Is there a role for statistics in artificial intelligence?

The research on and application of artificial intelligence (AI) has triggered a comprehensive scientific, economic, social and political discussion. Here we argue that statistics, as an interdisciplinary scientific field, plays a substantial role, both for the theoretical and practical understanding of AI and for its further development.

Contrary to the public perception, AI is not a new phenomenon. AI was already mentioned in 1956 at the Dartmouth Conference (Moor 2006; Solomonoff 1985), and the first data-driven algorithms such as Perceptron (Rosenblatt 1958), backpropagation (Kelley 1960) and the so-called ‘Lernmatrix’, an early neural system (Steinbuch 1961; Hilberg 1995), were developed in the 50s and 60s. The Lighthill Report in 1973 made a predominantly negative judgment on AI research in Great Britain and led to the fact that the financial support for AI research was almost completely stopped (the so-called first AI winter). The following phase of predominantly knowledge-based development ended in 1987 with the so-called second AI winter. A period of reduced public interest and funding in AI began. Nonetheless, in 1988, Judea Pearl published his book ‘Probabilistic Reasoning in Intelligent Systems’, for which he received the Turing Award in 2011 (Pearl 1988). From the beginning of the 1990s, AI has been developing again with major breakthroughs like Support Vector Machines (Cortes and Vapnik 1995), Random Forest (Breiman 2001), Bayesian Methods (Zhu et al. 2017), Boosting and Bagging (Freund and Schapire 1997; Breiman 1996), Deep Learning (Schmidhuber 2015) and Extreme Learning Machines (Huang et al. 2006).

Today, AI plays an increasingly important role in many areas of life. International organizations and national governments have currently positioned themselves or introduced new regulatory frameworks for AI. Examples are, among others, the AI strategy of the German government (Bundesregierung 2018), the statement of the Data Ethics Commission (Data Ethics Commission of the Federal Government, Federal Ministry of the Interior, Building and Community 2019) from 2019 and the report of the Nuffield Foundation in the UK (Nuffield Foundation 2019). Similarly, the European Commission recently published a white paper on AI (European Commission 2020b). Furthermore, regulatory authorities such as the US Food and Drug Administration (FDA) are now also dealing with AI topics and their evaluation. In 2018, for example, the electrocardiogram function of the Apple Watch was the first AI application to be approved by the FDA (MedTechIntelligence 2018).

There is no unique and comprehensive definition of artificial intelligence. Two concepts are commonly used distinguishing weak and strong AI. Searle (1980) defined them as follows: ‘According to weak AI, the principal value of the computer in the study of the mind is that it gives us a very powerful tool. [...] But according to strong AI, the computer is not merely a tool in the study of the mind; rather, the appropriately programmed computer really is a mind [...]’. Thus, strong AI essentially describes a form of machine intelligence that is equal to human intelligence or even improves upon it, while weak AI (sometimes also referred to as narrow AI) is limited to tractable applications in specific domains. Following this definition, we will focus on weak AI in this paper in the sense that we consider self-learning systems, which are solving specific application problems based on methods from mathematics, statistics and computer science. Consequently, we will focus on the data-driven aspects of AI in this paper. In addition, there are many areas in AI that deal with the processing of and drawing inference from symbolic data (Bock and Diday 2000; Billard and Diday 2006). In contrast to standard data tables, symbolic data may consist of, e.g. lists, intervals, etc. Thus, special methods for data aggregation and analysis are necessary, which will not be discussed here.

As for AI, there is neither a single definition nor a uniform assignment of methods to the field of machine learning (ML) in literature and practice. Often, ML is considered a subset of AI approaches. Based on Simon’s definition from 1983 (Simon 1983), learning describes changes of a system in such a way that a similar task can be performed more effectively or efficiently the next time it is performed. Bishop (2006) describes machine learning as the ‘automatic discovery of regularities in data through the use of computer algorithms [...]’. Following these concepts, we use AI in a very general sense in this paper whereas ML is used to refer to more specific (statistical) algorithms.

