# Calibrated simplex-mapping classification

arXiv: https://arxiv.org/abs/2103.02926 · HTML: https://mlsanity.com/paper/2103.02926/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 57 references that are in the map.
- First posted on arXiv 4 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Macro F1 and Macro F1](https://mlsanity.com/paper/1911.03347/) (2019)
- [A Survey on Metric Learning for Feature Vectors and Structured Data](https://mlsanity.com/paper/1306.6709/) (2013)
- [Adversarial Examples, Uncertainty, and Transfer Testing Robustness in Gaussian Process Hybrid Deep Networks](https://mlsanity.com/paper/1707.02476/) (2017)
- [MCMC for Variationally Sparse Gaussian Processes](https://mlsanity.com/paper/1506.04000/) (2015)
- [The Variational Gaussian Process](https://mlsanity.com/paper/1511.06499/) (2015)
- [Learning Scalable Deep Kernels with Recurrent Structure](https://mlsanity.com/paper/1610.08936/) (2016)
- [Improving Output Uncertainty Estimation and Generalization in Deep Learning via Neural Network Gaussian Processes](https://mlsanity.com/paper/1707.05922/) (2017)
- [Deep Gaussian Covariance Network](https://mlsanity.com/paper/1710.06202/) (2017)
- [Approximation, characterization, and continuity of multivariate monotonic regression functions](https://mlsanity.com/paper/2009.02317/) (2020)
- [Compensating data shortages in manufacturing with monotonicity knowledge](https://mlsanity.com/paper/2010.15955/) (2020)

## Built on by (most cited first, 3 of 3)

- [Which Examples to Annotate for In-Context Learning? Towards Effective and Efficient Selection](https://mlsanity.com/paper/2310.20046/) (2023)
- [Multiclass threshold-based classification](https://mlsanity.com/paper/2505.11276/) (2025)
- [Multiclass threshold-based classification and model evaluation](https://mlsanity.com/paper/2511.21794/) (2025)

## Abstract (arXiv)

We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular (n-1)-dimensional simplex, n being the number of classes. We design this representation in such a way that it well reflects the feature space distances of the datapoints to their own- and foreign-class neighbors. In a second step, the latent space representation of the training data is extended to the whole feature space by fitting a regression model to the transformed data. With this latent-space representation, our calibrated classifier is readily defined. We rigorously establish its core theoretical properties and benchmark its prediction and calibration properties by means of various synthetic and real-world data sets from different application domains.