Valid Generalisation from Approximate Interpolation

Anthony, Martin; Ishai, Yuval; Shawe‐Taylor, John

doi:10.1017/s096354830000198x

Cited by 8 publications

(5 citation statements)

References 23 publications

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“…The sample complexity upper bound in Theorem 19 increases at least as 1Â= 4 . It seems plausible that this rate is excessive; perhaps it is an artifact of the use of Jensen's inequality in the proof.…”

Section: Agnostic Learningmentioning

confidence: 96%

“…Natarajan [20] considers the problem of learning a class of real-valued functions in the presence of bounded observation noise and presents sufficient conditions for learnability. (Theorem 2 in [4] shows that these conditions are not necessary in our setting.) Merhav and Feder [18], and Auer, Long, Maass, and Woeginger [6] study function learning in a worst-case setting.…”

Section: Introductionmentioning

confidence: 94%

“…Haussler [15] gives sufficient conditions for agnostic learnability. Anthony, Bartlett, Ishai, and ShaweTaylor [4] give necessary and sufficient conditions that a function that approximately interpolates the target function is a good approximation to it (see also [5,3]). Natarajan [20] considers the problem of learning a class of real-valued functions in the presence of bounded observation noise and presents sufficient conditions for learnability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fat-Shattering and the Learnability of Real-Valued Functions

Long

Williamson

1996

Journal of Computer and System Sciences

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We consider the problem of learning real-valued functions from random examples when the function values are corrupted with noise. With mild conditions on independent observation noise, we provide characterizations of the learnability of a real-valued function class in terms of a generalization of the Vapnik Chervonenkis dimension, the fat-shattering function, introduced by Kearns and Schapire. We show that, given some restrictions on the noise, a function class is learnable in our model if an only if its fat-shattering function is finite. With different (also quite mild) restrictions, satisfied for example by guassion noise, we show that a function class is learnable from polynomially many examples if and only if its fat-shattering function grows polynomially. We prove analogous results in an agnostic setting, where there is no assumption of an underlying function class. ] 1996 Academic Press, Inc.

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Section: Agnostic Learningmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fat-Shattering and the Learnability of Real-Valued Functions

Long

Williamson

1996

Journal of Computer and System Sciences

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“…Then an estimate of the effect f that is ϵ-close to f * with probability 1-δ 1 indeed yields a solution to the original regression problem. The bound thus follows from Theorem 3 of Anthony et al (1996).…”

Section: Theoretical Analysismentioning

confidence: 91%

Learning Safe Numeric Action Models

Mordoch

Juba

Stern

2023

AAAI

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Powerful domain-independent planners have been developed to solve various types of planning problems. These planners often require a model of the acting agent's actions, given in some planning domain description language. Yet obtaining such an action model is a notoriously hard task. This task is even more challenging in mission-critical domains, where a trial-and-error approach to learning how to act is not an option. In such domains, the action model used to generate plans must be safe, in the sense that plans generated with it must be applicable and achieve their goals. Learning safe action models for planning has been recently explored for domains in which states are sufficiently described with Boolean variables. In this work, we go beyond this limitation and propose the NSAM algorithm. NSAM runs in time that is polynomial in the number of observations and, under certain conditions, is guaranteed to return safe action models. We analyze its worst-case sample complexity, which may be intractable for some domains. Empirically, however, NSAM can quickly learn a safe action model that can solve most problems in the domain.

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“…This is because unlike a binary classifier, which localizes errors on specific examples, a real-valued hypothesis can spread its error evenly over the entire sample, and it will not be affected by reweighting. The (η, γ)-weak learner, which has appeared, among other works, in Anthony et al [1996], Simon [1997], Avnimelech and Intrator [1999], Kégl [2003], gets around this difficulty -but provable general constructions of such learners have been lacking. Likewise, the heart of our sample compression engine, MedBoost, has been widely in use since Freund and Schapire [1997] in various guises.…”

Section: Related Workmentioning

confidence: 99%

Sample Compression for Real-Valued Learners

Hanneke¹,

Kontorovich²,

Sadigurschi³

2018

Preprint

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We give an algorithmically efficient version of the learner-to-compression scheme conversion in . In extending this technique to realvalued hypotheses, we also obtain an efficient regression-to-bounded sample compression converter. To our knowledge, this is the first general compressed regression result (regardless of efficiency or boundedness) guaranteeing uniform approximate reconstruction. Along the way, we develop a generic procedure for constructing weak real-valued learners out of abstract regressors; this may be of independent interest. In particular, this result sheds new light on an open question of H. Simon (1997). We show applications to two regression problems: learning Lipschitz and bounded-variation functions.

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Valid Generalisation from Approximate Interpolation

Cited by 8 publications

References 23 publications

Fat-Shattering and the Learnability of Real-Valued Functions

Fat-Shattering and the Learnability of Real-Valued Functions

Learning Safe Numeric Action Models

Sample Compression for Real-Valued Learners

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