Often the terms AI and ML are mentioned along with Big Data (Gudivada et al. 2015) or Data Science, sometimes even used interchangeably. However, neither are AI methods necessary to solve Big Data problems, nor are methods from AI only applicable to Big Data. Data Science, on the other hand, is usually considered as an intersection of computer science, statistics and the respective scientific discipline. Therefore, it is not bound to certain methods or certain data conditions.

This paper aims at contributing to the current discussion about AI by highlighting the relevance of statistical methodology in the context of AI development and application. Statistics can make important contributions to a more successful and secure use of AI systems, for example with regard to The remainder of the paper is organized as follows: First, we present an overview of AI applications and methods in Sect. 2. We continue by expanding on the points 1.–4. in Sects. 3, 4, 5 and 6. We conclude with Sect. 7. There, we also discuss the increased need for teaching and further education targeting the increase of AI-related literacy (particularly with respect to the underlying statistical concepts) at all educational levels.

Important categories of AI approaches are supervised learning, unsupervised learning and reinforcement learning (Sutton and Barto 2018). In supervised learning, AI systems learn from training data with known output such as true class labels or responses. Thus, the aim is to learn some function \(g: X \rightarrow Y\) describing the relationship between an \(n \times p\) matrix of given features \({\mathbf {X}} \subset X\) and the vector of labels \({\mathbf {Y}}= (y_1, \dots , y_n)' \subset Y\). Here, n denotes the number of observations, p is the number of features and X and Y describe the input and output space, respectively. Examples include, among others, support-vector machines, linear and logistic regression or decision trees. In contrast, unsupervised learning extracts patterns from unlabeled data, i.e. without the \(y_i\)s in the notation above. The most well-known examples include principal component analysis and clustering. Finally, reinforcement learning originates from robotics and describes the situation where an ‘agent’ (i.e. an autonomous entity with the ability to act and direct its activity towards achieving goals) learns through trial-and-error search. Markov decision processes from probability theory play an important role here (Sutton and Barto 2018). The input data to an AI algorithm can be measured values such as stock market prices, audio signals, climate data or texts, but may also describe very complex relationships, such as chess games. In the following, we provide some specific examples of AI applications.

The design of a study and the data to be considered is the basis for the validity of the conclusions. Unfortunately, AI applications often use data that were collected for a different purpose (so-called secondary data, observational studies). The collection and compilation of secondary data is in general not based on a specific purpose or a research question. Instead, it is collected for other purposes such as accounting or storage purposes. A typical case is the scientific use of routine data. For example, the AI models in a recent study about predicting medical events (such as hospitalization) are based on medical billing data (Lin et al. 2019). Another typical case concerns convenience samples, that is, samples that are not randomly drawn but instead depend on ‘availability’. Well-known examples are online questionnaires, which only reach those people who visit the corresponding homepage and take the time to answer the questions. The concept of knowledge discovery in databases (Fayyad et al. 1996) very clearly reflects the assumption that data are regarded as a given basis from which information and knowledge can be extracted by AI procedures. This is contrary to the traditional empirical research process, in which empirically testable research questions are derived from theoretical questions by conceptualizing and operationalizing. Importantly, the resulting measurement variables are then collected for this specific purpose.

‘Data is the new oil of the global economy.’ According to, e.g., the New York Times (New York Times 2018) or the Economist (The Economist 2017), this credo echoes incessantly through start-up conferences and founder forums. This metaphor is not only popular but false. First of all, data in this context corresponds to crude oil, which needs further refining before it can be used. In addition, the resource crude oil is limited. ‘For a start, while oil is a finite resource, data is effectively infinitely durable and reusable’ [Bernard Marr in Forbes (2018)]. All the more important is a responsible approach to data preprocessing (Fig. 3).

Ensuring data quality is of great importance in all analyses, according to the popular slogan ‘Garbage in, garbage out.’ As already mentioned in the previous section, we mainly use secondary data in the context of AI. In AI, the process of operationalization is often replaced by the ETL process: ‘Extract, Transform, Load’ (Theodorou et al. 2017). Relevant measurements are to be extracted from the data lake(s), then transformed and finally loaded into the (automated) analysis procedures. Many AI procedures are thereby expected to be able to distill relevant influencing variables from high-dimensional data.

