# Linear Discriminant Analysis with High-dimensional Mixed Variables

arXiv: https://arxiv.org/abs/2112.07145 · HTML: https://mlsanity.com/paper/2112.07145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 14 Dec 2021.

## Builds on (most cited first, 8 of 8)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Covariate-Adjusted Tensor Classification in High-Dimensions](https://mlsanity.com/paper/1805.04421/) (2018)
- [A Direct Approach for Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1510.00084/) (2015)
- [Multiclass Sparse Discriminant Analysis](https://mlsanity.com/paper/1504.05845/) (2015)
- [Dynamic Linear Discriminant Analysis in High Dimensional Space](https://mlsanity.com/paper/1708.00205/) (2017)
- [Semiparametric Sparse Discriminant Analysis](https://mlsanity.com/paper/1304.4983/) (2013)
- [RaSE: A Variable Screening Framework via Random Subspace Ensembles](https://mlsanity.com/paper/2102.03892/) (2021)
- [Asymptotic properties of a Nadaraya-Watson type estimator for regression functions of infinite order](https://mlsanity.com/paper/1604.06380/) (2016)

## Abstract (arXiv)

Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the recent progress made in modelling high-dimensional data for continuous variables, there is a scarcity of methods that can deal with a mixed set of variables. To fill this gap, this paper develops a novel approach for classifying high-dimensional observations with mixed variables. Our framework builds on a location model, in which the distributions of the continuous variables conditional on categorical ones are assumed Gaussian. We overcome the challenge of having to split data into exponentially many cells, or combinations of the categorical variables, by kernel smoothing, and provide new perspectives for its bandwidth choice to ensure an analogue of Bochner's Lemma, which is different to the usual bias-variance tradeoff. We show that the two sets of parameters in our model can be separately estimated and provide penalized likelihood for their estimation. Results on the estimation accuracy and the misclassification rates are established, and the competitive performance of the proposed classifier is illustrated by extensive simulation and real data studies.