Concentration of Gaussian random matrices
1
I know that if $X$ be a random matrix distributed as $N(0,I_n)$, then $frac{1}{n}X^TX$ is concentrated around the identity matrix. Does any body know the probability of $P(||frac{1}{n}X^TX-I||<delta)$?
probability-theory normal-distribution concentration-of-measure
asked Nov 27 at 3:44
S_Alex
858
add a comment |
1
I know that if $X$ be a random matrix distributed as $N(0,I_n)$, then $frac{1}{n}X^TX$ is concentrated around the identity matrix. Does any body know the probability of $P(||frac{1}{n}X^TX-I||<delta)$?
probability-theory normal-distribution concentration-of-measure
asked Nov 27 at 3:44
S_Alex
858
1
A relatively recent paper by Vershynin (arxiv/abs/1004.3484) shows how to answer this question. He's mainly interested in asymptotics, but working through the proof of Proposition 2.1 would give you the result you want.
– cdipaolo
Nov 27 at 4:05
Another approach that would be looser yet would be probably a bit easier to compute is to apply Tropp's matrix concentration inequalities and bound the norm of a Gaussian vector with high probability. See Section 1.6.3 of arxiv/abs/1501.01571 for this.
– cdipaolo
Nov 27 at 4:18
add a comment |
1
1
1
1
I know that if $X$ be a random matrix distributed as $N(0,I_n)$, then $frac{1}{n}X^TX$ is concentrated around the identity matrix. Does any body know the probability of $P(||frac{1}{n}X^TX-I||<delta)$?
probability-theory normal-distribution concentration-of-measure
asked Nov 27 at 3:44
S_Alex
858
I know that if $X$ be a random matrix distributed as $N(0,I_n)$, then $frac{1}{n}X^TX$ is concentrated around the identity matrix. Does any body know the probability of $P(||frac{1}{n}X^TX-I||<delta)$?
probability-theory normal-distribution concentration-of-measure
probability-theory normal-distribution concentration-of-measure
asked Nov 27 at 3:44
S_Alex
858
asked Nov 27 at 3:44
S_Alex
858
asked Nov 27 at 3:44
S_Alex
858
asked Nov 27 at 3:44
S_Alex
858
asked Nov 27 at 3:44
S_Alex
858
858
1
A relatively recent paper by Vershynin (arxiv/abs/1004.3484) shows how to answer this question. He's mainly interested in asymptotics, but working through the proof of Proposition 2.1 would give you the result you want.
– cdipaolo
Nov 27 at 4:05
Another approach that would be looser yet would be probably a bit easier to compute is to apply Tropp's matrix concentration inequalities and bound the norm of a Gaussian vector with high probability. See Section 1.6.3 of arxiv/abs/1501.01571 for this.
– cdipaolo
Nov 27 at 4:18
add a comment |
1
A relatively recent paper by Vershynin (arxiv/abs/1004.3484) shows how to answer this question. He's mainly interested in asymptotics, but working through the proof of Proposition 2.1 would give you the result you want.
– cdipaolo
Nov 27 at 4:05
Another approach that would be looser yet would be probably a bit easier to compute is to apply Tropp's matrix concentration inequalities and bound the norm of a Gaussian vector with high probability. See Section 1.6.3 of arxiv/abs/1501.01571 for this.
– cdipaolo
Nov 27 at 4:18
1
1
A relatively recent paper by Vershynin (arxiv/abs/1004.3484) shows how to answer this question. He's mainly interested in asymptotics, but working through the proof of Proposition 2.1 would give you the result you want.
– cdipaolo
Nov 27 at 4:05
A relatively recent paper by Vershynin (arxiv/abs/1004.3484) shows how to answer this question. He's mainly interested in asymptotics, but working through the proof of Proposition 2.1 would give you the result you want.
– cdipaolo
Nov 27 at 4:05
Another approach that would be looser yet would be probably a bit easier to compute is to apply Tropp's matrix concentration inequalities and bound the norm of a Gaussian vector with high probability. See Section 1.6.3 of arxiv/abs/1501.01571 for this.
– cdipaolo
Nov 27 at 4:18
Another approach that would be looser yet would be probably a bit easier to compute is to apply Tropp's matrix concentration inequalities and bound the norm of a Gaussian vector with high probability. See Section 1.6.3 of arxiv/abs/1501.01571 for this.
– cdipaolo
Nov 27 at 4:18
add a comment |
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1
A relatively recent paper by Vershynin (arxiv/abs/1004.3484) shows how to answer this question. He's mainly interested in asymptotics, but working through the proof of Proposition 2.1 would give you the result you want.
– cdipaolo
Nov 27 at 4:05
Another approach that would be looser yet would be probably a bit easier to compute is to apply Tropp's matrix concentration inequalities and bound the norm of a Gaussian vector with high probability. See Section 1.6.3 of arxiv/abs/1501.01571 for this.
– cdipaolo
Nov 27 at 4:18