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For performing regression tasks involved in various physics problems,enhancing the precision or equivalently reducing the uncertainty of regressionresults is undoubtedly one of the central goals. Here, somewhat surprisingly,we find that the unfavorable regression uncertainty in performing theregression tasks of inverse statistical problems actually contains hiddeninformation concerning the phase transitions of the system under consideration.By utilizing this hidden information, we develop a new unsupervised machinelearning approach for automated detection of phases of matter, dubbed learningfrom regression uncertainty. This is achieved by revealing an intrinsicconnection between regression uncertainty and response properties of thesystem, thus making the outputs of this machine learning approach directlyinterpretable via conventional notions of physics. We demonstrate the approachby identifying the critical points of the ferromagnetic Ising model and thethree-state clock model, and revealing the existence of the intermediate phasein the six-state and seven-state clock models. Comparing to the widely-usedclassification-based approaches developed so far, although successful, theirrecognized classes of patterns are essentially abstract, which hinders theirstraightforward relation to conventional notions of physics. These challengespersist even when one employs the state-of-the-art deep neural networks thatexcel at classification tasks. In contrast, with the core working horse being aneural network performing regression tasks, our new approach is not onlypractically more efficient, but also paves the way towards intriguingpossibilities for unveiling new physics via machine learning in a physicallyinterpretable manner.

Learning phase transitions from regression uncertainty: A new regression-based machine learning approach for automated detection of phases of matter