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Monthly Archives: December 2018

Interview on Machine Understanding

24 Monday Dec 2018

Posted by kbkorb in Bayesian networks, Causal Bayesian networks, Cognitive science

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Tags

AI, Bayesian networks, Foundations of AI, Understanding

Produced by Adam Ford:

If you are interested, some relevant references are:

  • On Bayesian networks: Korb, K. B., & Nicholson, A. E. (2010). Bayesian artificial intelligence. CRC press.
  • The Frame Problem in AI: Korb, K.B.The Frame Problem: An AI Fairy Tale Minds and Machines (1998) 8: 317.
  • Korb, K. B. (1995). Inductive learning and defeasible inference. Journal of Experimental & Theoretical Artificial Intelligence, 7(3), 291-324.
  • Korb, K. B., & Thompson, C. (1994). Primitive concept formation. In Intelligent Information Systems, 1994. Proceedings of the 1994 Second Australian and New Zealand Conference on (pp. 362-366). IEEE.
  • And there is Norman Fenton’s Bayes and the Law website, applying Bayesian nets to legal argument.

Post Hoc Ergo Propter Hoc, or Correlation Implies Causation

24 Monday Dec 2018

Posted by kbkorb in Causation, Cognitive science, Evidence, Inference

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#causality, #correlation, #fallacy, climate change, critical thinking, Informal Logic

Wikipedia confidently explains this in its first sentence for this entry: “Post hoc ergo propter hoc (Latin: “after this, therefore because of this”) is a logical fallacy that states ‘Since event Y followed event X, event Y must have been caused by event X.’” This so-called fallacy is curious for a number of reasons. Taken literally it is a fallacy that is almost never committed, at least relative to the opportunities to commit it. There are (literally, perhaps) uncountably many events succeeding other events where no one does, nor would, invoke causality. Tides followed by stock market changes, cloud formation followed by earthquakes, and so on and so on. People do attribute causality to successive events of course: bumping a glass causing it to spill, slipping on a kitchen floor followed by a bump to the head. In fact, that’s how as infants we learn to get about in the world. Generally speaking, it is not merely temporal proximity that leads us to infer a causal relation. Other factors, including spatial proximity and the ability to recreate the succession under some range of circumstances, figure prominently in our causal attributions.

Of course, people also make mistakes with this kind of inference. In the early 1980s AIDS was attributed by some specifically to homosexual behavior. The two were correlated in some western countries, but the attribution was more a matter of the ignorance of the earlier spread of the disease in Africa than of fallacious reasoning. Or, anti-vaxxers infer a causal relation between vaccines and autism. In that case, there is not even a correlation to be explained, but still the supposed conjunction of the two is meant to confer support to the causal claim. The mistake here is likely due to some array of cognitive problems, including confirmation bias and more generally conspiritorial reasoning (which I will address on another occasion). But mistakes with any type of inductive reasoning, which inference to a causal relation certainly is, are inevitable. If you simply must avoid making mistakes, become a mathematician (where, at least, you likely won’t publish them!). The very idea of fallacies is misbegotten: there are (almost) no kinds of inference which are faulty because of their logical form alone (see my “Bayesian Informal Logic and Fallacy”). What makes these examples of post hoc wrong is particular to the examples themselves, not their form.

The more general complaint hereabouts is that “correlation doesn’t imply causation”, and it is accordingly more commonly abused than the objection to post hoc reasoning. Any number of deniers have appealed to it as a supposed fallacy to evade objections to gun control or the anthropogenic origins of global warming. It’s well past time that methodologists should have put down this kind of cognitive crime.

This supposed disconnect between correlation and causation has been the orthodox statistician’s mantra at least since Sir Ronald Fisher (“If we are studying a phenomenon with no prior knowledge of its causal structure, then calculations of total or partial correlations will not advance us one step” [Fisher, Statistical Methods for Research Workers, 1925] – a statement thoroughly debunked by many decades thereafter of causal inference based on observational data alone). While there are more circumspect readings of this slogan than to proscribe any causal inference from evidence of correlation, that overly ambitious reading is quite common and does much harm. It is unsupportable by any statistical or methodological considerations.

The key to seeing through the appearance of sobriety in the mantra is Hans Reichenbach’s Principle of the Common Cause (in his The Direction of Time, 1956). Reichenbach argued that any correlation between A and B must be explained in one of three ways: the correlation is spurious and will disappear upon further examination; A and B are causally related, either as direct or indirect causes one of the other or as common effects of a common cause (or ancestor); or as the result of magic. The latter he ruled out as being contrary to science.

Of course, apparent associations are often spurious, the result of noise in measurement or small samples. The “crisis of replicability” widely discussed now in academic psychology is largely based upon tests of low power, i.e., small samples. If a correlation doesn’t exist, it doesn’t need to be explained.

It’s also true that an endurring correlation between A and B is often the result of some association other than A directly causing B. For example, B may directly cause A, or there may be a convoluted chain of causes between them. Or, again, they may have a common cause, directly or remotely. The latter case is often called “confounding” and dismissed as showing no causal relation between A and B. But it is confounding only if the common cause cannot be located (and held constant, for example) and what we really want to know, say, is how much any causal chain from A to B is explanatory of B’s state. Finding a common cause that explains the correlation between A and B is just as much a causal discovery as any other.