The success of this procedure fundamentally depends on the quality of the data. In line with Karr et al. (2006), data quality is defined here as the ability of data to be used quickly, economically and effectively for decision-making and evaluation (Karr et al. 2006). In this sense, data quality is a multi-dimensional concept that goes far beyond measurement accuracy and includes aspects such as relevance, completeness, availability, timeliness, meta-information, documentation and, above all, context-dependent expertise (Duke-Margolis 2018, 2019). In official statistics, relevance, accuracy and reliability, timeliness and punctuality, coherence and comparability, accessibility and clarity are defined as dimensions of data quality (European Statistical System 2019).

Increasing automation of data collection, e.g., through sensor technology, may increase measurement accuracy in a cost-effective and simple way. Whether this will achieve the expected improvement in data quality remains to be checked in each individual application. Missing values are a common problem of data analyses. In statistics, a variety of methods have been developed to deal with these, including imputation procedures, or methods of data enhancement (Rubin 1976; Seaman and White 2013; Van Buuren 2018). The AI approach of ubiquitous data collection allows the existence of redundant data, which can be used in a preprocessing step with appropriate context knowledge to complete incomplete data sets. However, this requires a corresponding integration of context knowledge into the data extraction process.

The data-hungry decision-making processes of AI and statistics are subject to a high risk with regard to relevance and timeliness, since they are implicitly based on the assumption that the patterns hidden in the data should perpetuate themselves in the future. In many applications, this leads to an undesirable entrenchment of existing stereotypes and resulting disadvantages, e.g., in the automatic granting of credit or the automatic selection of applicants. A specific example is given by the gender bias in Amazon’s AI recruiting tool (Dastin 2018).

In the triad ‘experiment - observational study - convenience sample (data lake)’, the field of AI, with regard to its data basis, is moving further and further away from the classical ideal of controlled experimental data collection to an exploration of given data based on pure associations. However, only controlled experimental designs guarantee an investigation of causal questions. This topic will be discussed in more detail in Sect. 5. Causality is crucial if the aim of the analysis is to explain relationships such as the function \(g: X \rightarrow Y\) linking the feature vector \(\{x_1,\dots , x_n\} \subset X\) to the outcome \(\{y_1, \dots , y_n\} \subset Y\). There are, however, other situations where one might not be primarily interested in causal conclusions. Good prediction, for example, can also be obtained by using variables that are not themselves causally related to the outcome but strongly correlated with some causal predictor instead.

Exploratory data analysis (Tukey 1962) provides a broad spectrum of tools to visualize the empirical distributions of the data and to derive corresponding key figures. This can be used in preprocessing to detect anomalies or to define ranges of typical values in order to correct input or measurement errors and to determine standard values. In combination with standardization in data storage, data errors in the measurement process can be detected and corrected at an early stage. This way, statistics helps to assess data quality with regard to systematic, standardized and complete recording. Survey methodology primarily focuses on data quality. The insights gained in statistical survey research to ensure data quality with regard to internal and external validity provide a profound foundation for corresponding developments in the context of AI. Furthermore, various procedures for imputing missing data are known in statistics, which can be used to complete the data depending on the existing context and expertise (Rubin 1976; Seaman and White 2013; Van Buuren 2018). Statisticians have dealt intensively with the treatment of missing values under different development processes [non-response, missing not at random, missing at random, missing completely at random (Rubin 1976; Molenberghs et al. 2014)], selection bias and measurement error (Keogh et al. 2020; Shaw et al. 2020).

Another point worth mentioning is parameter tuning, i.e. the determination of so-called hyperparameters, which control the learning behavior of ML algorithms: comprehensive parameter tuning of methods in the AI context often requires very large amounts of data. For smaller data volumes it is almost impossible to use such procedures. However, certain model-based (statistical) methods can still be used in this case (Richter et al. 2019).

