The relevance of causation in robotics: A review, categorization, and analysis

2.1 Philosophy

Causation is one of these concepts that continue to puzzle us, even after millennia of considerable intellectual effort. Viewpoints among scholars still vary widely, and there is not even an agreement that causation exists, let alone on what it is. Nevertheless, people use causal expressions daily, with a reasonably agreed upon meaning. Most people are also quite clear about the difference between causation and correlation, even if they not necessarily use these terms. As an example, let us imagine that the owner of an ice-cream shop observes the relation between electricity consumption and ice-cream sales during a hot summer month. It turns out that sales goes up during days with high electricity consumption and vise versa. Does that mean that the owner should switch on all lights in the shop in order to increase sales? Most of us would probably agree that this would be a bad idea and that the reason for the observed correlation between ice-cream and electricity consumption is a third variable, the outdoor temperature, which makes people buy more ice-cream, but also increases the electricity consumption, since the A/C has to work harder during hot days.

Not surprisingly, philosophers have not settled with such intuitive notions of causation. In the remainder of this subsection, we will merely scratch the surface of the substantial body of work on the nature of causation, focusing on philosophical theories that are relevant for the continued analysis and discussion.

Woodward [10] identifies two main kinds of philosophical views on what causation is. The difference-making views focus on how causes affect what happens in the world, such that the state of the world differs depending on whether the cause occurs or not. For example, a robot vacuum cleaner starting up in the middle of the night might be regarded as the cause of the owner waking up. The other kind of views are denoted as the geometrical-mechanical theories and focus on the idea that causes somehow are connected to their effects, often through transmission of a “force” from cause to effect. A typical example is a billiard ball hitting another ball, thereby stopping while the other ball starts moving due to the “transfer” of energy or momentum.

As is most often the case with theories on causation, compelling counterexamples for both views are easily formulated. The billiard ball example can be easily questioned by referring to fundamental physics principles of relativity of motion. One ball moving toward a second is equivalent to the second moving toward the first, but according to the geometrical–mechanical view different balls will be assigned as the cause in the two cases. A classical example, challenging the difference-making view, is a firing squad, where ten soldiers shoot a victim who dies. However, for each one of the soldiers can be said that he or she did not cause the death, since the outcome would have been the same had the soldier not fired the gun. Each individual soldier did not make a difference. On the other hand, there are lots of examples of events that make a difference, but are not commonly regarded as causes. Big bang, certainly made several differences, but it is usually not referred as a cause to things happening now, billions of years later. A more recent example is given in ref. [11, p. 127], where is it noted that having a liver is a necessary, albeit not sufficient, condition for having cirrhosis. Therefor, having a liver is a difference-maker for having that disease, even if is does not make sense to say that having a liver caused the disease.

This approach of reasoning about necessary and sufficient conditions was refined by Mackie [12,13], who argued that what we normally mean when we say that something is a cause is that it is “an Insufficient but Non-redundant part of a condition which is itself Unnecessary but Sufficient for the result.” Such a condition is called an INUS condition. As an example, consider a house that catches fire after a short-circuit occurred in the house, with flammable material nearby. The short-circuit is said to be the cause of the fire because: (a) it is part of a true condition “short-circuit and presence of flammable material”), (b) the short-circuit is an insufficient (since flammable material is also required) but necessary (i.e., non-redundant) (since the condition is a conjunction) part of the condition, (c) the condition is unnecessary since it can be replaced by other conditions (for example, “lightning and presence of flammable material,” and (d) the condition is sufficient since it, on its own, will result in the house catching fire.

David Lewis formulated a related theory of causation, based on counterfactual dependencies [14]. An effect is said to counterfactually depend on a cause; just in case if the cause had not occurred, the effect would not have occurred. Furthermore, A is said to be the cause of B if there is a causal chain of counterfactual dependencies linking A with B . The idea of counterfactual reasoning became both popular and influential (even if both Mackie’s and Lewis’s theories, of course, have been challenged by counterexamples).

