Generalization in Adaptive Data via Max-Information - PowerPoint Presentation

Slide1

Generalization in Adaptive Data via Max-Information

Vitaly FeldmanAccelerated Discovery LabIBM Research - Almaden

Cynthia Dwork Moritz Hardt Toni Pitassi Omer Reingold Aaron Roth Microsoft Res. Google Res. U. of Toronto Samsung Res. Penn, CSSlide2

Distribution

over  Analysis

Results

Param

. estimates

Classifier,Clusteringetc.

 Slide3

Statistical inference

Result + generalization guaranteesAlgorithmHypothesis testsRegressionLearning“Fresh” i.i.d. samples

0

Techniques

CLT

Model complexity

Rademacher

compl

.

Stability

…Slide4

Data analysis is adaptiveData cleaningExploratory data analysis

Variable selectionHyper-parameter tuningShared datasets….Steps depend on previous analyses of the same dataset

Data analyst(s)

 Slide5

It’s an old problem

“Quiet scandal of statistics”[Leo Breiman, 1992]Thou shalt not test hypotheses suggested by dataSlide6

Is this a real problem?

“Why Most Published Research Findings Are False” [Ioannidis 2005]Adaptive data analysis is one of the causes-hackingResearcher degrees of freedom [Simmons, Nelson, Simonsohn 2011]Garden of forking paths [Gelman, Loken 2015]

 “Irreproducible preclinical research exceeds 50%,

resulting in approximately

US$28B/year loss” [Freedman,Cockburn

,Simcoe 2015]Slide7

Existing approaches I

AbstinencePre-registration

© Center for Open ScienceSlide8

Existing approaches II

Selective/post-selection inference Examples:Model selection + parameter inferenceVariable selection + regressionSurvey: [Taylor,

Tibshirani 2015]Slide9

Existing approaches III

Sample splitting

B

A

Data

Data

Data

C

Data

Data

Data

Might be necessary for standard techniquesSlide10

Adaptive data analysis

Data analyst(s)

Assumption:

is “valid” with high prob.

Goal:

is “almost as good as”

w.h.p

.

Approach: control

the increase in probability of any

event as a result of dependence

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Adaptive statistical queries [DFHPRR14]

with high prob.  

Data analyst(s)

Statistical query oracle

[Kearns 93]

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Outcome stability/differential privacy [Dwork,McSherry,Nissim,Smith 06]

Randomized algorithm is -differentially private if for any two data sets such that

:

ratio bounded

A

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DP composes

adaptively

i

-DP

 Slide14

i

-

DP

DP composes

adaptivelySlide15

DP implies

generalizationDP composesadaptivelyComposition of -DP algorithms: for every , is

-DP

[Dwork,Rothblum,Vadhan

10]

-DP upper-bounds the increase in probability of any “bad” event

-

DP ensures generalization for SQs

[

DFHPRR 14

]

-DP

case strengthened/extended

[BNSSSU 15]

 Slide16

Description length

: Composes adaptivelyPreserves generalization (of subsequent analysis) 

Let :

be an algorithm

s.t.

Then for any event

, and

over

For any

:

s.t

.

and

:

s.t

.

Then for

Define

Then for

gives

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Max-information

Max-information:

=

For

:

s.t.

where

over

Then for any event

, and

For any

:

s.t

.

and

:

s.t

.

Then for

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Max-info from -DP

 By -DP for any adjacent and any

For any

and any

and so

Thus

For concentration event need

and so require

For

use concentration of divergence:

Implies that

suffices

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Approximate max-information:

Preserves

generalization Composes adaptively

-differential privacy

Description length,

 Slide20

Further developmentsAdditional approaches:Mutual information

[Russo, Zou 2016]KL-stability, TV-stability [Bassily,Nissim,Smith,Steinke,Stemmer,Ullman 2016]Typical stability [Bassily,Freund 2016]-Differential privacy and

[

Rogers,Roth,Smith,Thakkar

2016

]

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ConclusionsAdaptive data analysis:Ubiquitous in practiceInvalidates standard generalization guarantees

Possible to model and improve on standard approachesNew theoretical approaches are neededMax-info gives a general approach that captures differential privacy and description lengthKnown results can be rederived via max-infoAdaptive composition requires strong assumptionsPossibly too strong for some applicationsApplicationsReusable holdout [DFHPRR 15]Reusable holdout in ML competitions [Blum,Hardt 15]Selection problems [Russo,Zou 16]