We give a probabilistic interpretation of first-order formulas based on Valiants model of pac-learning. We study the resulting notion of probabilistic or approximate truth and take some first steps in developing its model theory. In particular we show that every fixed error parameter determining the precision of universal quantification gives rise to a different class of tautologies. Finally we...

In this paper, we further characterize the complexity of noise-tolerant learning in the PAC model. Specifically, we show a general lower bound of Ω ( log(1/δ) ε(1−2η) ) on the number of examples required for PAC learning in the presence of classification noise. Combined with a result of Simon, we effectively show that the sample complexity of PAC learning in the presence of classification noise...

We describe a methodology for upgrading existing attribute value learners towards rst order logic. This method has several advantages: one can proot from existing research on propositional learners (and inherit its eeciency and eeectiveness), relational learners (and inherit its expressiveness) and PAC-learning (and inherit its theoretical basis). Moreover there is a clear relationship between ...

We present a 2 ~ O(p n) time exact learning algorithm for polynomial size DNF using equivalence queries only. In particular, DNF is PAC-learnable in subexponential time under any distribution. This is the rst subexponential time PAC-learning algorithm for DNF under any distribution.

The probably approximately correct (PAC) model of learning and its extension to real-valued function classes sets a rigorous framework based upon which the complexity of learning a target from a function class using a finite sample can be computed. There is one main restriction, however, that the function class have a finite VC-dimension or scale-sensitive pseudo-dimension. In this paper we pre...

Abstract. Aeolus carries the Atmospheric LAser Doppler INstrument (ALADIN), first high-spectral-resolution lidar (HSRL) in space. Although ALADIN is optimized to measure winds, its two measurement channels can also be used derive optical properties of atmospheric particles, including a direct retrieval ratio. This paper presents standard correct algorithm and Mie algorithm, main algorithms prod...

A classical conjecture in generative linguistics is that universal restrictions on determiners in Natural Language (e.g. monotonicity, invariance, and conservativity) serve the purpose of simplifying the language acquisition task. This paper formalizes this conjecture within the PAC-learnability framework.

This paper studies the PAC and agnostic PAC learnability of some standard function classes in the learning in higher-order logic setting introduced by Lloyd et al. In particular, it is shown that the similarity between learning in higher-order logic and traditional attributevalue learning allows many results from computational learning theory to be ‘ported’ to the logical setting with ease. As ...

There are a number of established paradigms to study the learnability of classes of functions or languages: Query learning, Identification in the limit, Probably Approximately Correct learning. Comparison between these paradigms is hard. Moreover, when to the question of converging one adds computational constraints, the picture becomes even less clear. We concentrate here on just one class of ...

Mining class-imbalanced data is a common yet challenging problem in data mining and machine learning. When the class is imbalanced, the error rate of the rare class is usually much higher than that of the majority class. How many samples do we need in order to bound the error of the rare class (and the majority class)? If the misclassification cost of the class is known, can the costweighted er...