There are a variety of domains where it is desirable to learn a representationof an environment defined by a stream of sensori-motor experience.Thisdissertation introduces and formalizes subjective mapping, a novel approach tothis problem.A learned representation is subjective if it is constructedalmost entirely from the experience stream, minimizing the requirement ofadditional domain-specific information (which is often not readily obtainable).In many cases the observational data may be too plentiful to be feasibly stored.In these cases, a primary feature of a learned representation is that it becompact---summarizing information in a way that alleviates storage demands.Consequently, the first key insight of the subjective mapping approach is tophrase the problem as a variation of the well-studied problem of dimensionalityreduction.The second insight is that knowing the effects of actions iscritical to the usefulness of a representation.Therefore enforcing thatactions have a consistent and succinct form in the learned representation isalso a key requirement.This dissertation presents a new framework, action respecting embedding (ARE),which builds on a recent effective dimensionality reduction algorithm calledmaximum variance unfolding, in order to solve the newly introduced subjectivemapping problem.The resulting learned representations are shown to be usefulfor reasoning, planning and localization tasks.At the heart of the newalgorithm lies a semidefinite program leading to questions about ARE;;s abilityto handle sufficiently large input sizes.The final contribution of thisdissertation is to provide a divide-and-conquer algorithm as a first step toaddressing this issue.
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