# Soft Bayesian Context Tree Models for Real-Valued Time Series

arXiv: https://arxiv.org/abs/2601.11079 · HTML: https://mlsanity.com/paper/2601.11079/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 47 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## Builds on (most cited first, 8 of 8)

- [Streaming Variational Bayes](https://mlsanity.com/paper/1307.6769/) (2013)
- [Bayesian Context Trees: Modelling and exact inference for discrete time series](https://mlsanity.com/paper/2007.14900/) (2020)
- [Probability Distribution on Full Rooted Trees](https://mlsanity.com/paper/2109.12825/) (2021)
- [Posterior Representations for Bayesian Context Trees: Sampling, Estimation and Convergence](https://mlsanity.com/paper/2202.02239/) (2022)
- [Truly Bayesian Entropy Estimation](https://mlsanity.com/paper/2212.06705/) (2022)
- [Batch Updating of a Posterior Tree Distribution over a Meta-Tree](https://mlsanity.com/paper/2303.09705/) (2023)
- [The Bayesian Context Trees State Space Model for time series modelling and forecasting](https://mlsanity.com/paper/2308.00913/) (2023)
- [Context-tree weighting for real-valued time series: Bayesian inference with hierarchical mixture models](https://mlsanity.com/paper/2106.03023/) (2021)

## Built on by (most cited first, 2 of 2)

- [Variable Splitting Binary Tree Models Based on Bayesian Context Tree Models for Time Series Segmentation](https://mlsanity.com/paper/2601.16112/) (2026)
- [A Mixture Autoregressive Image Generative Model on Quadtree Regions for Gaussian Noise Removal via Variational Bayes and Gradient Methods](https://mlsanity.com/paper/2605.11585/) (2026)

## Abstract (arXiv)

This paper proposes the soft Bayesian context tree model (Soft-BCT), which is a novel BCT model for real-valued time series. The Soft-BCT considers soft (probabilistic) splits of the context space, instead of hard (deterministic) splits of the context space as in the previous BCT for real-valued time series. A learning algorithm of the Soft-BCT is proposed based on the variational inference. The results of experiments demonstrate the superiority of the Soft-BCT compared to the previous BCT for some datasets.