Exact limits

SAS® Macros for Exact Confidence Limits

Confidence intervals have a long history and have become an indispensable tool in statistical applications. The computation of confidence intervals for a mean based on normal (large sample) theory is straightforward and readily available in the SAS system through such procedures as PROC ANOV A and PROC GLM. For the case of small samples and non-normal distributions, however, normal theory based...

Limits on Exact Learning from Membership and Equivalence Queries

In this paper we look at different combinatorial properties of concept classes that give bounds on the query complexity of exact learning. We consider learning from equivalence queries, membership queries and a combination of equivalence and membership queries. We examine and present proofs regarding efficient query-learnability as it relates to the notions of polynomial certificates, approxima...

Exact Fundamental Limits of the First and Second Hyperpolarizabilities.

Nonlinear optical interactions of light with materials originate in the microscopic response of the molecular constituents to excitation by an optical field, and are expressed by the first (β) and second (γ) hyperpolarizabilities. Upper bounds to these quantities were derived seventeen years ago using approximate, truncated state models that violated completeness and unitarity, and far exceed t...

Limits of Exact Algorithms For Inference ofMinimum Size Finite State

We address the problem of selecting the minimum sized nite state machine consistent with given input/output samples. The problem can be solved by computing the minimum nite state machine equivalent to a nite state machine without loops obtained from the training set. We compare the performance of four algorithms for this task: two algorithms for incompletely speciied nite state machine reductio...

Generalized Covering Groups and Direct Limits