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Modern machine learning algorithms are capable of providing remarkably accurate point-predictions; however, questions remain about their statistical reliability. Unlike conventional machine learning methods, conformal prediction algorithms return confidence sets (i.e., set-valued predictions) that correspond to a given significance level. Moreover, these confidence sets are valid in the sense that they guarantee finite sample control over type 1 error probabilities, allowing the practitioner to choose an acceptable error rate. In our paper, we propose inductive conformal prediction (ICP) algorithms for the tasks of text infilling and part-of-speech (POS) prediction for natural language data. We construct new ICP-enhanced algorithms for POS tagging based on BERT (bidirectional encoder representations from transformers) and BiLSTM (bidirectional long short-term memory) models. For text infilling, we design a new ICP-enhanced BERT algorithm. We analyze the performance of the algorithms in simulations using the Brown Corpus, which contains over 57,000 sentences. Our results demonstrate that the ICP algorithms are able to produce valid set-valued predictions that are small enough to be applicable in real-world applications. We also provide a real data example for how our proposed set-valued predictions can improve machine generated audio transcriptions. 

Abstract Selective conversion of methane (CH 4 ) into value-added chemicals represents a grand challenge for the efficient utilization of rising hydrocarbon sources. We report here dimeric copper centers supported on graphitic carbon nitride (denoted as Cu 2 @C 3 N 4 ) as advanced catalysts for CH 4 partial oxidation. The copper-dimer catalysts demonstrate high selectivity for partial oxidation of methane under both thermo- and photocatalytic reaction conditions, with hydrogen peroxide (H 2 O 2 ) and oxygen (O 2 ) being used as the oxidizer, respectively. In particular, the photocatalytic oxidation of CH 4 with O 2 achieves >10% conversion, and >98% selectivity toward methyl oxygenates and a mass-specific activity of 1399.3 mmol g Cu −1 h −1 . Mechanistic studies reveal that the high reactivity of Cu 2 @C 3 N 4 can be ascribed to symphonic mechanisms among the bridging oxygen, the two copper sites and the semiconducting C 3 N 4 substrate, which do not only facilitate the heterolytic scission of C-H bond, but also promotes H 2 O 2 and O 2 activation in thermo- and photocatalysis, respectively.