Annexe 2: Algorithmic techniques

Algorithm type	Basic description	Possible uses	Interpretability
Linear regression (LR)	Makes predictions about a target variable by summing weighted input/predictor variables.	Advantageous in highly regulated sectors like finance (eg credit scoring) and healthcare (predict disease risk given eg lifestyle and existing health conditions) because it’s simpler to calculate and have oversight over.	High level of interpretability because of linearity and monotonicity. Can become less interpretable with increased number of features (ie high dimensionality).
Logistic regression	Extends linear regression to classification problems by using a logistic function to transform outputs to a probability between 0 and 1.	Like linear regression, advantageous in highly regulated and safety-critical sectors, but in use cases that are based in classification problems such as yes/no decisions on risks, credit, or disease.	Good level of interpretability but less so than LR because features are transformed through a logistic function and related to the probabilistic result logarithmically rather than as sums.
Regularised regression (LASSO and Ridge)	Extends linear regression by adding penalisation and regularisation to feature weights to increase sparsity/ reduce dimensionality.	Like linear regression, advantageous in highly regulated and safety-critical sectors that require understandable, accessible, and transparent results.	High level of interpretability due to improvements in the sparsity of the model through better feature selection procedures.
Generalised linear model (GLM)	To model relationships between features and target variables that do not follow normal (Gaussian) distributions a GLM introduces a link function that allows for the extension of LR to non-normal distributions.	This extension of LR is applicable to use cases where target variables have constraints that require the exponential family set of distributions (for instance, if a target variable involves number of people, units of time or probabilities of outcome, the result has to have a non-negative value).	Good level of interpretability that tracks the advantages of LR while also introducing more flexibility. Because of the link function, determining feature importance may be less straightforward than with the additive character of simple LR, a degree of transparency may be lost.
Generalised additive model (GAM)	To model non-linear relationships between features and target variables (not captured by LR), a GAM sums non-parametric functions of predictor variables (like splines or tree-based fitting) rather than simple weighted features.	This extension of LR is applicable to use cases where the relationship between predictor and response variables is not linear (ie where the input-output relationship changes at different rates at different times) but optimal interpretability is desired.	Good level of interpretability because, even in the presence of non-linear relationships, the GAM allows for clear graphical representation of the effects of predictor variables on response variables.
Decision tree (DT)	A model that uses inductive branching methods to split data into interrelated decision nodes which terminate in classifications or predictions. DT’s moves from starting ‘root’ nodes to terminal ‘leaf’ nodes, following a logical decision path that is determined by Boolean-like ‘if-then’ operators that are weighted through training.	Because the step-by-step logic that produces DT outcomes is easily understandable to non-technical users (depending on number of nodes/ features), this method may be used in high-stakes and safety-critical decision-support situations that require transparency as well as many other use cases where volume of relevant features is reasonably low.	High level of interpretability if the DT is kept manageably small, so that the logic can be followed end-to-end. The advantage of DT’s over LR is that the former can accommodate non-linearity and variable interaction while remaining interpretable.
Rule/decision lists and sets	Closely related to DT’s, rule/decision lists and sets apply series of if-then statements to input features in order to generate predictions. Whereas decision lists are ordered and narrow down the logic behind an output by applying ‘else’ rules, decision sets keep individual if-then statements unordered and largely independent, while weighting them so that rule voting can occur in generating predictions.	As with DT’s, because the logic that produces rule lists and sets is easily understandable to non-technical users, this method may be used in high-stakes and safety-critical decision-support situations that require transparency as well as many other use cases where the clear and fully transparent justification of outcomes is a priority.	Rule lists and sets have one of the highest degrees of interpretability of all optimally performing and non-opaque algorithmic techniques. However, they also share with DT’s the same possibility that degrees of understandability are lost as the rule lists get longer or the rule sets get larger.
Case-based reasoning (CBR)/ Prototype and criticism	Using exemplars drawn from prior human knowledge, CBR predicts cluster labels by learning prototypes and organising input features into subspaces that are representative of the clusters of relevance. This method can be extended to use maximum mean discrepancy (MMD) to identify ‘criticisms’ or slices of the input space where a model most misrepresents the data. A combination of prototypes and criticisms can then be used to create optimally interpretable models.	CBR is applicable in any domain where experience-based reasoning is used for decision-making. For instance, in medicine, treatments are recommended on a CBR basis when prior successes in like cases point the decision maker towards suggesting that treatment. The extension of CBR to methods of prototype and criticism has meant a better facilitation of understanding of complex data distributions, and an increase in insight, actionability, and interpretability in data mining.	CBR is interpretable-by-design. It uses examples drawn from human knowledge in order to syphon input features into human recognisable representations. It preserves the explainability of the model through both sparse features and familiar prototypes.
