# Thurstonian Boltzmann Machines: Learning from Multiple Inequalities

arXiv: https://arxiv.org/abs/1408.0055 · HTML: https://mlsanity.com/paper/1408.0055/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2014.

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

- [Energy-based survival modelling using harmoniums](https://mlsanity.com/paper/2110.01960/) (2021)

## Abstract (arXiv)

We introduce Thurstonian Boltzmann Machines (TBM), a unified architecture that can naturally incorporate a wide range of data inputs at the same time. Our motivation rests in the Thurstonian view that many discrete data types can be considered as being generated from a subset of underlying latent continuous variables, and in the observation that each realisation of a discrete type imposes certain inequalities on those variables. Thus learning and inference in TBM reduce to making sense of a set of inequalities. Our proposed TBM naturally supports the following types: Gaussian, intervals, censored, binary, categorical, muticategorical, ordinal, (in)-complete rank with and without ties. We demonstrate the versatility and capacity of the proposed model on three applications of very different natures; namely handwritten digit recognition, collaborative filtering and complex social survey analysis.