# Learning Nonlinear Regime Transitions via Semi-Parametric State-Space Models

arXiv: https://arxiv.org/abs/2604.04963 · HTML: https://mlsanity.com/paper/2604.04963/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 20 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Learning in Asset Pricing](https://mlsanity.com/paper/1904.00745/) (2019)
- [Hilbert Space Embeddings of Predictive State Representations](https://mlsanity.com/paper/1309.6819/) (2013)
- [Semiparametric stochastic volatility modelling using penalized splines](https://mlsanity.com/paper/1308.5836/) (2013)
- [Penalized estimation of flexible hidden Markov models for time series of counts](https://mlsanity.com/paper/1901.03275/) (2019)

## Abstract (arXiv)

We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility when transitions depend on nonlinear and context-dependent effects. We replace this assumption with learned functions f0, f1 ∈ calH, where calH is either a reproducing kernel Hilbert space or a spline approximation space, and define transition probabilities as pjk,t = sigmoid(f(bxt-1)). The transition functions are estimated jointly with emission parameters using a generalized Expectation-Maximization algorithm. The E-step uses the standard forward-backward recursion, while the M-step reduces to a penalized regression problem with weights from smoothed occupation measures. We establish identifiability conditions and provide a consistency argument for the resulting estimators. Experiments on synthetic data show improved recovery of nonlinear transition dynamics compared to parametric baselines. An empirical study on financial time series demonstrates improved regime classification and earlier detection of transition events.