invariant

[[concept]]

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Definition

Invariant

Let G be a group acting on a (data) set X. Then F:X→Y is invariant if

F(g∘x)=F(x)∀g∈G and x∈X

^definition

Random Matrix Theory

Orthogonal Invariance

Let x∈Rd be a random vector. We say that x (or its law Law(x)) is orthogonally invariant if for each (deterministic) orthogonal matrix Q∈O(d) we have

Law(Qx)=Law(x)
Note

The law is the distribution of the random vector.
We sometimes use "model" instead of "law" or "distribution" to remind us that our choice includes assumptions and judgements.

References

References

See Also

Mentions

Mentions

File Last Modified
2025-01-21 equivariant lecture 1 2025-08-17
2025-02-18 equivariant lecture 3 2025-02-18
2025-02-19 graphs lecture 9 2025-03-17
2025-02-24 graphs lecture 10 2025-03-17
2025-02-25 equivariant lecture 4 2025-03-17
2025-03-05 graphs lecture 12 2025-03-17
2025-04-01 equivariant lecture 9 2025-04-01
2025-04-26 SIAM Soledad 2025-04-26
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Equivariant Machine Learning Projects 2025-08-17
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Functional Analysis Lecture 6 2025-07-08
injective GNNs are as powerful as the WL test 2025-03-03
orthogonally invariant distribution on the unit sphere 2025-09-05
Random Matrix Lecture 01 2025-09-11
Random Matrix Lecture 06 2025-09-11
standard gaussian random vectors are orthogonally invariant 2025-09-05
the WL test is at least as powerful as a GNN for detecting graph non-isomorphism 2025-03-02

{ .block-language-dataview}
Created 2025-02-01 ֍ Last Modified 2025-09-11