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Rademacher-Sketch: A Dimensionality-Reducing Embedding for Sum-Product Norms, with an Application to Earth-Mover Distance
[chapter]

2012
*
Lecture Notes in Computer Science
*

that generalizes

doi:10.1007/978-3-642-31594-7_70
fatcat:rxolqh5eybd2pixl6eburgj3zy
*earth*-*mover**distance*). ... In particular, composing this*embedding**with*another well-known*embedding*of Indyk [18], we get*an*O(1/ )-distortion*embedding*from the*earth*-*mover*metric EMD∆ on the grid ⊗EEMD∆ (where EEMD is*a**norm*... In this paper we show*dimensionality*-*reducing**embeddings*in*sum*-*product**normed*spaces: the goal is, given*a**normed*space Y = n 1 ⊗X,*to*find*a*small-distortion*embedding*of Y into*a*smaller-*dimensional*...##
###
Nearly-optimal bounds for sparse recovery in generic norms, with applications to k-median sketching
[article]

2015
*
arXiv
*
pre-print

*Earth*-

*Mover*

*Distance*

*norm*). ... $m \times n$ matrices $

*A*$

*with*the property that

*for*any $x$, given $Ax$, we can recover

*a*$k$-sparse approximation

*to*$x$ in the given

*norm*

*with*probability at least $1-P$? ...

*Rademacher*-

*sketch*:

*A*

*dimensionality*-

*reducing*

*embedding*

*for*

*sum*-

*product*

*norms*,

*with*

*an*

*application*

*to*

*Earth*-

*Mover*

*Distance*. ...

##
###
Nearly-optimal bounds for sparse recovery in generic norms, with applications to k-median sketching

2015
*
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
*

*A*

*with*the property that

*for*any x, given Ax, we can recover

*a*k-sparse approximation

*to*x in the given

*norm*

*with*probability at least 1 − P? ... By applying our result

*to*specific

*norms*, we cast known measurement bounds in our general framework (

*for*the ℓ p

*norms*, p ∈ [1, 2]) as well as provide new, measurement-efficient schemes (

*for*the

*Earth*-

*Mover*...

*Rademacher*-

*sketch*:

*A*

*dimensionality*-

*reducing*

*embedding*

*for*

*sum*-

*product*

*norms*,

*with*

*an*

*application*

*to*

*Earth*-

*Mover*

*Distance*. ...

##
###
Oblivious sketching for logistic regression
[article]

2021
*
arXiv
*
pre-print

Our sketch can be computed in input sparsity time over

arXiv:2107.06615v1
fatcat:m62a2523tnft3bz64mlolu3yhq
*a*turnstile data stream and*reduces*the size of*a*$d$-*dimensional*data set from $n$*to*only $\operatorname{poly}(\mu d\log n)$ weighted points, where ... We also show how*to*obtain*an*$O(1)$-approximation*with*slight modifications. Our sketches are fast, simple, easy*to*implement, and our experiments demonstrate their practicality. ... Acknowledgements We thank the anonymous reviewers*for*their valuable comments. Alexander Munteanu ...