Pattern Recognition and Density Estimation under the General i.i.d. Assumption

Nouretdinov, Ilia; Vovk, Vladimir; Vyugin, Michael V.; Gammerman, Alexander

doi:10.1007/3-540-44581-1_22

Cited by 28 publications

(18 citation statements)

References 8 publications

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“…PAC theory only assumes that the instances are generated independently by some completely unknown distribution, but for the resulting bounds to be interesting in practice, the data set must be quite clean. Unfortunately, this is rarely the case for real-world data, which will lead to very loose bounds, see e.g., Nouretdinov et al (2001), where the crudeness of PAC theory is demonstrated. In addition, the PAC bounds are for the overall error and not for individual predictions.…”

Section: Related Workmentioning

confidence: 99%

Regression conformal prediction with random forests

et al. 2014

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Regression conformal prediction produces prediction intervals that are valid, i.e., the probability of excluding the correct target value is bounded by a predefined confidence level. The most important criterion when comparing conformal regressors is efficiency; the prediction intervals should be as tight (informative) as possible. In this study, the use of random forests as the underlying model for regression conformal prediction is investigated and compared to existing state-of-the-art techniques, which are based on neural networks and k-nearest neighbors. In addition to their robust predictive performance, random forests allow for determining the size of the prediction intervals by using out-of-bag estimates instead of requiring a separate calibration set. An extensive empirical investigation, using 33 publicly available data sets, was undertaken to compare the use of random forests to existing stateof-the-art conformal predictors. The results show that the suggested approach, on almost all confidence levels and using both standard and normalized nonconformity functions, produced significantly more efficient conformal predictors than the existing alternatives.

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Section: Related Workmentioning

confidence: 99%

Regression conformal prediction with random forests

et al. 2014

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“…If this is not the case, which is not for the majority of data sets, the bounds obtained from these methods are very loose and as such they are not very useful in practice. A demonstration of the crudeness of PAC bounds can be found in (Nouretdinov et al, 2001a), where there is an example of Littlestone and Warmuth's bound (found in (Cristianini & Shawe-Taylor, 2000), Theorems 4.25 and 6.8) applied to the USPS data set. In addition, PAC theory has two other drawbacks: (a) the majority of relevant results either involve large explicit constants or do not specify the relevant constants at all; (b) the bounds obtained by PAC theory are for the overall error and not for individual test examples.…”

Section: Introductionmentioning

confidence: 99%

Inductive Conformal Prediction: Theory and Application to Neural Networks

Papadopoulos¹

2008

Tools in Artificial Intelligence

152

143

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“…Nouretdinov also illustrated in [51] that the error bound becomes 0.74 when the Littlestone-Warmuth theorem is extended to multi-class classifiers for this dataset. In summary, the limitations of the PAC learning theory in the context of obtaining reliable confidence measure values are:…”

Section: Limitationsmentioning

confidence: 78%

“…However, the error bound values generated by such approaches are often not very practical, as demonstrated by Proedrou in [41], and by Nouretdinov in [51]. For example, Littlestone-Warmuth's Theorem is known to be one of the most sound results in PAC theory.…”

Section: Limitationsmentioning

confidence: 99%

Conformal predictions in multimedia pattern recognition

Balasubramanian¹

2011

SIGMultimedia Rec.

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The fields of pattern recognition and machine learning are on a fundamental quest to design systems that can learn the way humans do. One important aspect of human intelligence that has so far not been given sufficient attention is the capability of humans to express when they are certain about a decision, or when they are not. like a bird', in his words). I cannot thank him enough for his strong belief in me over the years, for setting standards of excellence that will take me a lifetime to scale, for housing me in an environment suffused with bright minds and numerous opportunities for exposure and growth, and most importantly, for his never-failing support through every high and low of my PhD.

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Pattern Recognition and Density Estimation under the General i.i.d. Assumption

Cited by 28 publications

References 8 publications

Regression conformal prediction with random forests

Regression conformal prediction with random forests

Inductive Conformal Prediction: Theory and Application to Neural Networks

Conformal predictions in multimedia pattern recognition

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