Causal Learning: Psychology, Philosophy, and Computation
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However, people may also learn that an effect is only generated when an individual cause is present see, Lucas and Griffiths Waldmann showed that for extensional properties e. A causal framework theory is the assumption that observable causal relations among particular events or objects tokens are instantiations of more general causal laws connecting types of events or objects Kemp, Goodman, and Tenenbaum Such a framework theory entails that events or objects of the same type i generate the same effects with the same likelihood, and ii share the same features.
We will describe a respective HBM in the next section of the paper. Note that none of these highly abstract theories includes any assumptions about the entities being causally related or the nature of the causal relation. Theoretical knowledge, however, could also be domain-specific. It may include assumptions about the causally relevant entities, their properties and potential relations Griffiths and Tenenbaum Research in developmental psychology has shown that infants and young children already have domain-specific expectations about causal entities and their relations Carey For example, while children expect temporal and spatial contiguity to be necessary for causation in a mechanical system, they accept causation at a distance when the agents are persons.
Finally, theoretical assumptions may concern the nature of the causal mechanisms. Many studies have shown that people draw different inferences from the same observations depending on whether they know about a potential mechanism underlying the observed relation Ahn, Kalish, Medin, and Gelman For example, a moderate statistical relation was seen as good evidence for causation when a plausible mechanism was known, while this was not the case when no mechanism could be envisioned Koslowski Developmental research found that children being familiar with causation via electric wiring did not require spatio-temporal contiguity to infer causality while younger children did Bullock, Gelman, and Baillargeon Research also shows that people have a hard time to induce causal models, when they have very little abstract knowledge e.
In general, performance in causal induction increases substantially, when people can observe temporal relations or can intervene Lagnado and Sloman Research on the control of complex systems shows that participants often gain very limited knowledge about the underlying causal structure despite extensive learning experience Osman HBMs can explain this finding as the available evidence in these studies was often compatible with numerous causal hypotheses, and participants normally lacked domain specific knowledge see, Hagmayer, Meder, Osman, Mangold, and Lagnado , for a more detailed discussion.
In sum, there are many forms of abstract theoretical causal knowledge that may guide causal induction. This abstract knowledge can be domain-general or domain-specific. A growing body of evidence shows that such abstract causal knowledge affects causal induction. Causal relations may hold between particular objects or event tokens, but also between types of causes and effects. Causal relations on a type level have been called causal laws Schulz, Goodman, Tenenbaum, and Jenkins Causal laws specify the structure and strength of the causal relations between types of causes and types of effects.
To induce causal laws, both categories of causes and effects as well as the causal relations between them have to be learnt. HBMs allow us to model these inferences Kemp et al. Figure 2 provides an illustration. On the most abstract level, there is a framework theory assuming that there are causal relations between types of causes and effects without specifying what these types are. There is also the assumption that tokens of the same type share certain features. On the level of causal laws are causal relations between cause and effect types.
Representations of causal relations between types and their features can also be found on this level. Causal models are characterised by causal relations between a type and a token. Data are observations of single causal relations between token causes and token effects and observations of the features of cause and effect tokens.
On the Importance of Causal Taxonomy
Hierarchical Bayesian model of category learning and causal induction. Some research has been conducted investigating the induction of categories during causal learning. Lien and Cheng presented participants with objects having different colours and sizes which caused an effect with a certain probability.
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By manipulating the probabilities, they were able to show that participants induced categories of objects e. Crucially, participants used the new categories to predict the effect of objects they had not seen before. Kemp et al. Waldmann, Hagmayer and colleagues Waldmann and Hagmayer ; Waldmann, Meder, von Sydow, and Hagmayer extended this research and showed that both causes and effects are spontaneously categorised according to the causal relations they are part of, and that these categories are transferred to later learning episodes even when they do not allow for optimal predictions.
