Artificial Intelligence?

The subject of ‘Artificial Intelligence’ (AI) has long provided ample scope for long and inconclusive debates. Wikipedia seems to have settled on a view, that we may take as straw-man:

Every aspect of learning or any other feature of intelligence can be so precisely described that a machine can be made to simulate it. [Dartmouth Conference, 1956] The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds. [John Searle’s straw-man hypothesis]

Readers of my blog will realise that I agree with Searle that his hypothesis is wrong, but for different reasons. It seems to me that mainstream AI (mAI) is about being able to take instruction. This is a part of learning, but by no means all. Thus – I claim – mAI is about a sub-set of intelligence. In many organisational settings it may be that sub-set which the organisation values. It may even be that an AI that ‘thought for itself’ would be a danger. For example, in old discussions about whether or not some type of AI could ever act as a G.P. (General Practitioner – first line doctor) the underlying issue has been whether G.P.s ‘should’ think for themselves, or just apply their trained responses. My own experience is that sometimes G.P.s doubt the applicability of what they have been taught, and that sometimes this is ‘a good thing’. In effect, we sometimes want to train people, or otherwise arrange for them to react in predictable ways, as if they were machines. mAI can create better machines, and thus has many key roles to play. But between mAI and ‘superhuman intelligence’  there seems to be an important gap: the kind of intelligence that makes us human. Can machines display such intelligence? (Can people, in organisations that treat them like machines?)

One successful mainstream approach to AI is to work with probabilities, such a P(A|B) (‘the probability of A given B’), making extensive use of Bayes’ rule, and such an approach is sometimes thought to be ‘logical’, ‘mathematical, ‘statistical’ and ‘scientific’. But, mathematically, we can generalise the approach by taking account of some context, C, using Jack Good’s notation P(A|B:C) (‘the probability of A given B, in the context C’). AI that is explicitly or implicitly statistical is more successful when it operates within a definite fixed context, C, for which the appropriate probabilities are (at least approximately) well-defined and stable. For example, training within an organisation will typically seek to enable staff (or machines) to characterise their job sufficiently well for it to become routine. In practice ‘AI’-based machines often show a little intelligence beyond that described above: they will monitor the situation and ‘raise an exception’ when the situation is too far outside what it ‘expects’. But this just points to the need for a superior intelligence to resolve the situation. Here I present some thoughts.

When we state ‘P(A|B)=p’ we are often not just asserting the probability relationship: it is usually implicit that ‘B’ is the appropriate condition to consider if we are interested in ‘A’. Contemporary mAI usually takes the conditions a given, and computes ‘target’ probabilities from given probabilities. Whilst this requires a kind of intelligence, it seems to me that humans will sometimes also revise the conditions being considered, and this requires a different type of intelligence (not just the ability to apply Bayes’ rule). For example, astronomers who refine the value of relevant parameters are displaying some intelligence and are ‘doing science’, but those first in the field, who determined which parameters are relevant employed a different kind of intelligence and were doing a different kind of science. What we need, at least, is an appropriate way of interpreting and computing ‘probability’ to support this enhanced intelligence.

The notions of Whitehead, Keynes, Russell, Turing and Good seem to me a good start, albeit they need explaining better – hence this blog. Maybe an example is economics. The notion of probability routinely used would be appropriate if we were certain about some fundamental assumptions. But are we? At least we should realise that it is not logical to attempt to justify those assumptions by reasoning using concepts that implicitly rely on them.

Dave Marsay

Traffic bunching

In heavy traffic, such as on motorways in rush-hour, there is often oscillation in speed and there can even be mysterious ’emergent’ halts. The use of variable speed limits can result in everyone getting along a given stretch of road quicker.

Soros (worth reading) has written an article that suggests that this is all to do with the humanity and ‘thinking’ of the drivers, and that something similar is the case for economic and financial booms and busts. This might seem to indicate that ‘mathematical models’ were a part of our problems, not solutions. So I suggest the following thought experiment:

Suppose a huge number of  identical driverless cars with deterministic control functions all try to go along the same road, seeking to optimise performance in terms of ‘progress’ and fuel economy. Will they necessarily succeed, or might there be some ‘tragedy of the commons’ that can only be resolved by some overall regulation? What are the critical factors? Is the nature of the ‘brains’ one of them?

