# A Christoffel-like function for high-dimensional support inference in graphical models

arXiv: https://arxiv.org/abs/2409.15965 · HTML: https://mlsanity.com/paper/2409.15965/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2024.

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

- [Scalable anomaly detection via a univariate Christoffel function](https://mlsanity.com/paper/2606.12483/) (2026)

## Abstract (arXiv)

Christoffel polynomials are classical tools from approximation theory. They can be used to estimate the (compact) support of a measure μ on ℝd based on its low-degree moments. Recently, they have been applied to problems in data science, including outlier detection and support inference. A major downside of Christoffel polynomials in such applications is the fact that, in order to compute their coefficients, one must invert a moment matrix whose size grows rapidly with the dimension d. In this paper, we propose a modification of the Christoffel polynomial which is significantly cheaper to compute, but retains many of its desirable properties. In particular, it (1) exhibits a so-called support dichotomy and (2) it is a rational function, whose numerator and denominator factor into `lower-dimensional' Christoffel polynomials whose coefficients can be computed by inverting potentially much smaller moment matrices. Our approach relies on sparsity of the underlying measure μ, described by a graphical model. The complexity of our modification depends on the treewidth of this model.