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On the other hand, some models such as kernelized support-vector machines and kernel ridge regression involve non-linear transformations that lead to obfuscation of the relationship between the original features and the target variable. When given a choice, it may sometimes be worth a small tradeoff in cross-validation predicted accuracy for better explanatory power when comparing two candidate models.
For example, in the perovskite formability case above, using a more complicated gradient boosted decision tree reduced the variance in the cross validation accuracy a few percentage points, but did not allow for a simple visual schematic Pilania et al. Data transformations that lead to further abstraction like PCA should not be used as inputs to models if there is no clear reason why features should be covariant.
A model with clear justification for why it possesses the uncertainty it has is less likely to result in unpleasant surprises later. Because there is no universally agreed upon workflow for a materials informatics problem, we make an attempt at describing one possibility as others have done Ghiringhelli et al. Our workflow can be divided into four sections as depicted in Figure 4.
A schematic of the steps involved in designing a materials informatics model. The workflow starts with A collection of data relevant to the property of interest. Next, comes B building a simple model to explore correlations followed by C refinement of the model to satisfactory predictive accuracy and D final training and deployment. Starting with a less complex model supports a priori physical reasoning instead of post facto explanations. Like any materials science problem, one should begin with accessing what domain knowledge already exists Figure 4 A. This domain knowledge should then be used to enumerate a first set of features that will be collected and processed for use in a model.
The role of the machine learning algorithms is to find underlying structure in the data, not to make correlation where none exists.
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The selection of primary features overlaps in many ways with that of descriptors as explained earlier. Once the primary features have been assembled and made ready for parsing , it is common practice to make an exploratory model with something like ridge regression or a decision tree and vary the features to begin understanding which of them are the most important in the model formulation Figure 4 B. Observe the effect of adding or removing primary features on the cross-validation measured error and contextualize this within your prior expertise.
It is not recommended to jump straight into using the most complicated model, e. If none of the primary features show much more of a correlation with the output than would be expected from chance, this is an indication that either the sampling is bad or the causal feature is missing from the data. As a rule of thumb, if the number of samples is 10 times the number of features and no significant correlation is seen, there is likely something being missed. Eliminating features with low impact on accuracy from early testing may reduce the level of noise a model has to contend with.
If the features are highly correlated with each other, a data dimension reduction technique like PC analysis, as discussed above, can eliminate redundant information. If one has reason to suspect some functional transformation of the data could help e. Last but not least, the type of machine learning algorithm chosen can impact the performance as well.
A good workflow will have several types of models that are compared using cross-validation rather than picking just one initially.
Density functional theory in materials science
Each algorithm has its strengths and weaknesses. Random forests are known to be accurate and resistant to outliers but slow to train for large datasets. Naive Bayesian classifiers are very fast to train but produce unreliable probability estimates. Knowledge of the relative pros and cons for a given algorithm is strongly recommended before use [see for example Ref. Scikit-learn developers and Raschka ]. Once refinement yields a satisfactory choice of model and hyperparameters, the last step before deployment is to train on the whole dataset to maximize the information contained in the final model Figure 4 D.
The final round of cross-validation performed before this should provide a reasonable margin of error in line with your prior domain knowledge. By proceeding in an iterative fashion upwards in complexity, one can avoid much of the backtracking to find a simpler model that would be required if proceeding less deterministically. Once the model performance is acceptable, its important findings should be broken down into guidelines and new data generated to improve the description further. We have shown some of the things to be aware of when applying machine learning techniques to materials science.
There is much more that could be discussed, and with such rapid innovations in machine learning, some of the techniques presented here are bound to become obsolete.
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What will not change is the importance of scientific reasoning in discovering reliable structure—property-processing models. The role of theorists and experimentalists in identifying descriptors and quantifying uncertainty has never been more important. Data without science are like marble without a sculptor, trapped beauty waiting to be set free.
JR supervised the research and NW performed the simulations and analysis. NW wrote the first draft of the manuscript and both authors edited and commented on the manuscript. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. NW and JR thank L. Balachandran, and colleagues at the Opportunities in Materials Informatics Conference for useful discussions. Springer International Publishing , — Identification of phases, symmetries and defects through local crystallography.
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Mode crystallography of distorted structures. Classification of ABO3 perovskite solids: Induction of decision trees. Principal component analysis and dimensional analysis as materials informatics tools to reduce dimensionality in materials science and engineering. What is principal component analysis? Top-down induction of decision trees classifiers-a survey.
Principal component analysis of catalytic functions in the composition space of heterogeneous catalysts. Cross-validatory choice and assessment of statistical predictions. Digital Image Processing and Analysis: Coupling and electronic control of structural, orbital and magnetic orders in perovskites.
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