Only a few decades ago, the greatest challenge of AI research was to program machines to associate a potential cause to a set of observable feature values, e.g. through Bayesian networks (Pearl 1988). The rapid development of AI in recent years (both in terms of the theory and methodology of statistical learning processes and the computing power of computers) has led to a multitude of algorithms and methods that have now mastered this task. One example are deep learning methods, which are used in robotics (Levine et al. 2018) and autonomous driving (Teichmann et al. 2018), as well as in computer-aided detection and diagnostic systems [e.g., for breast cancer diagnosis (Burt et al. 2018)], drug discovery in pharmaceutical research (Chen et al. 2018) and agriculture (Kamilaris and Prenafeta-Boldú 2018). With their often high predictive power, AI methods can uncover structures and relationships in large volumes of data based on associations. Due to the excellent performance of AI methods in large data sets, they are also frequently used in medicine to analyze register and observational data that have not been collected within the strict framework of a randomized study design (Sect. 3). However, the discovery of correlations and associations (especially in this context) is not equivalent to establishing causal claims.

An important step in the further development of AI is therefore to replace associational argumentation with causal argumentation. Pearl (2010) describes the difference as follows: ‘An associational concept is any relationship that can be defined in terms of a joint distribution of observed variables, and a causal concept is any relationship that cannot be defined from the distribution alone.’

Even the formal definition of a causal effect is not trivial. The fields of statistics and clinical epidemiology, for example, use the Bradford Hill criteria (Hill 1965) and the counterfactual framework introduced by Rubin (1974). The central problem in observational data are covariate effects, which, in contrast to the randomized controlled trial, are not excluded by design and whose (non-)consideration leads to distorted estimates of causal effects. In this context, a distinction must be made between confounders, colliders, and mediators (Pearl 2009). Confounders are unobserved or unconsidered variables that influence both the exposure and the outcome, see Fig. 4a. This can distort the effects of exposure if naively correlated. Fisher identified this problem in his book ‘The Design of Experiments’ published in 1935. A formal definition was developed in the field of epidemiology in the 1980s (Greenland and Robins 1986). Later, graphical criteria such as the Back-Door Criterion (Greenland et al. 1999; Pearl 1993) were developed to define the term confounding.

In statistics, the problem of confounding is taken into account either in the design (e.g., randomized study, stratification, etc.) or evaluation [propensity score methods (Cochran and Rubin 1973), marginal structural models (Robins et al. 2000), graphical models (Didelez 2007)]. In this context, it is interesting to note that randomized studies (which have a long tradition in the medical field) have recently been increasingly used in econometric studies (Athey and Imbens 2017; Duflo et al. 2007; Kohavi et al. 2020). In the case of observational data, econometrics has made many methodological contributions to the identification of treatment effects, e.g., via the potential outcome approach (Rosenbaum 2017, 2002, 2010; Rubin 1974, 2006) as well as the work on policy evaluation (Heckman 2001).

In contrast to confounders, colliders and mediators lead to distorted estimates of causal effects precisely when they are taken into account during estimation. Whereas colliders represent common consequences of treatment and outcome (Fig. 4b), mediators are variables that represent part of the causal mechanism by which the treatment affects the outcome (Fig. 4c). Especially in the case of longitudinal data, it is therefore necessary to differentiate in a theoretically informed manner which relationships the covariates in the observed data have with the treatment and outcome variables, thus avoiding bias in the causal effect estimates by (not) having taken them into account.

By integrating appropriate statistical theories and methods into AI, it will be possible to answer causal questions and simulate interventions. In medicine, e.g., questions such as ‘What would be the effect of a general smoking ban on the German health care system’ could then be investigated and reliable statements could be made, even without randomized studies which would not be possible here. Pearl’s idea goes beyond the use of ML methods in causal analyses (which are used, for example, in connection with targeted learning (Van der Laan and Rose 2011) or causal random forest (Athey and Imbens 2015)). His vision is rather to integrate the causal framework (Pearl 2010) described by him with ML algorithms to enable the machines to draw causal conclusions and simulate interventions.

The integration of statistical methods to detect causality in AI also contributes to increasing its transparency and thus the acceptance of AI methods, since a reference to probabilities or statistical correlations in the context of an explanation is not as effective as a reference to causes and causal effects (Miller 2019).

Uncertainty quantification is often neglected in AI applications. One reason may be the above discussed misconception that ‘Big Data’ automatically leads to exact results, making uncertainty quantification redundant. Another key reason is the complexity of the methods which hampers the construction of statistically valid uncertainty assessments. However, most statisticians would agree that any comprehensive data analysis should contain methods to quantify the uncertainty of estimates and predictions. Its importance is also stressed by the American statistician David B. Dunson who writes that: ‘it is crucial to not over-state the results and appropriately characterize the (often immense) uncertainty to avoid flooding the scientific literature with false findings.’ (Dunson 2018).

