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Wed 22 Mar 2023 14:54:32
How do spectral norms depend on sample size?
How do spectral norms depend on sample size?
mathoverflow question: https://mathoverflow.net/questions/442811/norms-of-wigner-matrices-under-power-law-decay
Utilities: sgd-vs-gd.nb
Utilities: sgd-vs-gd.nb
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SF=StringForm;h=1/Range[30];d=Length[h];Print["h is ",h];(*Gaussiansampler*)SeedRandom[1,Method->"MKL"];gaussianSampler[diag_]:=With{d=Length[diag]},Compile{{n,_Integer}},Module{vals,diagSqrt},diagSqrt=Norm[h,∞]+Norm[h,1]bounds=Plot[{None,guess[b]},{b,1,maxB},PlotLegends->{Block[{h},HoldForm[Evaluate@guess[b]]]},ScalingFunctions->"Log",PlotRange->{0,Norm[h,1]}];Show[bounds,simulation,AxesLabel->{"b","||X/b||"}]
diag
;vals=diagSqrt*#&/@RandomVariate[NormalDistribution[],{n,d}];sampler=gaussianSampler[h];maxB=3*d;norm[b_?NumericQ]:=With[{X=sampler[Round@b]},Norm[X.X/b]];simulation=DiscretePlot[Mean[Table[norm[b],200]],{b,1,maxB,2},PlotRange->{0,1.1*Total[h]},ScalingFunctions->"Log"];guess[b_]:=b+1
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