# Sequential Regression Learning with Randomized Algorithms

arXiv: https://arxiv.org/abs/2507.03759 · HTML: https://mlsanity.com/paper/2507.03759/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 3 of 3)

- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Variable Rate Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06085/) (2015)
- [The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than 1/k2](https://mlsanity.com/paper/1510.08740/) (2015)

## Abstract (arXiv)

This paper presents ``randomized SINDy", a sequential machine learning algorithm designed for dynamic data that has a time-dependent structure. It employs a probabilistic approach, with its PAC learning property rigorously proven through the mathematical theory of functional analysis. The algorithm dynamically predicts using a learned probability distribution of predictors, updating weights via gradient descent and a proximal algorithm to maintain a valid probability density. Inspired by SINDy (Brunton et al. 2016), it incorporates feature augmentation and Tikhonov regularization. For multivariate normal weights, the proximal step is omitted to focus on parameter estimation. The algorithm's effectiveness is demonstrated through experimental results in regression and binary classification using real-world data.