In fact, in order to achieve the main goal of highly accurate predictions, assumptions about underlying distributions and functional relationships are deliberately dropped in AI applications. On the one hand, this allows for a greater flexibility of the procedures. On the other hand, however, this also complicates an accurate quantification of uncertainty, e.g., to specify valid prediction and confidence regions for target variables and parameters of interest. As Bühlmann and colleagues put it: ‘The statistical theory serves as guard against cheating with data: you cannot beat the uncertainty principle.’ (Bühlmann and van de Geer 2018). In recent years, proposals for uncertainty quantification in AI methods have already been developed by invoking Bayesian approximations, bootstrapping, jackknifing and other cross-validation techniques, Gaussian processes, Monte Carlo dropout etc., see e. g., Gal and Ghahramani (2016), Garnelo et al. (2018), Osband et al. (2016), Srivastava et al. (2014), Wager et al. (2014). However, their theoretical validity (e.g., that a prediction interval actually covers future values 95% of the time) has either not been demonstrated yet or has only been proven under very restrictive or at least partially unrealistic assumptions.

In contrast, algorithmic methods could be embedded in statistical models. While potentially less flexible, they permit a better quantification of the underlying uncertainty by specifying valid prediction and confidence intervals or allow for a better interpretation of the results. We give two examples: In time-to-event analyses mathematically valid simultaneous confidence bands for cumulative incidence functions can be constructed by combinations of nonparametric estimators of Kaplan-Meier or Aalen-Johansen-type and algorithmic resampling (Bluhmki et al. 2018; Dobler et al. 2017). Similarly, in the context of time series prediction, hybrid combinations of artificial neural networks with ARIMA models or within hierarchical structures allow for better explainability (Aburto and Weber 2007; Wickramasuriya et al. 2019).

Moreover, the estimated parameters of many AI approaches (such as deep learning) are difficult to interpret. Pioneering work from computer science on this topic is, for example, Valiant (1984, 2013), for which Leslie Valiant was awarded the Turing Award in 2010. Further research is nevertheless needed to improve interpretability. This also includes uncertainty quantification of patterns identified by an AI method, which heavily rely on statistical techniques. A tempting approach to achieve more interpretable AI methods is the use of auxiliary models. These are comparatively simple statistical models which, after adaptation of a deep learning approach, describe the most important patterns represented by the AI method and potentially can also be used to quantify uncertainty (Molnar 2019; Peltola 2018; Ribeiro et al. 2016a, b). In fact, as in computational and statistical learning theory (Györfi et al. 2002; Kearns and Vazirani 1994; Vapnik 1998), statistical methods and AI learning approaches can (and should) complement each other. Another important aspect is the model complexity which can, e.g., be captured by entropies (such as VC dimensions) or compression barriers (Langford 2005). These concepts as well as different forms of regularization (Tibshirani 1996; Wager et al. 2013; Zaremba et al. 2014), i.e. the restriction of the parameter space, allow to recognize or even to correct an overfitting of a learning procedure. Here, the application of complexity reducing concepts can be seen as a direct implementation of the Lex Parsimoniae principle and often increases the interpretability of resulting models (Ross et al. 2017; Tibshirani 1997). In fact, regularization and complexity reducing concepts are an integral part of many AI methods. However, they are also basic principles of modern statistics, which were already proposed before their introduction to AI. Examples are given in connection with empirical Bayesian or shrinkage methods (Röver and Friede 2020). In addition to that, AI and statistics have numerous concepts in common which give rise to an exchange of methods in these fields.

Furthermore, uncertainty aspects also apply to quality criteria (e.g., accuracy, sensitivity and specificity) of AI algorithms. The corresponding estimators are also random but their uncertainty is usually not quantified at all.

