# L_1-regularized Boltzmann machine learning using majorizer minimization

arXiv: https://arxiv.org/abs/1503.03132 · HTML: https://mlsanity.com/paper/1503.03132/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2015.

## Built on by (most cited first, 1 of 1)

- [Assessment of image generation by quantum annealer](https://mlsanity.com/paper/2103.08373/) (2021)

## Abstract (arXiv)

We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is L1 regularization, which is often used in compressed sensing, a technique for reconstructing sparse input signals from undersampled outputs. L1 regularization impedes the simple application of the gradient method, which optimizes the cost function that leads to accurate estimations, owing to the cost function's lack of smoothness. In this study, we utilize the majorizer minimization method, which is a well-known technique implemented in optimization problems, to avoid the non-smoothness of the cost function. By using the majorizer minimization method, we elucidate essentially relevant biases and interactions from given data with seemingly strongly-correlated components.