Name
Title | ||
|---|---|---|
Learning the Differential Correlation Matrix of a Smooth Function From Point Samples. |
Abstract | ||
|---|---|---|
Consider an open set $mathbb{D}subseteqmathbb{R}^n$, equipped with a probability measure $mu$. An important characteristic of a smooth function $f:mathbb{D}rightarrowmathbb{R}$ is its $differential$ $correlation$ $matrix$ $Sigma_{mu}:=int nabla f(x) (nabla f(x))^* mu(dx) inmathbb{R}^{ntimes n}$, where $nabla f(x)inmathbb{R}^n$ is the gradient of $f(cdot)$ at $xinmathbb{D}$. For instance, the span of the leading $r$ eigenvectors of $Sigma_{mu}$ forms an $active$ $subspace$ of $f(cdot)$, thereby extending the concept of $principal$ $component$ $analysis$ to the problem of $ridge$ $approximation$. In this work, we propose a simple algorithm for estimating $Sigma_{mu}$ from point values of $f(cdot)$ $without$ imposing any structural assumptions on $f(cdot)$. Theoretical guarantees for this algorithm are provided with the aid of the same technical tools that have proved valuable in the context of covariance matrix estimation from partial measurements. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Information Theory | Mathematical analysis,Covariance matrix,Smoothness,Mathematics |
DocType | Volume | Citations |
Journal | abs/1612.06339 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Armin Eftekhari | 1 | 129 | 12.42 |
| Ping Li | 2 | 322 | 42.76 |
| Michael B. Wakin | 3 | 4299 | 271.57 |
| Rachel Ward | 4 | 221 | 15.52 |