This transfer, however, seems to depend on people's abstract causal knowledge Hagmayer, Meder, von Sydow, and Waldmann Categories of causes are only used to predict novel effects if these new effects are plausible effects of the type of cause i. Abstract structural knowledge also seems to be important. Categories based on one causal relation were transferred to a second causal relation only if the second relation was connected to the first relation forming a continuous causal chain Hagmayer et al.
Otherwise people preferred to induce separate categories for each causal relation. Developmental research shows that even pre-schoolers use the causal effects to categorise objects Gopnik and Sobel and that these categories may even override perceptual differences between objects Nazzi and Gopnik Later studies indicate that pre-schoolers even have the ability to abstract causal laws Schulz et al.
Children in these studies categorised coloured blocks with respect to their capacity to generate certain sounds when touching other types of blocks. Crucially, children used the observation of one effect to categorise an object and then use the category to make predictions about another effect. HBMs can account for this transfer effect Schulz et al. The problem of causal induction is a challenge for computational and cognitive theories of causal reasoning. HBMs provide a formal framework which allows us to model causal induction and inferences as well as the induction of causal laws.
As the overview provided in the previous sections shows, HBMs have been very successful in describing the inductive behaviour of children and adults see also Chater and Oaksford, Importantly, HBMs explain how causal induction based on very limited data is possible when abstract causal knowledge is available to constrain the set of hypotheses.
Second, HBMs explain how types of causes and effects can be inferred from the observation of particular objects and events while causal relations on the type level are induced. Other theories have difficulties to account for rapid induction of causal models, causal categories and causal laws Waldmann and Hagmayer, in press.
Data-driven accounts assuming that categories and causal relations are learnt from observations would require huge amounts of learning data and, therefore, fail to explain the findings. Nevertheless, HBMs have a number of limitations. First, they strongly rely on the existence of previous abstract causal knowledge without providing any explanation about the origin of this knowledge. At least some constraints seem to be necessary to enable causal induction.
Hence, some innate knowledge has to be assumed but see Goodman, Ullman, and Tenenbaum , although this knowledge might be revised based on the given observations Griffiths and Tenenbaum The causal principles described above are likely candidates. To gain more insights, not only developmental research is needed, but also cross-cultural comparisons.
Recent research has shown that western, educated forms of reasoning may or may not conform to reasoning in other cultural groups Henrich, Heine, and Norenzayan Currently, rather little is known about abstract causal beliefs in other cultures Beller, Bender, and Song More research is clearly needed in this regard. A second open question is how to account for domain-specific abstract knowledge. Obviously, the causal assumptions underlying intuitive theories of physics, biology and psychology are rather distinct Carey It still needs to be shown that HBMs can explain the learning of these differences.
A second point of critique is that there is growing evidence that people's representations of causal models do not conform to causal Bayes nets. A pivotal assumption of causal Bayes nets is the so-called Markov assumption, which informally states that each variable in a causal structure is independent of all variables other than its direct and indirect effects once the state of its direct causes are known. This assumption has a number of implications which can be tested experimentally.
For example, consider a model in which a common cause generates two effects. The Markov condition states that the probability of the second effect is the same when the common cause is present regardless of whether the first effect is present or absent. Respective empirical studies did not support the predictions of causal Bayes nets Rehder and Burnett The same is true for the prediction of a single effect from a cause Fernbach, Darlow, and Sloman Counter to the implications of causal Bayes nets, participants neglected the influence of other causes on the effect in their predictions.
Third, HBMs and causal Bayes nets are formal accounts that do not aim to describe the actual cognitive processes people employ, although some researchers seem to assume that people use some form of Bayesian updating in causal inferences Gopnik et al. It has been proposed that people use simpler cognitive heuristics whose performance approaches a Bayesian model Sloman ; Fernbach and Sloman For example, Mayrhofer and Waldmann devised a simple heuristic that may underlie causal induction.
This heuristic simply counts how often a potential cause fails to bring about an effect. Causal relations that minimise that score are assumed to hold. Simulation studies showed that this heuristic is extremely powerful and is likely to find the causal structure underlying a set of data, given some plausible assumptions.
