In this paper we consider an approach to passive learning. In contrast to the classical PAC model we do not assume that the examples are independently drawn according to an underlying distribution, but that they are generated by a time-driven process. We define deterministic and probabilistic learning models of this sort and investigate the relationships between them and with other models. The fact that successive examples are related can often be used to gain additional information similar to the information gained by membership queries. We show that this can be used to design on-line prediction algorithms. In particular, we present efficient algorithms for exactly identifying Boolean threshold functions, 2-term RSE, and 2-term-DNF, when the examples are generated by a random walk on {0,1}n.

Article Learning and robust learning of product distributions Share on Author: Klaus-U. Höffgen View Profile Authors Info & Claims COLT '93: Proceedings of the sixth annual conference on Computational learning theoryAugust 1993 Pages 77–83https://doi.org/10.1145/168304.168314Published:01 August 1993 21citation479DownloadsMetricsTotal Citations21Total Downloads479Last 12 Months23Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

We investigate the problem of learning concepts by presenting labeled and randomly chosen training–examples to single neurons. It is well-known that linear halfspaces are learnable by the method of linear programming. The corresponding (Mc-Culloch-Pitts) neurons are therefore efficiently trainable to learn an unknown halfspace from examples. We want to analyze how fast the learning performance degrades when the representational power of the neuron is overstrained, i.e., if more complex concepts than just halfspaces are allowed. We show that a neuron cannot efficently find its probably almost optimal adjustment (unless RP = NP). If the weights and the threshold of the neuron have a fixed constant bound on their coding length, the situation is even worse: There is in general no polynomial time training method which bounds the resulting prediction error of the neuron by k.opt for a fixed constant k (unless RP = NP). Other variants of learning more complex concepts than halfspaces by single neurons are also investigated. We show that neither heuristical learning nor learning by sigmoidal neurons with a constant reject-rate is efficiently possible (unless RP = NP).