Development of high throughput data acquisition technologies, together with advances in computing, and communications have resulted in an explosive growth in the number, size, and diversity of potentially useful information sources. This has resulted in unprecedented opportunities in data-driven knowledge acquisition and decision-making in a number of emerging increasingly data-rich application domains such as bioinformatics, environmental informatics, enterprise informatics, and social informatics (among others). However, the massive size, semantic heterogeneity, autonomy, and distributed nature of the data repositories present significant hurdles in acquiring useful knowledge from the available data. This paper introduces some of the algorithmic and statistical problems that arise in such a setting, describes algorithms for learning classifiers from distributed data that offer rigorous performance guarantees (relative to their centralized or batch counterparts). It also describes how this approach can be extended to work with autonomous, and hence, inevitably semantically heterogeneous data sources, by making explicit, the ontologies (attributes and relationships between attributes) associated with the data sources and reconciling the semantic differences among the data sources from a user's point of view. This allows user or context-dependent exploration of semantically heterogeneous data sources. The resulting algorithms have been implemented in INDUS - an open source software package for collaborative discovery from autonomous, semantically heterogeneous, distributed data sources.