A certain frustration of failing to define what “causation is” can be sensed in emotional statements by several prominent scientists. Bertrand Russell, who engaged heavily in the debate, concluded in 1913: “The law of causation, … is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.” [15].^[1]

By this we move on to how causation has been, and is, treated in statistics and computer science.

2.2 Statistics and computer science

We start by summarizing the relation between statistics and causation: probabilities alone cannot distinguish between cause and effect. This fact was realized by statisticians early on, but with unfortunate consequences. Karl Pearson, English mathematician and one of the founders of mathematical statistics, dismissed causation altogether in his book from 1911 [17], where he called it “a fetish amidst the inscrutable arcana of modern science.” Still, as Judea Pearl remarks [18, p. 412], statistics is unable to express simple statements such as mud does not cause rain. There have, however, been several attempts to formulate causation in probabilistic terms. In line with the previously mentioned view of causation as a difference-maker, a cause C can be seen as something that raises the probability for an event E to occur. In its simplest form this can be expressed as

While this at first may look like a promising definition of a cause–effect relation, it has several problems [19]. First of all, it is symmetric in the sense that equation (1) is equivalent with

Hence, if C is the cause of E , then E is also the cause of C , which goes against most intuitive and formal notions of causation. Second, it does not differentiate between genuine causation and spurious correlation. Returning to previously mentioned ice-cream example, electricity consumption would pass as the cause of increased sales according to equation (1), with the probabilities estimated from observations. The formal reason for this incorrect inference is that a “lurking variable,” the outdoor temperature, is a common cause or confounding variable to both electricity consumption and sales.^[2]

Attempts to repair the definition have been made, for example, by conditioning on background variables:

For the ice-cream case, letting K be the outdoor temperature would avoid the false conclusion that electricity consumption ( C ) causes higher sales ( E ). For example, equation (3) would probably not hold for observations with K = 2 5 ° C (or any other fixed value).^[3] However, giving a general answer to which variables to include in K turns out to be far from trivial. Nancy Cartwright proposed that K should include all “causally relevant factors” [21], which may be correct but unfortunately does not provide a way to determine what these factors are. More recent approaches are suggested and discussed in ref. [22].

A simple and intuitive way to test whether electricity consumption really causes higher sales would be to try it out in reality, by some days switching on all lamps and electrical devices in the shop and observing how sales is affected. To be sure about the result, the process should of course be repeated at several random occasions. This approach has been formalized in the technique Randomized Controlled Trials (RCT), which was popularized by Ronald Fisher in 1925 [23]. RCT has ever since been a standard tool to find and test causal relations. The important word “randomized” stands for the intervention, where we some days deliberately increase electricity consumption. If this is done at random, the values of the background variables K become equally distributed between the intervened and not intervened cases [24], even if we do not know what the variables in K are (see Section 3.3.4 for a discussion on the role of RCTs in robotics). It is important to note that an RCT estimates causality at population-level and computes the average causal effect, also referred to as the average treatment effect. This may have very little to say about causality at the individual level. Consider, as an example, a medication that makes all men healthier, but all women sicker. An RCT with equally many men and women, would estimate the average treatment effect to zero, even if the medication causally affected every person in the experiment.

One of the two major frameworks for causal inference is the Neyman–Rubin Causal Model [25,26], where the causal effect of a binary variable C is defined as the difference between the potential outcome if C occurred and the potential outcome if C did not occur. However, for a specific instance, only one potential outcome can be observed, depending on whether C occurred or not. This general problem, that we cannot observe counter factuals, is called the fundamental problem of causal inference [27, p. 947]. The second major framework was popularized by Pearl with the do-calculus [28] (for a shorter introduction see e.g., ref. [29]). Using this formalism, we say that C causes E if [30]:

The do-operator encapsulates the notion of intervention, and while P ( E ∣ C ) describes what value E took when a certain value of C was observed, P ( E ∣ d o ( C ) ) describes what values E would take if C was set to a certain value. The “trick” with introducing the do-operator is that the whole discussion about what causation “ís” gets circumvented by an axiomatic approach, in a similar way as done in for example Euclidean geometry, number theory, and probability theory.

