Tom Fearn

This paper describes some statistical tests for comparing the predictive performance of two or more prediction rules. It covers the cases of both quantitative and qualitative predictions, that is, both regression and classification problems. Worked examples are included for both cases.

Understanding the governing dopant feature for cyclic discharge capacity is vital for the design and discovery of new doped lithium nickel–cobalt–manganese (NCM) oxide cathodes for lithium-ion battery applications. We herein apply six machine-learning regression algorithms to study the correlations of the structural, elemental features of 168 distinct doped NCM systems with their respective initial discharge capacity (IC) and 50th cycle discharge capacity (EC). First, a Pearson correlation coefficient study suggests that the lithium content ratio is highly correlated to both discharge capacity variables. Among all six regression algorithms, gradient boosting models have demonstrated the best prediction power for both IC and EC, with the root-mean-square errors calculated to be 16.66 mAhg^–1 and 18.59 mAhg^–1, respectively, against a hold-out test set. Furthermore, a game-theory-based variable-importance analysis reveals that doped NCM materials with higher lithium content, smaller dopant content, and lower-electronegativity atoms as the dopant are more likely to possess higher IC and EC. This study has demonstrated the exciting potentials of applying cutting-edge machine-learning techniques to accurately capture the complex structure–property relationship of doped NCM systems, and the models can be used as fast screening tools for new doped NCM structures with more superior electrochemical discharging properties.

The electrochemical potentials of spinel lithium manganese oxide (LMO) have long been plagued by the significant Mn³⁺ dissolution during long cycle discharging, resulting in rapid capacity fading and short cycle life. Although the doping mechanisms are effective in suppressing these reactions, the correlations of their effects on the material properties and the improved discharging performance still remain uncovered. In this study, seven machine learning (ML) methods are applied to a manually curated dataset of 102 doped LMO spinel systems to predict the initial discharge capacities (IC) and 20^th cycle end discharge capacities (EC) from fundamental system properties like material molar mass and crystal structure dimension. Gradient boosting models achieved the best prediction powers for IC and EC with their errors estimated to be 11.90 and 11.77 mAhg⁻¹, respectively. Besides, a higher formula molar mass of doped LMO can improve both capacities and additionally, a shorter crystal lattice dimension with a dopant with smaller electronegativity can slightly improve the value of the IC and EC, respectively. This study demonstrates the great potential of using ML models to both predict the discharging performance of doped spinel cathodes and identify the governing material properties for controlling the discharging performance.

The notations F_p,ν1,ν2 and χ²_p,ν in Eqs. (1), (2) and (3)

Energy dispersive X‐ray diffraction (EDXRD) and maximum likelihood principal component analysis multivariate curve resolution‐alternating least squares (MLPCA‐MCR‐ALS) with correlation constraint were used to quantify the composition of packaged pharmaceutical formulations. Recorded EDXRD profiles from unpackaged and packaged samples of ternary mixtures were modelled together in order to recover the concentrations as well as the pure profiles of the constituent compounds. MLPCA was used as a data pretreatment step to MCR‐ALS, accounting for the high noise and nonconstant variance observed in the EDXRD profiles and was shown to improve the resolution accuracy of MCR‐ALS for the data set. Local correlation constraints were applied in the MCR‐ALS procedure in order to model unpackaged and packaged samples simultaneously while accounting for the matrix effect of the packaging materials. The composition of the formulations was estimated with root‐mean‐square error of prediction for each component, including paracetamol, being approximately 2.5 %w/w for unpackaged and packaged samples. Paracetamol concentration was resolved simultaneously for the unpackaged and packaged samples to a greater degree of accuracy than achieved by partial least squares regression (PLSR) when modelling the contexts separately. By modelling the effects of the packaging and incorporating accurate reference information of unpackaged samples into the resolution of packaged samples, the potential of EDXRD and MLPCA‐MCR‐ALS for the identification and quantification of packaged solid‐dosage medicine in nondestructive screening and counterfeit medicine detection has been raised.