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Point defects or impurities are either naturally present in semiconductors or may be intentionally introduced to tune their electronic and optical properties. The nature of impurity energy levels can strongly influence the performance of a semiconductor in applications ranging from solar cells to photodiodes to infrared sensors to qubits for quantum computing. In this work, we develop a framework powered by machine learning (ML) and high-throughput density functional theory (DFT) computations for the prediction and screening of functional impurities in group IV, III-V, and II-VI zinc blende semiconductors. Elements spanning the length and breadth of the periodic table are considered as impurity atoms at the cation, anion, or interstitial sites in supercells of 34 candidate semiconductors, leading to a chemical space of   12,000 points, 10% of which are used to generate a DFT dataset of charge dependent defect formation energies. Descriptors based on tabulated elemental properties, defect coordination environment, and relevant semiconductor properties are used to train ML regression models for the DFT computed properties, resulting in statistical predictions of the neutral state formation energies and charge transition levels of all possible impurities in the given set of compounds. Kernel ridge regression, Gaussian process regression, and neural networks, with appropriate feature selection and hyperparameter optimization, are seen to yield similar predictive performances and meaningful uncertainty estimates. We apply the ML framework to screen all impurities with lower formation energy than dominant native defects in all group IV, III-V, and II-VI zinc blende semiconductors. An online tool resulting from this work for predicting and visualizing defect properties in semiconductors is made available on github.