Statistics can help to increase the validity and interpretability of AI methods by providing contributions to the quantification of uncertainty. To achieve this, we can assume specific probabilistic and statistical models or dependency structures which allow comprehensive mathematical investigations (Athey et al. 2019; Bartlett et al. 2004; Devroye et al. 2013; Györfi et al. 2002; Scornet et al. 2015; Wager and Athey 2018; Ramosaj and Pauly 2019a), e.g., by investigating robustness properties, proving asymptotic consistency or (finite) error bounds. On the other hand this also includes the elaboration of (stochastic) simulation designs (Morris et al. 2019) and the specification of easy to interpret auxiliary statistical models. Finally, it allows for a detailed analysis of quality criteria of AI algorithms.

AI has been a growing research area for years, and its development will probably continue in the coming decades. In addition to ethical and legal problems, there are still many open questions regarding the collection and processing of data. Statistical methods must be considered as integral part of AI systems, from the formulation of the research questions, the development of the research design, through the analysis up to the interpretation of the results. Particularly in the field of methodological development, statistics can, e.g., serve as multiplier and strengthen the scientific exchange by establishing broad and strongly interconnected networks between users and developers.

In the context of clinical trials, statistics also provides guidelines for important aspects of trial design, data analysis and reporting. Many of these guidelines are currently being extended for AI applications, e.g. the TRIPOD statement (Collins et al. 2015; Collins and Moons 2019) or the CONSORT and SPIRIT guidelines (Liu et al. 2020; Rivera et al. 2020). Moreover, initiatives such as STRATOS (STRengthening Analytical Thinking for Observational Studies, https://​stratos-initiative.​org/​) aim to provide guidance for applied statisticians and other data analysts with varying levels of statistical education.

As a core element of AI, statistics is the natural partner for other disciplines in teaching, research and practice. Therefore, it is advisable to incorporate statistical aspects into AI teaching and to bridge the gap between the two disciplines. This begins with school education, where statistics and computer science should be integral elements of the curricula, and continues with higher education as well as professional development and training. By developing professional networks, participating methodologists can be brought together with users/experts to establish or maintain a continuous exchange between the disciplines. In addition to AI methods, these events should also cover the topics of data curation, management of data quality and data integration.

Statistics is a broad cross-scientific discipline. Statisticians provide knowledge and experience of all aspects of data evaluation: starting with the research question through design and analysis to the interpretation. In particular, the following contributions of statistics to the field of artificial intelligence can be summarized: With respect to some points raised in this paper, a few comments are in place. First, as mentioned in the introduction there is no unique definition of AI or ML according to the literature and distinguishing between the two is not easy. A broader consensus in the scientific community is necessary to facilitate common discussions. Second, as an anonymous referee commented, it might be helpful to distinguish between different frameworks concerning data and problems. The proposal is to distinguish between (a) problems and data with random or partly random aspects and (b) problems with a deterministic background such as graph theoretical structures or optimum configurations. While the first is a natural field of application for statistics, the second may also benefit from statistical approaches, e.g. concerning robustness or sensitivity. A related issue concerns the fact that the evaluation of AI methods must be seen in the context of the corresponding application. In life sciences and medicine we often assume the existence of some underlying ‘ground truth’ which needs to be estimated. Thus, modeling concepts such as bias or accuracy can be used for evaluation. In other areas such as economy or marketing, the idea rather is to derive a somewhat ‘useful’ or ‘effective’ strategy from the data. In such a situation, statistics can still be used for evaluation, for example by making predictions and comparing their accuracy with the observed data.

Another important aspect concerns the combination of data and results obtained from different studies. In evidence based medicine, systematic reviews and meta-analyses play a key role in combining results from multiple studies to give a quantitative summary of the literature. In contrast, meta-analysis methods to combine results from AI applications have not been developed yet. Initiatives to enable the sharing of data and models in AI include federated learning and software frameworks such as DataSHIELD (DataSHIELD 2018; Gaye et al. 2014), which enables remote and nondisclosive analysis of sensitive data, see also Bonofiglio et al. (2020). Thus, both fields could profit from an exchange of methods in this context.

The objective of statistics related to AI must be to facilitate or enable the interpretation of data. As Pearl puts it: ‘Data alone are hardly a science, regardless how big they get and how skillfully they are manipulated’ (Pearl 2018). What is important is the knowledge gained that will enable future interventions.