<ul><li>The relationship between learnability of a 'base class' of functions on a set X and learnability of a class of statistical functions derived from the base class is considered.</li><li>The study examines Probably Approximately Correct (PAC) learning and online learning in terms of sample complexity and combinatorial dimensions of the base class.</li><li>Improved bounds on the sample complexity of learning for statistical classes are established by using techniques from model theory.</li><li>The focus is on classes derived from logical formulas, and the article discusses the relationship between learnability and properties of the formula.</li></ul>

Logical perspectives on learning statistical objects

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