The causal relations between a number of variables can be conveniently represented by a Causal Bayesian Network, which is a Directed Acyclic Graph (DAG), where the nodes represent variables, and the directed links (i.e., arrows) represent causal dependencies going from parent nodes to children nodes. Hence, a parent node “causes” its child node to take a specific value. Each node has an associated table with conditional probabilities given their parents. Given a DAG, the do-calculus enables inference of answers to causal questions about relations between the variables in the DAG. The DAG may be created in several ways. Conducting RCTs is one alternative but is often expensive, time-consuming, and sometimes even impossible. However, the graph structure may also be learned from observational data through causal discovery [7, pp. 142–154], [31], for example with the LiNGAM [32] algorithm and the PC and FCI algorithms [33], or from a formal structural causal model [29] based on prior knowledge about the problem domain. It should be noted that the directions of the causal links in the DAG cannot be learned from observational data alone without additional domain information or assumptions. For example, the LiNGAM algorithm builds on the assumption that there are no unobserved confounding variables.

To facilitate practical usage, several researchers and companies offer implementations of algorithms for statistical causal learning and inference. Microsoft has launched a software library DoWhy, with a programmatic interface for several causal inference methods (https://github.com/Microsoft/dowhy). The Center for Causal Discovery offers several tools, including the Tetrad causal discovery tool (https://www.ccd.pitt.edu/tools/). Elias Bareinboim offers Fusion, a tool based on Pearl’s book [30] (http://bit.ly/36qUz4y). CausalWorld is a benchmark for causal structure and transfer learning in a simulated robotic manipulation environment [34] (https://sites.google.com/view/causal-world). Links to other software packages can be found in ref. [31], and new software is of course constantly being developed.

2.3 Cognitive psychology

Causal reasoning was, until about three decades ago, absent in cognitive psychology research. One reason may have been the general scepticism about causation in philosophy and statistics (see Section 2.1), with the result that earlier work in psychology was mostly based on correlations and associations. Reasons for this can be traced back to, at least, Hume’s work in the 18th century (for an analysis of this influence, see e.g., ref. [35]).

One example of how causality enters cognitive psychology research is causal perception [36], which is the immediate perception of certain observed sequences of events as causal. This effect appears automatically, and is often hard to resist. For example, if the lights in the house go out exactly when you close a door, you may perceive that you caused the lights to go out, even if you know that it is totally incorrect. However, in many cases, the perception of a causal relation is correct and valuable, and causal perception can be observed already in 6-month-old infants [36, p. 4].

A historically influential model of humans causal reasoning is the Rescorla–Wagner model [37], which incrementally estimates the association between a conditioned and unconditioned stimuli based on observations. This and similar associative models were for a long time quite successful in modeling human behavior, but studies also indicated that human causal reasoning sometimes cannot be explained with covariation information alone [1]. A step toward causal theories were probabilistic theories such as the Δ P model [38,39], aiming at modeling how humans learn the strength between a potential cause C and an effect E . The causal power Δ P is given by

where the probabilities may be estimated from observed frequency data. The Δ P model follows the previously described philosophical view of causes being difference makers (see Section 2.1). It can be seen as a variant of equation (1) and hence suffers from the same shortcomings of symmetry and common causes.

To clarify the distinction between correlation and causation: equation (5) quantifies the correlation between E and C . The two variables may very well be causally connected, but this fact cannot be established from Δ P . The reason is that both E and C may have a third variable as common cause, which may be manifested as a strong correlation, and a large Δ P . For the example given in Section 2.1, the consumption of ice-cream and electricity would have a large Δ P , even though there is no causal connection between the two variables.

The power PC theory [39] builds on the Δ P model and aims at modeling causal power from covariation data complemented by background knowledge. Some studies indicate that the model conforms with certain aspects of human causal reasoning. However, neither the Δ P model nor the power PC theory is seen as fully adequate to explain human causal induction [40].

