On the Learnability of Shuffle Ideals

Angluin, Dana; Aspnes, James; Kontorovich, Aryeh

doi:10.1007/978-3-642-34106-9_12

Cited by 4 publications

(8 citation statements)

References 35 publications

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“…A natural question then is Why modify the identification in the limit paradigm when the PAC framework can be utilized instead? We argue that the PAC paradigm is not well-adapted to learning formal languages, as even very simple and well characterized classes of languages are not PAC-learnable [4]. Several theoretical reasons explain this inadequacy, and each of them relates to aspects of the formal grammars used to describe formal languages.…”

Section: Pac Paradigmmentioning

confidence: 93%

“…The characteristic sample is a finite set of data that ensures the correct convergence of the algorithm on any presentation as soon as it is included in the data seen so far. In this paradigm [17], it is required that the algorithm needs a characteristic sample whose size 4 is polynomial in the size of the target representation. Formerly:…”

Section: Characteristic Samplementioning

confidence: 99%

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Efficiency in the Identification in the Limit Learning Paradigm

Eyraud¹,

Heinz²,

Yoshinaka³

2016

Topics in Grammatical Inference

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International audienceTwo different paths exist when one is interested in validating an idea for a learning algorithm. On the one hand, the practical approach consists in using the available data to test the quality of the learning algorithm (for instance the widely used cross-validation technique). On the other hand, a theoretical approach is possible by using a learning paradigm, which is an attempt to formalize what learning means. Such models provide a framework to study the behavior of learning algorithms and to formally establish their soundness. The most widely used learning paradigm in Grammatical Inference is the one known as identification in the limit. The original definition has been found lacking because no efficiency bound is required. It remains an open problem how to best incorporate a notion of efficiency and tractability in this framework. This chapter surveys the different refinements that have been developed and studied, and the challenges they face. Main results for each formalisation, along with comparisons, are provided

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Section: Pac Paradigmmentioning

confidence: 93%

Section: Characteristic Samplementioning

confidence: 99%

Efficiency in the Identification in the Limit Learning Paradigm

Eyraud¹,

Heinz²,

Yoshinaka³

2016

Topics in Grammatical Inference

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“…If the directional interactions are pre-defined, structural equation modeling (SEM) can be used, whereas Granger causality measures the connectivity on directional interactions derived from the data ( 82 , 89 , 93 ). Other effective connectivity methods are directed coherence, dynamic causal modeling, linear non–Gaussian, conditional Bayes, and Bayes network methods ( 94 – 99 ). The main difference between functional and effective connectivity is that functional connectivity illustrates statistical dependencies, whereas effective connectivity is based on a mechanistic model of the causal effects that generated the data ( 87 , 100 ).…”

Section: Different Source Localization Models Techniques and Connecti...mentioning

confidence: 99%

Contributions of Magnetoencephalography to Understanding Mechanisms of Generalized Epilepsies: Blurring the Boundary Between Focal and Generalized Epilepsies?

2022

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According to the latest operational 2017 ILAE classification of epileptic seizures, the generalized epileptic seizure is still conceptualized as “originating at some point within and rapidly engaging, bilaterally distributed networks.” In contrast, the focal epileptic seizure is defined as “originating within networks limited to one hemisphere.” Hence, one of the main concepts of “generalized” and “focal” epilepsy comes from EEG descriptions before the era of source localization, and a presumed simultaneous bilateral onset and bi-synchrony of epileptiform discharges remains a hallmark for generalized seizures. Current literature on the pathophysiology of generalized epilepsy supports the concept of a cortical epileptogenic focus triggering rapidly generalized epileptic discharges involving intact corticothalamic and corticocortical networks, known as the cortical focus theory. Likewise, focal epilepsy with rich connectivity can give rise to generalized spike and wave discharges resulting from widespread bilateral synchronization. Therefore, making this key distinction between generalized and focal epilepsy may be challenging in some cases, and for the first time, a combined generalized and focal epilepsy is categorized in the 2017 ILAE classification. Nevertheless, treatment options, such as the choice of antiseizure medications or surgical treatment, are the reason behind the importance of accurate epilepsy classification. Over the past several decades, plentiful scientific research on the pathophysiology of generalized epilepsy has been conducted using non–invasive neuroimaging and postprocessing of the electromagnetic neural signal by measuring the spatiotemporal and interhemispheric latency of bi-synchronous or generalized epileptiform discharges as well as network analysis to identify diagnostic and prognostic biomarkers for accurate diagnosis of the two major types of epilepsy. Among all the advanced techniques, magnetoencephalography (MEG) and multiple other methods provide excellent temporal and spatial resolution, inherently suited to analyzing and visualizing the propagation of generalized EEG activities. This article aims to provide a comprehensive literature review of recent innovations in MEG methodology using source localization and network analysis techniques that contributed to the literature of idiopathic generalized epilepsy in terms of pathophysiology and clinical prognosis, thus further blurring the boundary between focal and generalized epilepsy.

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“…As mentioned in the introduction, the simple block-regular patterns constitute precisely the subclass of finitely distinguishable patterns over any alphabet of size at least 4 [7,Theorem 3]. The language generated by a simple blockregular pattern is known as a principal shuffle ideal in word combinatorics [25, §6.1], and the family of all such languages is an important object of study in the PAC learning model [5].…”

Section: Simple Block-regular Patternsmentioning

confidence: 99%

“…. , n − 1}, let q j be the position of w 1 occupied by the specific occurrence of a ij indicated with braces in Equation (5).…”

Section: Example For Lemmamentioning

confidence: 99%

The Teaching Complexity of Erasing Pattern Languages with Bounded Variable Frequency

Gao

2019

Developments in Language Theory

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Patterns provide a concise, syntactic way of describing a set of strings, but their expressive power comes at a price: a number of fundamental decision problems concerning (erasing) pattern languages, such as the membership problem and inclusion problem, are known to be NPcomplete or even undecidable, while the decidability of the equivalence problem is still open; in learning theory, the class of pattern languages is unlearnable in models such as the distribution-free (PAC) framework (if P/poly = N P/poly). Much work on the algorithmic learning of pattern languages has thus focussed on interesting subclasses of patterns for which positive learnability results may be achieved. A natural restriction on a pattern is a bound on its variable frequency -the maximum number m such that some variable occurs exactly m times in the pattern. This paper examines the effect of limiting the variable frequency of all patterns belonging to a class Π on the worst-case minimum number of labelled examples needed to uniquely identify any pattern of Π in cooperative teaching-learning models. Two such models, the teaching dimension model as well as the preference-based teaching model, will be considered.

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On the Learnability of Shuffle Ideals

Cited by 4 publications

References 35 publications

Efficiency in the Identification in the Limit Learning Paradigm

Efficiency in the Identification in the Limit Learning Paradigm

Contributions of Magnetoencephalography to Understanding Mechanisms of Generalized Epilepsies: Blurring the Boundary Between Focal and Generalized Epilepsies?

The Teaching Complexity of Erasing Pattern Languages with Bounded Variable Frequency

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