Supersparse linear integer model (SLIM)	SLIM utilises data-driven learning to generate a simple scoring system that only requires users to add, subtract, and multiply a few numbers in order to make a prediction. Because SLIM produces such a sparse and accessible model, it can be implemented quickly and efficiently by non-technical users, who need no special training to deploy the system.	SLIM has been used in medical applications that require quick and streamlined but optimally accurate clinical decision-making. A version called Risk-Calibrated SLIM (RiskSLIM) has been applied to the criminal justice sector to show that its sparse linear methods are as effective for recidivism prediction as some opaque models that are in use.	Because of its sparse and easily understandable character, SLIM offers optimal interpretability for human-centred decision-support. As a manually completed scoring system, it also ensures the active engagement of the interpreter-user, who implements it.
Naïve Bayes	Uses Bayes rule to estimate the probability that a feature belongs to a given class, assuming that features are independent of each other. To classify a feature, the Naïve Bayes classifier computes the posterior probability for the class membership of that feature by multiplying the prior probability of the class with the class conditional probability of the feature.	While this technique is called naïve for reason of the unrealistic assumption of the independence of features, it is known to be very effective. Its quick calculation time and scalability make it good for applications with high dimensional feature spaces. Common applications include spam filtering, recommender systems, and sentiment analysis.	Naïve Bayes classifiers are highly interpretable, because the class membership probability of each feature is computed independently. The assumption that the conditional probabilities of the independent variables are statistically independent, however, is also a weakness, because feature interactions are not considered.
K-nearest neighbour (KNN)	Used to group data into clusters for purposes of either classification or prediction, this technique identifies a neighbourhood of nearest neighbours around a data point of concern and either finds the mean outcome of them for prediction or the most common class among them for classification.	KNN is a simple, intuitive, versatile technique that has wide applications but works best with smaller datasets. Because it is non-parametric (makes no assumptions about the underlying data distribution), it is effective for non-linear data without losing interpretability. Common applications include recommender systems, image recognition, and customer rating and sorting.	KNN works off the assumption that classes or outcomes can be predicted by looking at the proximity of the data points upon which they depend to data points that yielded similar classes and outcomes. This intuition about the importance of nearness/proximity is the explanation of all KNN results. Such an explanation is more convincing when the feature space remains small, so that similarity between instances remains accessible.
Support vector machines (SVM)	Uses a special type of mapping function to build a divider between two sets of features in a high dimensional feature space. An SVM therefore sorts two classes by maximising the margin of the decision boundary between them.	SVM’s are extremely versatile for complex sorting tasks. They can be used to detect the presence of objects in images (face/no face; cat/no cat), to classify text types (sports article/arts article), and to identify genes of interest in bioinformatics.	Low level of interpretability that depends on the dimensionality of the feature space. In context-determined cases, the use of SVM’s should be supplemented by secondary explanation tools.
Artificial neural net (ANN)	Family of non-linear statistical techniques (including recurrent, convolutional, and deep neural nets) that build complex mapping functions to predict or classify data by employing the feedforward—and sometimes feedback—of input variables through trained networks of interconnected and multi-layered operations.	ANN’s are best suited to complete a wide range of classification and prediction tasks for high dimensional feature spaces—ie cases where there are very large input vectors. Their uses may range from computer vision, image recognition, sales and weather forecasting, pharmaceutical discovery, and stock prediction to machine translation, disease diagnosis, and fraud detection.	The tendencies towards curviness (extreme non-linearity) and high-dimensionality of input variables produce very low-levels of interpretability in ANN’s. They are considered to be the epitome of ‘black box’ techniques. Where appropriate, the use of ANN’s should be supplemented by secondary explanation tools.
Random Forest	Builds a predictive model by combining and averaging the results from multiple (sometimes thousands) of decision trees that are trained on random subsets of shared features and training data.	Random forests are often used to effectively boost the performance of individual decisions trees, to improve their error rates, and to mitigate overfitting. They are very popular in high-dimensional problem areas like genomic medicine and have also been used extensively in computational linguistics, econometrics, and predictive risk modelling.	Very low levels of interpretability may result from the method of training these ensembles of decision trees on bagged data and randomised features, the number of trees in a given forest, and the possibility that individual trees may have hundreds or even thousands of nodes.
Ensemble methods	As their name suggests, ensemble methods are a diverse class of meta-techniques that combines different ‘learner’ models (of the same or different type) into one bigger model (predictive or classificatory) in order to decrease the statistical bias, lessen the variance, or improve the performance of any one of the sub-models taken separately.	Ensemble methods have a wide range of applications that tracks the potential uses of their constituent learner models (these may include DT’s, KNN’s, Random Forests, Naïve Bayes, etc.).	The interpretability of Ensemble Methods varies depending upon what kinds of methods are used. For instance, the rationale of a model that uses bagging techniques, which average together multiple estimates from learners trained on random subsets of data, may be difficult to explain. Explanation needs of these kinds of techniques should be thought through on a case-by-case basis.