abs/1908.09915 · HTML: https://mlsanity.com/paper/1908.09915/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2019.

## Built on by (most cited first, 7 of 7)

- [Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems](https://mlsanity.com/paper/2105.11558/) (2021)
- [Finite Sample Identification of Bilinear Dynamical Systems](https://mlsanity.com/paper/2208.13915/) (2022)
- [Learning Linear Dynamics from Bilinear Observations](https://mlsanity.com/paper/2409.16499/) (2024)
- [Finite Sample Identification of Partially Observed Bilinear Dynamical Systems](https://mlsanity.com/paper/2501.07652/) (2025)
- [Online Stochastic Gradient Descent Learns Linear Dynamical Systems from A Single Trajectory](https://mlsanity.com/paper/2102.11822/) (2021)
- [The Complexity of Sequential Prediction in Dynamical Systems](https://mlsanity.com/paper/2402.06614/) (2024)
- [System Identification via Nuclear Norm Regularization](https://mlsanity.com/paper/2203.16673/) (2022)

## Abstract (arXiv)

We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide a sample complexity for this estimator in the case of stable dynamics, where the nonlinear recursion has a certain contraction property, and under certain regularity conditions on the input distribution. We evaluate the performance of the estimator by simulation on synthetic data. These numerical experiments also suggest the extent at which the imposed theoretical assumptions may be relaxed.