Algorithms for causal inference using machine learning (see Section 2.4) have also been considered as models of human causal reasoning. Several experiments indicate that people distinguish between observations and interventions in the same fashion as Casual Bayesian Networks (see Section 2.2) [41,42,43]. One general concern is that these algorithms require large amounts of training data, while humans often manage to learn causal relations based on just a few observations. In cases with more than a few variables, it becomes impossible for humans to estimate all required covariations, and experiments show how humans, beside covariation data, use mechanism knowledge to draw causal conclusions. Studies also show that people use prior knowledge about temporal delays of different mechanisms [44]. For example, if I suddenly become nauseous, I may assume that a drug I took 2 hours ago was the cause, and not the food I ate 1 minute ago (example from ref. [1]), thereby reducing the number of covariations I need to consider. People also use cues such as spatial contiguity (the assumption that an effect is spatially close to its cause), temporal order (the assumption that a cause cannot occur before its effect) [45], and other temporal cues [46,47]. Waldmann [1,35] argues that humans employ such so called knowledge-based causal induction rather than Bayesian approaches based on statistical inference. Gärdenfors [48] supports this view and further argues that human causal cognition is based on an understanding of forces involved in events, and he also provides guidelines for implementations of such causal reasoning in robots.

2.4 Causation in machine learning

In machine learning, the recent progress in deep learning has been achieved without any explicit notion of causation. The results from applications in speech recognition [50], natural language translation, and image processing [51] can be seen as the victory of data over models, as claimed already in 2009 by Halevy, Norvig, and Pereira in their article The Unreasonable Effectiveness of Data [52]. A common view seems to have been, and to a large extent still is, that most problems can be solved by providing sufficient amounts of data to sufficiently large computers running sufficiently large neural networks. As an extreme example, the current state-of-the-art model for language processing, GPT-3 [53], was trained with almost 500 billion tokens and contains 175 billion parameters. Given that the size of the model is of the same order of magnitude as the modeled data, the comparison with a giant lookup table is not far-fetched. Nevertheless, when GPT-3 was introduced, it outperformed previous state-of-the-art on a large range of natural language processing tasks, including translation, question-answering, and generation of news articles.

Despite the unquestionable success of such purely data-driven approaches, critical voices have expressed concerns about their true “íntelligence.” Judea Pearl, one of the pioneers in AI and causal reasoning, argues that deep learning is stuck on the level of associations, essentially doing advanced curve fitting [8,54] and clustering, and only modeling correlations in data. As such it works for predictions, answering questions such as “What will the outcome of the election be?” However, it cannot answer causal questions, like “Would we have won with a different financial policy?,” or “How can we make more people vote for us?” The former question requires counterfactual reasoning about possible alternatives to events that have already occurred. An answer to the latter question provides an action for control, such as “By lowering the interest rates.” Both counterfactuality and control are out of reach for methods using observational data only.

The reliance on predictive algorithms in machine learning, combined with a dramatic increase in the use of machine learning for real-world tasks, is for these reasons seen a serious problem [55].

Léon Bottou, a leading researcher in deep learning, points to the fundamental problem of machine learning “recklessly absorbing all the correlations found in training data” [56]. This leads to sensitivity to spurious correlations stemming from data bias,^[4] and a failure in identifying causal relations, for example, between features and classification of objects in images. Examples of such failures, and an argumentation for a general need to incorporate causation in models of human-like intelligence can, for example, be found in ref. [4]. The specific connection between causality and generalization is analyzed in ref. [58].

