# Multi-convex Programming for Discrete Latent Factor Models Prototyping

arXiv: https://arxiv.org/abs/2504.01431 · HTML: https://mlsanity.com/paper/2504.01431/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Learning Mixtures of Linear Regressions with Nearly Optimal Complexity](https://mlsanity.com/paper/1802.07895/) (2018)
- [Let's Make Block Coordinate Descent Converge Faster: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence](https://mlsanity.com/paper/1712.08859/) (2017)
- [Convex Optimization in Julia](https://mlsanity.com/paper/1410.4821/) (2014)
- [Multi-intention Inverse Q-learning for Interpretable Behavior Representation](https://mlsanity.com/paper/2311.13870/) (2023)
- [Disciplined Multi-Convex Programming](https://mlsanity.com/paper/1609.03285/) (2016)
- [Bayesian Active Learning for Discrete Latent Variable Models](https://mlsanity.com/paper/2202.13426/) (2022)
- [Solving Inverse Problem for Multi-armed Bandits via Convex Optimization](https://mlsanity.com/paper/2501.18945/) (2025)

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

- [Disciplined Biconvex Programming](https://mlsanity.com/paper/2511.01813/) (2025)

## Abstract (arXiv)

Discrete latent factor models (DLFMs) are widely used in various domains such as machine learning, economics, neuroscience, psychology, etc. Currently, fitting a DLFM to some dataset relies on a customized solver for individual models, which requires lots of effort to implement and is limited to the targeted specific instance of DLFMs. In this paper, we propose a generic framework based on CVXPY, which allows users to specify and solve the fitting problem of a wide range of DLFMs, including both regression and classification models, within a very short script. Our framework is flexible and inherently supports the integration of regularization terms and constraints on the DLFM parameters and latent factors, such that the users can easily prototype the DLFM structure according to their dataset and application scenario. We introduce our open-source Python implementation and illustrate the framework in several examples.