Are these problems the preserve of psychologists, or does mathematics have anything useful to say?

Dave Marsay

Risks to scientists from mis-predictions

The recent conviction of six seismologists and a public official for reassuring the public about the risk of an earthquake when there turned out to be one raises many issues, mostly legal, but I want to focus on the scientific aspects, specifically the assessment and communication of uncertainty.

A recent paper by O’Hagan  notes that there is “wide recognition that the appropriate representation for expert judgements of uncertainty is as a probability distribution for the unknown quantity of interest …”.  This conflicts with UK best practice, as described by Spiegelhalter at understanding uncertainty. My own views have been formed by experience of potential and actual crises where evaluation of uncertainty played a key role.

From a mathematical perspective, probability theory is a well-grounded theory depending on certain axioms. There are plausible arguments that these axioms are often satisfied, but these arguments are empirical and hence should be considered at best as scientific rather than mathematical or ‘universally true’.  O’Hagan’s arguments, for example, start from the assumption that uncertainty is nothing but a number, ignoring Spiegelhalter’s ‘Knightian uncertainty‘.

Thus, it seems to me, that where there are rare critical decisions with a lack of evidence to support a belief in the axioms, one should recognize the attendant non-probabilistic uncertainty, and that failure to do so is a serious error, meriting some censure. In practice, one needs relevant guidance such as the UK is developing, interpreted for specific areas such as seismology. This should provide both guidance (such as that at understanding uncertainty) to scientists and material to be used in communicating risk to the public, preferably with some legal status. But what should such guidance be? Spiegelhalter’s is a good start, but needs developing.

My own view is that one should have standard techniques that can put reasonable bounds on probabilities, so that one has something that is relatively well peer-reviewed, ‘authorised’ and ‘scientific’ to inform critical decisions. But in applying any methods one should recognize any assumptions that have been made to support the use of those methods, and highlight them. Thus one may say that according to the usual methods, ‘the probability is p’, but that there are various named factors that lead you to suppose that the ‘true risk’ may be significantly higher (or lower). But is this enough?

Some involved in crisis management have noted that scientists generally seem to underestimate risk. If so, then even the above approach (and the similar approach of understanding uncertainty) could tend to understate risk. So do scientists tend to understate the risks pertaining to crises, and why?

It seems to me that one cannot be definitive about this, since there are, from a statistical perspective – thankfully – very few crises or even near-crises. But my impression is that could be something in it. Why?

As at Aquila, human and organisational factors seem to play a role, so that some answers seem to need more justification that others. Any ‘standard techniques’ would need take account of these tendancies. For example, I have often said that the key to good advice is to have a good customer, who desires an adequate answer – whatever it is – who fully appreciates the dangers of misunderstanding arising, and is prepared to invest the time in ensuring adequate communication. This often requires debate and perhaps role-playing, prior to any crisis. This was not achieved at Aquila. But is even this enough?

Here I speculate even more. In my own work, it seems to me that where a quantity such as P(A|B) is required and scientists/statisticians only have a good estimate of P(A|B’) for some B’ that is more general than B, then P(A|B’) will be taken as ‘the scientific’ estimate for P(A|B). This is so common that it seems to be a ‘rule of pragmatic inference’, albeit one that seems to be unsupported by the kind of arguments that O’Hagan supports. My own experience is that it can seriously underestimate P(A|B).

The facts of the Aquila case are not clear to me, but I suppose that the scientists made their assessment based on the best available scientific data. To put it another way, they would not have taken account of ad-hoc observations, such as amateur observations of radon gas fluctuations. Part of the Aquila problem seems to be that the amateur observations provided a warning which the population were led to discount on the basis of ‘scientific’ analysis. More generally, in a crisis, one often has a conflict between a scientific analysis based on sound data and non-scientific views verging on divination. How should these diverse views inform the overall assessment?

