Model selection for learning boolean hypothesis

Castro, Joel Edu Sanchez

doi:10.11606/t.45.2019.tde-02042019-231050

Cited by 3 publications

(16 citation statements)

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“…If H is given by the set of Boolean functions h : {0, 1} d → {0, 1} we have the special case of a Boolean Partition Lattice, which is studied in [6], where simulation studies involving the U-curve property may be found. Observe that the Feature Selection Learning Space when X ⊂ R d , |X | < ∞ and Y = {0, 1} is a sub-lattice of the Partition Lattice Learning Space.…”

Section: Examples Of Learning Spacesmentioning

confidence: 99%

“…Nonetheless, even when no U-curve property is satisfied, one may still apply an U-curve algorithm and obtain a suitable suboptimal solution. This has been done successfully in feature selection (see [3,6,19,20,21,22] for more details). As it is outside the scope of this paper, which is to define a general framework for model selection via Learning Spaces, an interesting topic for future research would be to find conditions on L(H) and for the U-curve properties, especially in cases of interest as linear classifiers, feature selection and neural networks.…”

Section: Definition 5 a Learning Space L(h) Under Loss Function Satis...mentioning

confidence: 99%

“…There are L is an estimator of the out-of-sample error and is given by the expectation of a loss function under P . See [1,Chapter 4] and [6] for more details. specialized solvers to approach this problem, which can explore the U-curve property observed in the chains of the Boolean lattice of subsets of H which constitutes this search space (see [3,19,20,21,22] for more details).…”

Section: Introductionmentioning

confidence: 99%

“…L is an estimator of the out-of-sample error and is given by the expectation of a loss function under P . This idea is presented in more details in [6].…”

Section: Introductionmentioning

confidence: 99%

“…Figure 1: State-of-the-art solution to the model selection problem, in which P is an estimator of the joint distribution of the input X and output Y .L is an estimator of the out-of-sample error and is given by the expectation of a loss function under P . See [1, Chapter 4] and[6] for more details.…”

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confidence: 99%

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Learning the Hypotheses Space from data: Learning Space and U-curve Property

Marcondes,

Simonis,

Barrera

2020

Preprint

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The agnostic PAC learning model consists of: a Hypothesis Space H, a probability distribution P , a sample complexity function m H ( , δ) : [0, 1] 2 → Z + of precision and confidence 1 − δ, a finite i.i.d. sample D N , a cost function and a learning algorithm A(H, D N ), which estimates ĥ ∈ H that approximates a target function h ∈ H seeking to minimize out-of-sample error. In this model, prior information is represented by H and , while problem solution is performed through their instantiation in several applied learning models, with specific algebraic structures for H and corresponding learning algorithms. However, these applied models use additional important concepts not covered by the classic PAC learning theory: model selection and regularization. This paper presents an extension of this model which covers these concepts. The main principle added is the selection, based solely on data, of a subspace of H with a VC-dimension compatible with the available sample. In order to formalize this principle, the concept of Learning Space L(H), which is a poset of subsets of H that covers H and satisfies a property regarding the VC dimension of related subspaces, is presented as the natural search space for model selection algorithms. A remarkable result obtained on this new framework are * D. Marcondes has received financial support from CNPq during the development of this paper. J.

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Section: Examples Of Learning Spacesmentioning

confidence: 99%

Section: Definition 5 a Learning Space L(h) Under Loss Function Satis...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…L is an estimator of the out-of-sample error and is given by the expectation of a loss function under P . This idea is presented in more details in [6].…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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