I do not wish to be taken as suggesting that causal inference is simple. There are many other complications and difficulties to causal inference. For example, selection biases, including self-selection biases, can and do muck up any number of experiments, leading to incorrect conclusions. But nowhere amongst such cases will you find biases operating which are not themselves part of the causal story. Human experimenters are very complex causal stories themselves, and as much subject to bias as anyone else. So, our causal inferences often go wrong. That’s probably one reason why replicability is taken seriously by most scientists; it is no reason at all to dismiss the search for causal understanding.

There is now a science of causal discovery applying these ideas for data analysis in computer programs, one that has become a highly successful subdiscipline of machine learning, at least since Glymour, Scheines, Spirtes and Kelly’s Discovering Causal Structure (1987). (Their Part I, by the way, is a magnificent debunking of the orthodox mantra.)

The general application of “correlation doesn’t imply causation” to dismiss causal attributions is an example of a little learning being a dangerous thing – also known as the Dunning-Kruger effect.

 

The Sixth Extinction: A Review

04 Tuesday Dec 2018

Posted by kbkorb in Review

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Tags

climate change, extinction, global warming

Elizabeth Kolbert’s The Sixth Extinction is a highly readable, discursive review of the state of the biosphere in the Anthropocene — i.e., now. It’s aimed at a general audience and entertains as much as it informs, relating a wide variety of anecdotes, mostly derived from Kolbert’s travels and investigations while writing this book. I think it a very worthwhile book, especially perhaps as a present for those in your life who are skeptical about global warming or science in general. Not that Kolbert is a scientist or pretends to be one, but it offers an outsiders’ view of a fair few scientists in action, chronicling the decline of many species.

Kolbert’s report is necessarily pessimistic about the general prospects for a healthy biosphere, given that the evidence of species endangerment and decline is all around and she has spent some years now documenting it. But she tries to be as optimistic as possible. She points out a variety of successes in evading or mitigating other “tragedies of the commons”, such as the banning of DDT after Rachel Carson’s warning that our springs risked going silent. Or the prominent case of the missing (well, smaller) ozone hole.

On matters that are contentious within science, Ms Kolbert aims for neutrality. For example, what killed off the megafauna — such as the marsupial lion in Australia, cave bears and saber tooth cats in America, mammoths and aurochs in Europe — that was widespread prior to the presence of homo sapiens? One school suggests that climate change, say, in the form of retreating ice sheets, was the culprit. She points out that doubts arising from the fact that the extinctions of the megafauna occurred at quite different times and, indeed, in each case shortly after the arrival of humans, militate against climate change as a sole cause. The main alternative is, of course, that these are the first extinctions due to human activity, so that the Sixth Extinction began well before the industrial age. Kolbert points out that advocates for climatic causation criticize the anthropogenic crowd for having fallen for the post hoc ergo propter hoc fallacy. But neutrality on this point is a mistake. While correlation doesn’t strictly imply direct causation, it does strictly imply direct-or-indirect causation: Hans Reichenbach in The Direction of Time made the compelling point that if there is an enduring correlation between event types (not some haphazard result of small samples and noise), then there is either a direct causal chain, a common cause, or an indirect causal chain that will explain the correlation. Everything else is magic, and science abhors magic. Given that the extinctions and the arrivals of humans fit like a hand in a glove, it is implausible that there is no causal relationship between them. As sane Bayesians (i.e., weighers of evidence) we must at a minimum consider it the leading hypothesis until evidence against it is discovered. Of course, the existence of one cause does not preclude another (even if it makes it less likely); that is, climatic changes may well have contributed to human-induced extinctions in some cases.

On a final point Kolbert again opts for neutrality: does the Sixth Extinction imply our own? Can we survive the removal of so many plants and animals that the Anthropecene should be counted as one of the Great Extinction events? Will humanity’s seemingly boundless technological creativity find us a collective escape route?

I find the enthusiasm of some futurologists for planetary escape a bit baffling. The crunch of Global Warming will be hitting civilization pretty hard within 50 years, judging by anything but the most extremely optimistic projections. The ability to deal directly with Global Warming, and the related phenomena of overutilization of earth’s resources to support around 10 billion people at an advanced economic level of activity, is possibly within our grasp, but it is very much in doubt that we will collectively grasp that option. The ability to terraform and make, say, Mars habitable in a long-term sustainable way is not within our grasp and is not in any near term prospect. Simply escaping from our own earthly crematorium is not (yet) an option. If Elon Musk succeeds in reaching Mars, he will almost certainly soon thereafter die there.

The situation on earth isn’t so dissimilar. If Global Warming leads to massive agricultural failure, the watery entombment of half the major cities on earth, unheard of droughts, floods and typhoons, resource wars and human migrations, the strain on the instruments and processes of civilization is reasonably likely to break them. If civilization comes undone, it will be impossible to avoid massive starvation and societal collapse. The dream of some to wait it out in a bunker and emerge to a new utopia thereafter is about as likely as the descendants of Musk building a new civilization on Mars. Whether the extinction of civilization entails the final extinction of humanity is a moot point. But human life after civilization will surely be nasty, brutish and short.

The best alternative is to put a stop to Global Warming now, and use the energy and human resources that effort saves to solve the remaining problems of resource depletion, habitat destruction and human overpopulation. That requires a sense of urgency and a collective will so far absent.

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