In most cases one can make a reasonable scientific analysis based on sound data and ‘authorised assumptions’, taking account of recognized factors. I think that one should always strive to do so, and to communicate the results. But if that is all that one does then one is inevitably ignoring the particulars of the case, which may substantially increase the risk. One may also want to take a broader decision-theoretic view. For example, if the peaks in radon gas levels were unusual then taking them as a portent might be prudent, even in the absence of any relevant theory. The only reason for not doing so would be if the underlying mechanisms were well understood and the gas levels were known to be simply consequent on the scientific data, thus providing no additional information. Such an approach is particularly indicated where – as I think is the case in seismology – even the best scientific analysis has a poor track record.

The bottom line, then, is that I think that one should always provide ‘the best scientific analysis’ in the sense of an analysis that gives a numeric probability (or probability range etc) but one needs to establish a best practice that takes a broader view of the issue in question, and in particular the limitations and potential biases of ‘best practice’.

The O’Hagan paper quoted at the start says – of conventional probability theory – that  “Alternative, but similarly compelling, axiomatic or rational arguments do not appear to have been advanced for other ways of representing uncertainty.” This overlooks Boole, Keynes , Russell and Good, for example. It may be timely to reconsider the adequacy of the conventional assumptions. It might also be that ‘best scientific practice’ needs to be adapted to cope with messy real-world situations. Aquila was not a laboratory.

See Also

My notes on uncertainty and on current debates.

Dave Marsay

Assessing and Communicating Risks and Uncertainty

David Spielgelhalter Assessing and Communicating Risks and Uncertainty Science in Parliament vol 69, no. 2, pp. 21-26. This is part of the IMA’s Mathematics Matters: A Crucial Contribution to the Country’s Economy.

This starts with a Harvard study showing that “a daily portion of red meat was associated with an increase in the annual risk of death by 13% over the period of the study”. Does this mean, as the Daily Express claimed, that “10% of all deaths could be avoided”?

David S uses ‘survival analysis’ to show that “a 40 year-old  man who eats a quarter-pound burger for his working lunch each day can expect, on average, to live to 79, while his mate who avoids the burger can expect to live to 80.” He goes on: “over a lifetime habit, each daily portion of red meat is associated with about 30 minutes off your life expectancy .. ” (my emphasis.)

As a mathematician advising politicians and other decision-makers, I would not be comfortable that policy-makers understood this, and would act appropriately. They might, for example, assume that we should all be discouraged from eating too much red meat.

Even some numerate colleagues with some exposure to statistics might, I think, suppose that their life expectancy was being reduced by eating red meat. But all that is being said is that if a random person were selected from the population as a whole then – knowing nothing about them – a statistician would ‘expect’ them to have a shorter life if they eat red meat. But every actual individual ‘you’ has a family history and many by 40 will have had cholesterol tests. It is not clear what the relevance to them is of the statistician’s ‘averaged’ figures.

Generally speaking, statistics gathered for one set of factors cannot be used to draw precise conclusions about  other sets of factors, much less about individuals. David S’s previous advice at Don’t Know, Can’t Know applies. In my experience, it is not safe to assume that the audience will appreciate these finer points. All that I would take from the Harvard study is that if you eat red meat most days it might be a good idea to consult your doctor. I would also hope that there was research going on into the factors in the apparent dangers.

See Also

I would appreciate a link to the original study.

Dave Marsay

NRC’s Assessing … Complex Models

Committee on Mathematical Foundations of Verification, Validation, and Uncertainty Quantification Board on Mathematical Sciences and Their Applications Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification (US) NRC, 2012

The team were tasked to “examine practices for VVUQ of large-scale computational simulations”. Such simulations are complicated. The title seems misleading in using the term ‘complex’. The summary seems like a reasonable consensus summary of the state of the art in its focus area, and of research directions, with no surprises. But the main body does provide some ammunition for those who seek to emphasise deeper uncertainty issues, considering mathematics beyond computation.

