Learning from Examples with Unspecified Attribute Values

We introduce the UAV learning model in which some of the attributes in the examples are unspecified. In our model, an example x is classified positive (resp., negative) if all possible assignments for the unspecified attributes result in a positive (resp., negative) classification. Otherwise the classificatoin given to x is ? (for unknown). Given an example x in which some attributes are unspecified, the oracle UAV-MQ responds with the classification of x. Given a hypothesis h, the oracle UAV-EQ returns an example x (that could have unspecified attributes) for which h(x) is incorrect. We show that any class learnable in the exact model using the MQ and EQ oracles is also learnable in the UAV model using the MQ and UAV-EQ oracles as long as the counterexamples provided by the UAV-EQ oracle have a logarithmic number of unspecified attributes. We also show that any class learnable in the exact model using the MQ and EQ oracles is also learnable in the UAV model using the UAV-MQ and UAV-EQ oracles as well as an oracle to evaluate a given boolean formula on an example with unspecified attributes. (For some hypothesis classes such as decision trees and unate formulas the evaluation can be done in polynomial time without an oracle.) We also study the learnability of a universal class of decision trees under the UAV model and of DNF formulas under a representation-dependent variation of the UAV model

Agnostic Learning of Geometric Patterns

Goldberg, Goldman, and Scott demonstrated how the problem of recognizing a landmark from a one-dimensional visual image can be mapped to that of learning a one-dimensional geometric pattern and gave a PAC algorithm to learn that class. In this paper, we present an efficient on-line agnostic learning algorithm for learning the class of constant-dimension geometric patterns. Our algorithm can tolerate both classification and attribute noise. By working in higher dimensional spaces we can represent more features from the visual image in the geometric pattern. Our mapping of the data to a geometric pattern, and hence our learning algorithm, is applicable to any data representable as a constant-dimensional array of values, e.g. sonar data, temporal difference information, or amplitudes of a waveform. To our knowledge, these classes of patterns are more complex than any class of geometric patterns previously studied. Also, our results are easily adapted to learn the union of fixed-dimensional boxes from multiple-instance examples. Finally, our algorithms are tolerant of concept shift

Real-valued multiple-instance learning with queries

AbstractWhile there has been a significant amount of theoretical and empirical research on the multiple-instance learning model, most of this research is for concept learning. However, for the important application area of drug discovery, a real-valued classification is preferable. In this paper we initiate a theoretical study of real-valued multiple-instance learning. We prove that the problem of finding a target point consistent with a set of labeled multiple-instance examples (or bags) is NP-complete, and that the problem of learning from real-valued multiple-instance examples is as hard as learning DNF. Another contribution of our work is in defining and studying a multiple-instance membership query (MI-MQ). We give a positive result on exactly learning the target point for a multiple-instance problem in which the learner is provided with a MI-MQ oracle and a single adversarially selected bag

Association of maternal Vitamin D status with glucose tolerance and caesarean section in a multi-ethnic Asian cohort: the growing up in Singapore towards healthy outcomes study

10.1371/journal.pone.0142239PLoS ONE10111-16GUSTO (Growing up towards Healthy Outcomes

Learning From Examples With Unspecified Attribute Values (Extended Abstract)

We introduce the UAV learning model in which some of the attributes in the examples are unspecified. In our model, an example x is classified positive (resp., negative) if all possible assignments for the unspecified attributes result in a positive (resp., negative) classification. Otherwise the classification given to x is "?" (for unknown). Given an example x in which some attributes are unspecified, the oracle UAV-MQ responds with the classification of x. Given a hypothesis h, the oracle UAV-EQ returns an example x (that could have unspecified attributes) for which h(x) is incorrect. We show that any class learnable in the exact model using the..

Learning From Examples With Unspecified Attribute Values

We introduce the UAV learning model in which some of the attributes in the examples are unspecified. In our model, an example x is classified positive (resp., negative) if all possible assignments for the unspecified attributes result in a positive (resp., negative) classification. Otherwise the classification given to x is "?" (for unknown). Given an example x in which some attributes are unspecified, the oracle UAV-MQ responds with the classification of x. Given a hypothesis h, the oracle UAV-EQ returns An earlier version appears in the Tenth Annual ACM Conferenceon ComputationalLearning Theory, 1997 y Supported in part by NSF NYI Grant CCR-9357707 with matching funds provided by Xerox PARC and WUTA. an example x (that could have unspecified attributes) for which h(x) is incorrect. We show that any class learnable in the exact model using the MQ and EQ oracles is also learnable in the UAV model using the MQ and UAV-EQ oracles as long as the counterexamples provided by the UAV-..

Agnostic Learning of Geometric Patterns (Extended Abstract)

) Sally A. Goldman Dept. of Computer Science Washington University St. Louis, MO 63130 [email protected] Stephen S. Kwek Dept. of Computer Science Washington University St. Louis, MO 63130 [email protected] Stephen D. Scott Dept. of Computer Science Washington University St. Louis, MO 63130 [email protected] Abstract Goldberg, Goldman, and Scott demonstrated how the problem of recognizing a landmark from a one-dimensional visual image can be mapped to that of learning a one-dimensional geometric pattern and gave a PAC algorithm to learn that class. We present an on-line agnostic learning algorithm for learning the class of one-dimensional geometric patterns. Since, when moving from the processed visual image to a one-dimensional pattern some key information is lost, we define a class of two-dimensional geometric patterns for which the important features from the visual image are incorporated in the geometric pattern, and show how to extend our agnostic learning algorithm to t..

Agnostic Learning of Geometric Patterns (Extended Abstract)

) Sally A. Goldman Dept. of Computer Science Washington University St. Louis, MO 63130 [email protected] Stephen S. Kwek Dept. of Computer Science Washington University St. Louis, MO 63130 [email protected] Stephen D. Scott Dept. of Computer Science Washington University St. Louis, MO 63130 [email protected] Abstract Goldberg, Goldman, and Scott demonstrated how the problem of recognizing a landmark from a one-dimensional visual image can be mapped to that of learning a one-dimensional geometric pattern and gave a PAC algorithm to learn that class. We present an on-line agnostic learning algorithm for learning the class of one-dimensional geometric patterns. Since, when moving from the processed visual image to a one-dimensional pattern some key information is lost, we define a class of two-dimensional geometric patterns for which the important features from the visual image are incorporated in the geometric pattern, and show how to extend our agnostic learning algorithm to t..