Download presentation

Presentation is loading. Please wait.

Published byOdalys Brammell Modified over 2 years ago

1
Ryan ’Donnell Carnegie Mellon University Institute for Advanced Study O

2
def: For f : {−1,1} n → ℝ, “δ-noisy-influence of i on f” is “Invariance Principles” usually work under the assumption of “low noisy-influences”:

3
Theorem: [O–Servedio–Tan–Wan] ∀, δ, γ > 0, ∀ f : {−1,1} n → ℝ with E[f 2 ] = 1, ∃ a decision tree of depth ≤ s.t. all but a γ fraction of subfunctions f L satisfy

4
Proof: “Energy increment” argument. Build tree inductively. Energy = ∈ [0,1]. Recall Stab 1−δ [g] = If a leaf L has replacing it with a query to x j increases the leaf’s contribution to the energy by ≥ δ. If doable for a γ fraction of leaves, make the replacements and increase energy by ≥ δγ.

5
Applications:

7
“Majority Is Stablest Theorem” [MOO’05]: If Inf i [f] = o(1) ∀ i, Stab ρ [f] ≤ Stab ρ [Majority] + o(1). One application: Can weaken hypothesis to

Similar presentations

OK

Ryan ’Donnell Carnegie Mellon University O. f : {−1, 1} n → {−1, 1} is “quasirandom” iff fixing O(1) input coords changes E[f(x)] by only o (1)

Ryan ’Donnell Carnegie Mellon University O. f : {−1, 1} n → {−1, 1} is “quasirandom” iff fixing O(1) input coords changes E[f(x)] by only o (1)

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Emergency dentist appt on saturday Ppt on sales promotion techniques Presentation ppt on internet A ppt on albert einstein Ppt on sea level rise data Ppt on online examination system in core java Ppt on indian industrial revolution Ppt on teamviewer Ppt on cross site scripting internet Ppt on standing order form