Summary

Principles

Highlighted principles include:

    1. A validation assessment is well defined only in terms of specified quantities of interest (QOIs) and the accuracy needed for the intended use of the model.
    2. A validation assessment provides direct information about model accuracy only in the domain of applicability that is “covered” by the physical observations employed in the assessment.

Comments

The notion of a model here would be something like ‘all swans are white’. The first principle suggests that we need tolerance for what is regarded as ‘white’. The second principle suggests that if we have only considered British swans, we should restrict the domain of applicability of the model.

In effect, the model is being set within a justification, much as the conclusion of a mathematical theorem is linked to axioms by the proof. This is contrary to much school science practice, which simply teaches models: we need to understand the (empirical) theory. Typically, when we read ‘all swans are white’ we should understand that it really only means ‘all British swans are white-ish’.

Swans are relatively simple. The only problem is our limited observations of them. Economics, for example, is more complex. The quantities of interest are controversial, as are the relevant observations. Such complex situations seem beyond the intended scope of this report.

Research Topics

  1. Development of methods that help to define the “domain of applicability” of a model, including methods that help quantify the notions of near neighbors, interpolative predictions, and extrapolative predictions.
  2. Development of methods to assess model discrepancy and other sources of uncertainty in the case of rare events, especially when validation data do not include such events.

Comments

These topics are easier if one has an overarching theory of which the model is a specialisation, whose parameters are to be determined. In such cases the ‘domain of applicability’ could be based on an established classifying schema, and uncertainty could be probabilistic, drawing on established probabilistic models. The situation is more challenging, with broader uncertainties, where there is no such ruling theory, as in climate science.

Recommendations

  1. An effective VVUQ [verification, validation and uncertainty quantification] education should encourage students to confront and reflect on the ways that knowledge is acquired, used, and updated.
  2. The elements of probabilistic thinking, physical-systems modeling, and numerical methods and computing should become standard parts of the respective core curricula for scientists, engineers, and statisticians.

Comments

Most engineers and statisticians will be working pragmatically, assuming some ruling theory that guides their work. This report seems most suitable for them. Ideally, scientists acting as science advisors would also be working in such a way. However, surprises do happen, and scientists working on science should be actively doubting any supposed ruling theory. Thus it is sometimes vital to know the difference between a situation where an agreed theory should be regarded as, for example, ‘fit for government work’, and where it is not, particularly where extremes of complexity or uncertainty call for a more principled approach. In such cases it is not obvious that uncertainty can be quantified. For example, how does one put a number on ‘all swans are white’ when one has not been outside Britain?

As well as using mathematics to work out the implications of a ruling theory in a particular case, one needs to be able to use different mathematics to work out the implications of a particular case for theory.

Introduction

This cites Savage,  but in his terms it is implicitly addressing complicated but ‘small’ worlds rather than more complex ‘large’ ones, such as that of interest to climate science.

Sources of Uncertainty and Error

The general issue is whether formal validation of models of complex systems is actually feasible. This issue is both philosophical and practical and is discussed in greater depth in, for example, McWilliams (2007), Oreskes et al. (1994), and Stainforth et al. (2007).

There is a need to make decisions … before a complete UQ analysis will be available. … This does not mean that UQ can be ignored but rather that decisions need to be made in the face of only partial knowledge of the uncertainties involved. The “science” of these kinds of decisions is still evolving, and the various versions of decision analysis are certainly relevant.

Comment

 It seems that not all uncertainty is quantifiable, and that one needs to be able to make decisions in the face of such uncertainties.

In the case of ‘all swans are white’ the uncertainty arises because we have only looked in Britain. It is clear what can be done about this, even if we have no basis for assigning a number.

In the case of economics, even if we have a dominant theory we may be uncertainty because, for example, it has only been validated against the British economy for the last 10 years. We might not be able to put a number on the uncertainty, but it might be wise to look for more general theories, covering a broader range of countries and times, and then see how our dominant theory is situated within the broader theory. This might give us more confidence in some conclusions from the theory, even if we cannot assign a number. (One also needs to consider alternative theories.)

