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Learning with streaming data has received extensive attention during the past few years. Existing approaches assume the feature space is fixed or changes by following explicit regularities, limiting their applicability in dynamic environments where the data streams are described by an arbitrarily varying feature space. To handle such capricious data streams, we in this paper develop a novel algorithm, named OCDS (Online learning from Capricious Data Streams), which does not make any assumption on feature space dynamics. OCDS trains a learner on a universal feature space that establishes relationships between old and new features, so that the patterns learned in the old feature space can be used in the new feature space. Specifically, the universal feature space is constructed by leveraging the relatednesses among features. We propose a generative graphical model to model the construction process, and show that learning from the universal feature space can effectively improve performance with theoretical analysis. The experimental results demonstrate that OCDS achieves conspicuous performance on synthetic and real datasets.