# Partial Distance Correlation with Methods for Dissimilarities

arXiv: https://arxiv.org/abs/1310.2926 · HTML: https://mlsanity.com/paper/1310.2926/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2013.

## Built on by (most cited first, 20 of 20)

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- [Testing for context-dependent changes in neural encoding in naturalistic experiments](https://mlsanity.com/paper/2211.09295/) (2022)
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- [Causal Learning for Heterogeneous Subgroups Based on Nonlinear Causal Kernel Clustering](https://mlsanity.com/paper/2501.11622/) (2025)
- [DISCO: Mitigating Bias in Deep Learning with Conditional Distance Correlation](https://mlsanity.com/paper/2506.11653/) (2025)
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## Abstract (arXiv)

Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent literature, but the problem of defining the partial distance correlation has remained an open question of considerable interest. The problem of partial distance correlation is more complex than partial correlation partly because the squared distance covariance is not an inner product in the usual linear space. For the definition of partial distance correlation we introduce a new Hilbert space where the squared distance covariance is the inner product. We define the partial distance correlation statistics with the help of this Hilbert space, and develop and implement a test for zero partial distance correlation. Our intermediate results provide an unbiased estimator of squared distance covariance, and a neat solution to the problem of distance correlation for dissimilarities rather than distances.