Model Validation and Prediction

Comparison with reality

In simple settings validation could be accomplished by directly comparing model results to physical measurements for the QOI  …

Findings

  1. Mathematical considerations alone cannot address the appropriateness of a model prediction in a new, untested setting. Quantifying uncertainties and assessing their reliability for a prediction require both statistical  and subject-matter reasoning.
  2. The idea of a domain of applicability is helpful for communicating the conditions for which predictions (with uncertainty) can be trusted. However, the mathematical foundations have not been established for defining such a domain or its boundaries.

Comment

I take the view that a situation that can be treated classically is not complex, only at most complicated. Complex situations may always contain elements that are surprising to us. Hence bullet 1 applies to complex situations too. The responsibility for dealing with complexities seems to be shifted from the mathematicians to the subject matter experts (SMEs). But if one is dealing with a new ‘setting’ one is dealing with dynamic complexity, of the kind that would be a crisis if the potential impact were serious. In such situations it may not be obvious which subject is the relevant one, or there may be more than one vital subject. SMEs may be unused to coping with complexity or with collaboration under crisis or near-crisis conditions. For example, climate science might need not only climatologists but also experts in dealing with uncertainty.

My view is that sometimes one can only assess the relevance and reliability of a model in a particular situation, that one needs particular experts in this, and that mathematics can help – but it is a different mathematics.

Next Steps in Practice, Research, and Education for Verification, Validation, and Uncertainty Quantification

 For validation, “domain of applicability” is recognized as an important concept, but how one defines this domain remains an open question. For predictions, characterizing how a model differs from reality, particularly in extrapolative regimes, is a pressing need. … advances in linking a model to reality will likely broaden the domain of applicability and improve confidence in extrapolative prediction.

Comment

As Keynes pointed out, in some complex situations one can only meaningfully predict in the short-term. Thus in early 2008 economic predictions were not in error, as short-term predictions. It is just that the uncertain long-term arrived. What is needed, therefore, is some long-term forecasting ability. This cannot be a prediction, in the sense of having a probability distribution, but it might be an effective anticipation, just as one might have anticipated that there were non-white swans in foreign parts. Different mathematics is needed.

My Summary

The report focusses on the complicatedness of the models. But I find it hard to think of a situation where one needs a complicated model and the actual situation is not complex. Usually, for example, the situation is ‘reflexive’ because the model is going to be used to inform interaction with the world, which will change it. Thus, the problem as I see it is how to model a situation that is uncertain and possibly complex. While the report does give some pointers it does not develop them.

The common sense view of modelling is that a model is based on observations. In fact – as the report notes – it tends to be based on observations plus assumptions, which are refined into a model, often iteratively. But the report seems to suppose that one’s initial assumptions will be ‘true’. But one can only say that the model fits one’s observations, not that it will continue to fit all possible observations, unless one can be sure that the situation is very constrained. That is, one cannot say that a scientific theory is unconditionally and absolutely true, but only ‘true to’ ones observations and assumptions.

The report is thus mainly for those who have a mature set of assumptions which they wish to refine, not those who expect the unexpected. It does briefly mention ‘rare events’, but it sees these as outliers on a probability distribution whereas I would see these more as challenging assumptions.

See Also

The better nature blog provides a view of science that is complimentary to this report.

My notes on science and uncertainty.

Dave Marsay

Harris’s Free Will

This is a review of reviews of Sam Harris’s Free Will. I haven’t read the actual book. (One of Harris’s supporters says that I have no choice but to read the book: but I am not so sure.) 

New Scientist

The New Scientist has a review which says:

“We either live in a deterministic universe where the future is set, or an indeterminate one where thoughts and actions happen at random. Neither is compatible with free will.”

But why are these the only options? Harris is quoted as saying:

“You can do what you decide to do, but you cannot decide what you will decide to do.”

But what, then, is the point? 

