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Subspace Embeddings and ℓp-Regression Using Exponential Random Variables
Published on Aug 09, 20133240 Views
Oblivious low-distortion subspace embeddings are a crucial building block for numerical linear algebra problems. We show for any real p,1≤p<∞, given a matrix M∈Rn×d with n≫d, with constant probability
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Chapter list
Subspace Embeddings and lp-Regression Using Exponential Random Variables00:00
Subspace embeddings - 100:07
Subspace embeddings - 200:49
All matter: embedding time, dimension and distortion - 101:47
All matter: embedding time, dimension and distortion - 202:23
Regression - 103:46
Regression - 204:52
Our results - 105:04
Our results - 205:40
Our results - 306:09
Our subspace embedding matrices - 106:31
Our subspace embedding matrices - 207:17
Two distributions - 109:30
Two distributions - 210:12
Two distributions - 310:57
Two distributions - 411:05
Exponential distribution is superior than p-stables11:26
Analysis of distortions13:04
Analysis for subspace embedding13:08
Analysis for subspace embedding (cont.)16:14
High level ideas17:14
Distributed implementation18:44
Distributed implementation (cont.)19:26
Conclusions and open problems20:55
Thank you22:15