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Cue-based models of causal induction have also been devised Einhorn and Hogarth ; Lagnado et al. These models assume that people rely on cues to causality rather than engaging in complex hypothesis testing. For example, Fernbach and Sloman assume that people rely on local computations and generate hypotheses about causal structure from single observations considering cues like temporal order, co-occurrence, and consequences of interventions.
Cue-based models, however, also have to assume that people have intuitive abstract knowledge, which allows them to identify the cues indicating causal relatedness. Cognitive process models of causal induction have limitations, too.
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They cannot determine optimal inferences under given conditions. Thus, they do not distinguish whether cases of inductive failure are due to insufficient data or heuristic processing. Taken together, the discussion points out that HBMs and cognitive process models are both needed to understand how causal induction is possible and how people proceed, given a certain set of data and initial knowledge.
HBMs show what the optimal inference would be and cognitive process models how these inferences can be realised, given our cognitive limitations. Therefore, we think that that both kinds of models are crucial to explain people's causal reasoning and to create artificial intelligences. Ahn, W. Perception or cognition?
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In this paper, we employ the techniques of formal learning theory and model theory to explore the reliable inference of theories from data containing alternating quantifiers. We obtain a hierarchy of inductive problems depending on the quantifier prefix complexity of t… Read more Convergent realists desire scientific methods that converge reliably to informative, true theories over a wide range of theoretical possibilities.
We obtain a hierarchy of inductive problems depending on the quantifier prefix complexity of the formulas that constitute the data, and we provide bounds relating the quantifier prefix complexity of the data to the quantifier prefix complexity of the theories that can be reliably inferred from such data without background knowledge. We also examine the question whether there are theories with mixed quantifiers that can be reliably inferred with closed, universal formulas in the data, but not without. There is a popular view that the alleged meaning shifts resulting from scientific revolutions are somehow incompatible with the formulation of general norms for scientific inquiry.
We construct methods that can be shown to be maximally reliable at getting to the truth when the truth changes in response to the state of the scientist or his society. Scientific Revolutions. Why you'll never know whether Roger Penrose is a computer with Kevin Kelly. Convergence to the truth and nothing but the truth with Kevin T. One construal of convergent realism is that for each clear question, scientific inquiry eventually answers it.
In this paper we adapt the techniques of formal learning theory to determine in a precise manner the circumstances under which this ideal is achievable. In particular, we define two criteria of convergence to the truth on the basis of evidence. The first, which we call EA convergence, demands that the theorist converge to the complete truth "all at once".
The second, which we call AE co… Read more One construal of convergent realism is that for each clear question, scientific inquiry eventually answers it. The second, which we call AE convergence, demands only that for every sentence in the theorist's language, there is a time at which the theorist settles the status of the sentence. The relative difficulties of these criteria are compared for effective and ineffective agents. We then examine in detail how the enrichment of an agent's hypothesis language makes the task of converging to the truth more difficult.
In particular, we parametrize first-order languages by predicate and function symbol arity, presence or absence of identity, and quantifier prefix complexity. For nearly each choice of values of these parameters, we determine the senses in which effective and ineffective agents can converge to the complete truth on an arbitrary structure for the language.
Finally, we sketch directions in which our learning theoretic setting can be generalized or made more realistic. Scientific Truth Machine Learning. The first holistic revolution: alternative medicine in the nineteenth century with James C. Whorton and D. Wade Savage eds. Scientific Change, Misc Confirmation. AI is philosophy In James H. Fetzer ed. The Nature of Artificial Intelligence. What revisions does bootstrap testing need? A reply with John Earman. Nouns Philosophy of Cognitive Science. Philosophy of Psychology Philosophy of Cognitive Science.
Drawing substantive conclusions from linear causal models that perform acceptably on statistical tests is unreasonable if it is not known how alternatives fare on these same tests. We describe a computer program, TETRAD, that helps to search rapidly for plausible alternatives to a given causal structure. The program is based on principles from statistics, graph theory, philosophy of science, and artificial intelligence. We describe these principles, discuss how TETRAD employs them, and argue tha… Read more Drawing substantive conclusions from linear causal models that perform acceptably on statistical tests is unreasonable if it is not known how alternatives fare on these same tests.