Meissler

This is a sympathetic review. He quotes:

“Why didn’t I decide to drink a glass of juice (rather than water). The thought never occurred to me. Am I free to do that which does not occur to me to do? Of course not. And there is no way I can influence my desires–for what tools of influence would I use? Other desires? To say that I would have done otherwise had I wanted to is simply to say that I would have been in a different universe had I lived in a different universe.”

I would call such acts ‘habitual’ and often executed ‘on autopilot’, like much of driving. But does all of driving involve such ‘decisions’? Does all of life?

The next quote is:

“What I will do next, and why, remains, at bottom, a mystery–one that is fully determined by the prior state of the universe and the laws of nature (including the contributions of chance).”

This is certainly a wide-spread belief, but not one that I feel free to accept at face-value. Why? Is there any possibility of any kind of proof of this belief, or anything like it, or even a faintly convincing argument? It is stated that the actions of a person are determined by their atoms (presumable as configured into molecules etc.). But is this really true? 

Sam Harris

In his blog, Harris focusses on the ‘moral’ implications of free-will and the need for an ‘illusion of free-will’. But if we rely on a false belief, aren’t we motivated to be cynical about ‘scientific reason’? Or at least, Harris’s version of it? But do not the language and methods of science and Harris assume what Harris asserts, and thus aren’t science and Harris unable to prove their own assumptions?

See Also

An article on critical phenomena argues that they cannot be understood from a classical ‘scientific’ viewpoint, thus undermining Harris’ assertions, especially those quoted by the friendly atheist. Briefly, we are not just a mechanical assemblage of atoms.

Summary

Harris’s views seem reasonable for the type of ‘decisions’ that fill Harris’s ‘life’, and it does seem to be the case that the physical world leaves little space for free will. But there may be a critical difference between ‘little’ and ‘none’, a possibility that Harris appears preprogrammed not to address. But are the relatively automatable kinds of decisions that Harris considers all there is to his life? Is his life really like a computer simulation of life?

Addenda

Geopolicratus suggests that populations with an agricultural heritage are more institutionalised than those with a nomad heritage. If so, then those with an agricultural heritage might well be more disposed to believe things that suggest that there is no free will, since the two kinds of lives call for quite different kinds of decision making. Plato’s Republic, anyone? 

Dave Marsay

The End of a Physics Worldview (Kauffman)

Thought provoking, as usual. This video goes beyond his previous work, but in the same direction. His point is that it is a mistake to think of ecologies and economies as if they resembled the typical world of Physics. A previous written version is at npr, followed by a later development.

He builds on Kant’s notion of wholes, noting (as Kant did before him) that the existence of such wholes is inconsistent with classical notions of causality.  He ties this in to biological examples. This complements Prigogine, who did a similar job for modern Physics.

Kauffman is critical of mathematics and ‘mathematization’, but seems unaware of the mathematics of Keynes and Whitehead. Kauffman’s view seems the same as that due to Bergson and Smuts, which in the late 1920s defined ‘modern science’. To me the problem behind the financial crash lies not in science or mathematics or even in economics, but in the brute fact that politicians and financiers were wedded to a pre-modern (pre-Kantian) view of economics and mathematics. Kauffman’s work may help enlighten them on the need, but not on the potential role for modern mathematics.

Kauffman notes that at any one time there are ‘adjacent possibles’ and that in the near future they may come to pass, and that – conceptually – one could associate a probability distribution with these possibilities. But as new possibilities come to pass new adjacent possibilities arise. Kauffman supposes that it is not possible to know what these are, and hence one cannot have a probability distribution, much of information theory makes no sense, and one cannot reason effectively. The challenge, then, is to discover how we do, in fact, reason.

Kauffman does not distinguish between short and long run. If we do so then we see that if we know the adjacent possible then our conventional reasoning is appropriate in the short-term, and Kauffman’s concerns are really about the long-term: beyond the point at which we can see the potential possibles that may arise. To this extent, at least, Kauffman’s post-modern vision seems little different from the modern vision of the 1920s and 30s, before it was trivialized.

Dave Marsay