Making Generalization Robust Katrina Ligett HUJI & Caltech - - PowerPoint PPT Presentation

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Making Generalization Robust Katrina Ligett HUJI & Caltech - - PowerPoint PPT Presentation

Jul 31, 2023 336 likes •910 views

Making Generalization Robust Katrina Ligett HUJI & Caltech joint with Rachel Cummings, Kobbi Nissim, Aaron Roth, and Steven Wu A model for science A model for science Hypothesis Learning Alg domain: contains all possible

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Making Generalization Robust

Katrina Ligett HUJI & Caltech

joint with Rachel Cummings, Kobbi Nissim, Aaron Roth, and Steven Wu

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A model for science…

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A model for science…

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Learning Alg

Hypothesis

  • domain: contains all possible examples
  • hypothesis: X-> {0,1} labels examples
  • learning alg samples labeled examples, returns hypothesis
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Learning Alg

Hypothesis

The goal of science: Find hypothesis that has low true error on the distribution D: err(h) = Prx~D[h(x) ≠ h*(x)]

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Why does science work?

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Why does science work?

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Learning Alg

Hypothesis

The goal of science: Find hypothesis that has low true error on the distribution D: err(h) = Prx~D[h(x) ≠ h*(x)] Idea: find hypothesis that has low empirical error on S, plus guarantee that findings on the sample generalize to D

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Learning Alg

Hypothesis

Empirical error: errE(h) = 1/n ∑x ∈ S 1[h(x) ≠ h*(x)] Generalization: output h s.t. Pr[|h(S) - h(D) |] ≤ 𝛃] ≥ 1 - β

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taken from Understanding Machine Learning, Shai Shalev-Schwarts and Shai Ben-David

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Problem solved!

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Science doesn’t happen in a vacuum.

Problem solved?

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One thing that can go wrong: post-processing

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  • Learning an SVM: Output encodes Support Vectors (sample points)
  • This output could be post-processed to obtain a non-generalizing

hypothesis: “10% of all data points are x_k”

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Oh, man. Our approach on this Kaggle competition really failed on the test data. Oh well, let’s try again. Did you see that paper published by the Smith lab? Yeah, I bet they’d see an even bigger effect if they accounted for sunspots! The journal requires open access to the data—let’s try it and see!

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A second big problem: adaptive composition

q1 a1 q2 a2

. . .

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A second big problem: adaptive composition

q1 a1 q2 a2

. . .

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A second big problem: adaptive composition

Adaptive composition can cause overfitting! Generalization guarantees don’t “add up”

q1 a1 q2 a2

. . .

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A second big problem: adaptive composition

Adaptive composition can cause overfitting! Generalization guarantees don’t “add up”

q1 a1 q2 a2

. . .

  • Pick parameters; fit model
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A second big problem: adaptive composition

Adaptive composition can cause overfitting! Generalization guarantees don’t “add up”

q1 a1 q2 a2

. . .

  • Pick parameters; fit model
  • ML competitions
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A second big problem: adaptive composition

Adaptive composition can cause overfitting! Generalization guarantees don’t “add up”

q1 a1 q2 a2

. . .

  • Pick parameters; fit model
  • ML competitions
  • Scientific fields that share one dataset
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Some basic questions

  • Is it possible to get good learning algorithms that also are

robust to post-processing? Adaptive composition?

  • How to construct them? Existing algorithms? How much extra

data do they need?

  • Accuracy + generalization + post-processing-robustness = ?
  • Accuracy + generalization + adaptive composition = ?
  • What composes with what? How well (how quickly does

generalization degrade)? Why?

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Notice: generalization doesn’t require correct hypotheses, just that they perform the same on the sample as on the distribution Generalization alone is easy. What’s interesting: generalization + accuracy.

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  • Robust generalization

“no adversary can use output to find a hypothesis that

  • verfits”

information-theoretic (could think computational)

Generalization + post-processing robustness

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Robust Generalization

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Robust Generalization

  • Robust to post-processing
  • Somewhat robust to adaptive composition (more on this later)
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Do Robustly-Generalizing Algs Exist?

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Yes!

Do Robustly-Generalizing Algs Exist?

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Yes!

Do Robustly-Generalizing Algs Exist?

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Yes!

  • This paper: Compression Schemes -> Robust

Generalization

Do Robustly-Generalizing Algs Exist?

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Yes!

  • This paper: Compression Schemes -> Robust

Generalization

  • [DFHPRR15a]: Bounded description length -> Robust

Generalization

Do Robustly-Generalizing Algs Exist?

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Yes!

  • This paper: Compression Schemes -> Robust

Generalization

  • [DFHPRR15a]: Bounded description length -> Robust

Generalization

  • [BNSSSU16]: Differential privacy -> Robust Generalization

Do Robustly-Generalizing Algs Exist?

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Yes!

  • This paper: Compression Schemes -> Robust

Generalization

  • [DFHPRR15a]: Bounded description length -> Robust

Generalization

  • [BNSSSU16]: Differential privacy -> Robust Generalization

Do Robustly-Generalizing Algs Exist?

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Compression schemes

Hypothesis

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Compression schemes

Hypothesis

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Robust Generalization via compression

A A

algorithm

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What Can be Learned under RG?

Theorem (informal; thanks to Shay Moran): sample complexity of robustly generalizing learning is the same up to log factors, as the sample complexity of PAC learning

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Yes!

  • This paper: Compression Schemes -> Robust

Generalization

  • [DFHPRR15a]: Bounded description length -> Robust

Generalization

  • [BNSSSU16]: Differential privacy -> Robust Generalization

Do Robustly-Generalizing Algs Exist?

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Differential Privacy [DMNS ‘06]

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Differential Privacy [DMNS ‘06]

  • Robust to post-processing [DMNS ‘06] and adaptive composition [DRV

‘10]

  • Necessarily randomized output
  • No mention of how samples drawn!
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Does DP = RG?

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Does DP = RG?

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Does DP = RG?

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Does DP = RG?

No “quick fix” to make RG learner satisfy DP

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  • Robust generalization

“no adversary can use output to find a hypothesis that overfits”

  • Differential privacy [DMNS ‘06]

“similar samples should have the same output”

  • Perfect generalization

“output reveals nothing about the sample”

Notions of generalization

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Perfect Generalization

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  • Differential privacy gives privacy to the individual

Changing one entry in the database shouldn’t change the output too much

  • Perfect generalization gives privacy to the data provider

(e.g. school, hospital) Changing the entire sample to something “typical” shouldn’t change the output too much

PG as a privacy notion

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Exponential Mechanism [MT07]

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DP implies PG with worse parameters

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PG implies DP…sort of

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PG implies DP…sort of

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PG implies DP…sort of

Problems that are solvable under PG are also solvable under DP

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  • Robust generalization

“no adversary can use output to find a hypothesis that overfits”

  • Differential privacy [DMNS ‘06]

“similar samples should have the same output”

  • Perfect generalization

“output reveals nothing about the sample”

Notions of generalization

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Some basic questions

  • Is it possible to get good learning algorithms that also are

robust to post-processing? Adaptive composition?

  • How to construct them? Existing algorithms? How much extra

data do they need?

  • Accuracy + generalization + post-processing-robustness = ?
  • Accuracy + generalization + adaptive composition = ?
  • What composes with what? How well (how quickly does

generalization degrade)? Why?

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Making Generalization Robust

Katrina Ligett katrina.ligett@mail.huji.ac.il HUJI & Caltech

joint with Rachel Cummings, Kobbi Nissim, Aaron Roth, and Steven Wu