Important steps have also been taken to incorporate both causal inference and causal reasoning in machine learning, in general (see refs. [7,59] for overviews), and deep learning, in particular [4,60, 61,62,63]. Two specific techniques for supervised learning will be described in more detail. The Invariant Risk Minimization (IRM) paradigm [56] addresses the observed problems with “out-of-distribution” generalization in machine learning. To train neural networks that also function with previously unseen data, the training data are first divided into environments. The loss function is extended by a term penalizing performance differences between environments. This promotes networks that are invariant over environments, in a way that is fundamentally linked to causation. The Invariant Causal Prediction (ICP) approach [64] is a technique to identify features that are causally connected to a target variable (as opposed to only being connected through correlation). Combinations of features are used to build separate models for data from several different environments. Combinations that work well over all environments are likely to contain features that cause the target variable. The intersection of several such successful combinations are regarded as the overall causally relevant features.

3.1 Causation for sense–plan–act

Our categorization comprises eight categories of robot causal cognition at the sense–plan–act level. The underlying causal mechanisms are illustrated in Figure 1, with a robot, a human, and the (rest of the) world, affecting themselves and each other causally, illustrated by the arrows, and with numbers referring to the corresponding categories. The categories are illustrated in more detail in Figure 2. An interacting human’s internal causal processes are included since they are important for the robot’s causal reasoning. The top row shows the human Mind initiating (i.e., causing) Motor Forces (e.g., muscle activations) that result in Motor Actions, (e.g., limb motions). Motor Actions may in turn cause World Effects since the human is situated in the environment. The robot’s mind is modeled in a similar way, with additional World Effects added to model non-animate causal relations. For both the human and the robot, the term “mind” denotes the mechanism that, for one reason or another, causes Motor Forces. In a deterministic world, the activation of such a mechanism, of course, also has a cause. The usage of the word “mind,” with its associations to free will and non-determinism, indicates that we here regard the mind as “the ultimate cause.”

Figure 1

Causal mechanisms between a robot, a human, and the (rest of the) world. The arrows go from cause to effect, and the numbers refer to the corresponding category further described in the text.

Figure 2

The functions of the eight categories of robot causal cognition. Categories 1–3 refer to learning of causal relations (bold arrows). Categories 4–6 refer to inference of causes (thin solid arrows) related to an interacting human, while categories 7–8 refer to how the robot decides how to act.

In the figure, all causal relations are illustrated by thick arrows. Inference of causes is illustrated by thin arrows pointing toward the inferred entity.

Categories 1–3 have to do with Causal Learning, i.e., how a robot learns causal relations involving itself, interacting humans, and the world. Categories 4–6 have to do with the important cases of inference of causes related to an interacting human. Categories 7–8 have to do with how the robot decides how to act, with more or less sophisticated usage of causal reasoning.

3.2 Discussion on the categorization

Below we summarize the eight identified causal cognition categories. For ease of comparison, the most similar grade in the categorization of human causal cognition in Section 2.3.1 is given within parentheses. The related technique listed for each category refers to a causal concept or technique from robotics or one of the other reviewed scientific fields. As such they should only be seen as examples.

1. Sensory Motor Learning (1) – Related technique: Motor Babbling

2. Learning How the Robot Affects the World (-) – Related technique: Interventions

3. Learning About the Causal World (6) – Related technique: Experiments

4. Dyadic Causal Understanding (2) – Related technique: Mirror Neurons

5. Mind Reading (3,5) – Related technique: Intent Recognition

6. Detached Mind Reading (4) – Related technique: Statistical Causal Inference

7. Planning (-) – Related technique: Planning Algorithms

8. Causal Innovation (7) – Related technique: Counterfactual Reasoning

It is interesting to note that all seven grades of human causal cognition can be associated with existing techniques within robotics. In the other direction, categories 2 and 7 have no direct correspondence in the grades. However, it can be argued that category 2 is included in grade 1 and category 7 in grade 7.

We found earlier work in robotics that addressed all eight categories. However, for all but category 5, we found very few papers, in particular papers where the connections to causal concepts and reasoning are explicitly mentioned.

3.3 Causation beyond sense–plan–act

Robotics is more than designing functionality for robots to sense, plan, and act, and causation also plays an important role in these other areas and aspects of robotics. A few examples are given below, even if the list undoubtedly could have been made much longer.