Causal Modeling. Philosophers may even be puzzled as to what the fuss is all about. My guess is that the sorts of complaints philosophical readers are likely to make about Learner's paper are more the result of style than substance. The substance is very important. Econometrics Empirical Testing in Economics. The theory of your dreams In R. Laudan eds. Value Theory. Space-time and synonymy with Peter Spirtes. In "The Epistemology of Geometry" Glymour proposed a necessary structural condition for the synonymy of two space-time theories.
David Zaret has recently challenged this proposal, by arguing that Newtonian gravitational theory with a flat, non-dynamic connection FNGT is intuitively synonymous with versions of the theory using a curved dynamical connection CNGT , even though these two theories fail to satisfy Glymour's proposed necessary condition for synonymy. Zaret allowed that if FNGT and CNGT were not equally well bootstrap tested by the relevant phenomena, the two theories would in fact not be synonymous.
He argued, however, that when electrodynamic phenomena are considered, the two theories are equally well tested. We further show that the two extensions of FNGT and CNGT which are equally well tested when electrodynamic phenomena are considered and which could be considered intuitively synonymous not only satisfy Glymour's original proposed necessary condition for the synonymy of space-time theories, they satisfy a plausible stronger condition as well.
Internal Realism. Sigmund Freud. Nearly all accounts of the genesis of special relativity unhesitatingly assume that the theory was worked out in a roughly five week period following the discovery of the relativity of simultaneity. Not only is there no direct evidence for this common presupposition, there are numerous considerations which militate against it.
The evidence suggests it is far more reasonable that Einstein was already in possession of the Lorentz and field transformations, that he had applied these to the dynamics… Read more Nearly all accounts of the genesis of special relativity unhesitatingly assume that the theory was worked out in a roughly five week period following the discovery of the relativity of simultaneity. The evidence suggests it is far more reasonable that Einstein was already in possession of the Lorentz and field transformations, that he had applied these to the dynamics of the electron, and that portions of the paper had actually been drafted well before the epistemological analysis of time.
Physics of Time. Theory and Evidence with Isaac Levi.
Value Theory, Miscellaneous. The Joumal 0f Philosophy, Vol. Applications of Probability. The gravitational red shift as a test of general relativity: History and analysis with John Earman. General Relativity. Earman and John J. Aspects of Time. Foundations of Space-Time Theories with J. Earman and J. Lost in the tensors: Einstein's struggles with covariance principles — with John Earman. Space and Time Science, Logic, and Mathematics. Epistemological Sources. Relativity theorists, for example, are unanimous in the judgment that measurements of the gravitational red shift do not test the field equations of general relativity; psychoanalysts sometimes complain that experimental tests of Freudian theory are at best tests of rather peripheral hypotheses; astronomers do not regard observations of the positions of a single planet as a … Read more S CIENTISTS often claim that an experiment or observation tests certain hypotheses within a complex theory but not others.
Relativity theorists, for example, are unanimous in the judgment that measurements of the gravitational red shift do not test the field equations of general relativity; psychoanalysts sometimes complain that experimental tests of Freudian theory are at best tests of rather peripheral hypotheses; astronomers do not regard observations of the positions of a single planet as a test of Kepler's third law, even though those observations may test Kepler's first and second laws. Observations are regarded as relevant to some hypotheses in a theory but not relevant to others in that same theory.
There is another kind of scientific judgment that may or may not be related to such judgments of relevance: determinations of the accuracy of the predictions of some theories are not held to provide tests of those theories, or, at least, positive results are not held to support or confirm the theories in question.
There are, for example, special relativistic theories of gravity that predict the same phenomena as does general relativity, yet the theories are regarded as.. Evidence, Misc. If quanta had logic with Michael Friedman. Topology General Relativity.