One wonders, fourthly, where are recorded all the prior distributions of beliefs which this theory requires investigators to articulate before doing research.  Surely someone must be writing them down, so that we consumers of science can know that our researchers are honest, and hold them to potential account.   That there is such a disconnect between what Bayesian theorists say researchers do and what those researchers demonstrably do should trouble anyone contemplating a choice of statistical paradigms, surely.   Finally, one wonders how a theory that requires non-zero probabilities be allocated to models of which the investigators have not yet heard or even which no one has yet articulated, for those models to be tested, passes muster at the statistical methodology corral.

To my mind, Bayesianism is a theory from some other world – infinite gambles, imagined prior distributions, models that disregard time or requirements for constructability,  unrealistic abstractions from actual scientific practice – not from our own.

So, how could the Bayesians make as much headway as they have these last six decades? Perhaps it is due to an inherent pragmatism of statisticians – using whatever techniques work, without much regard as to their underlying philosophy or incoherence therein.  Or perhaps the battle between the two schools of thought has simply been asymmetric:  the Bayesians being more determined to prevail (in my personal experience, to the point of cultism and personal vitriol) than the adherents of frequentism.  Greg Wilson’s 2001 PhD thesis explored this question, although without finding definitive answers.

Now,  Andrew Gelman and the indefatigable Cosma Shalizi have written a superb paper, entitled “Philosophy and the practice of Bayesian statistics”.  Their paper presents another possible reason for the rise of Bayesian methods:  that Bayesianism, when used in actual practice, is most often a form of hypothesis-testing, and thus not as untethered to reality as the pure theory would suggest.  Their abstract:

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science.

Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.

References:

Andrew Gelman and Cosma Rohilla Shalizi [2010]:  Philosophy and the practice of Bayesian statistics.  Available from Arxiv.  Blog post here.

Technorati Tags: hypothesis-testing, statistics, Bayesianism, frequentism, inductive inference, hypothetico-deductivism

Choosing a PhD program is one of the hardest decisions we can make. For a start, most of us only make this decision once in our lives, and so we have no prior personal experience to go on.

Second, the success or otherwise of a PhD depends a great deal on factors about which we have little advanced knowledge or control, including, for example:

• The relationship between the student and the supervisor. A PhD is usually awarded only after a student has undertaken some original research. In some programs, this must also be significant. The key point here is that the student has to do this, not the supervisor, and not the two of them together. If you have never done research before, then you will have a period of learning. A good supervisor should be helpful, particularly at the beginning, but eventually wean you off his or her help. 
• The relationship between the student and the subject-matter. In formal subjects, such as pure mathematics, research is primarily undertaken in the head of the researcher. In experimental subjects, much of the effort involved in research may be taken up with creating the apparatus or system on which the experiments are conducted. In engineering, much of the effort may be taken up with designing and building the artefact or system which is the object of the research.One of the great features of Artificial Intelligence (AI) at this particular time in its history is that there are not yet established rules and procedures for how research in AI should be undertaken. Hence, people in AI use a mix of: the deductive analysis of formal systems (as in pure mathematics), computational experiment and simulation (as in the physical sciences and computational economics), the creation of artefacts (as in engineering, music or art), personal introspection (reasoning about our own reasoning and behaviours, as in parts of philosophy), reasoning about the reasoning processes of others (as in so-called rational-actor theories in economics, game theory, or political science), social introspection (reasoning about the behaviour of groups with which we are acquainted, as in sociology, social psychology, or the study of organizational behaviour), and reflective narrative and dialog (as in anthropology or business strategy). Some researchers emphasize one approach over others, some use a mix of approaches. Not everyone has the skills or aptitude for each approach. If you attempt a PhD centered on simulation, for example, without good software programming and debugging skills, you will not be playing to your strengths. It may still be possible to complete the PhD, but only at the cost of great personal pain.In my experience, academics are remarkably unwilling to engage in discussion about HOW they do research. I do not know if this is because they fear that talking about their methods will frighten away their muse, or because, like most people in most professions, they do not reflect much on what they do. Of all disciplines, AI ought to have the most self-reflective practitioners, but I have not found this. 
• The relationship between the student and the school. Despite their claims to the contrary, Universities are not at all meritocratic. Having now had personal working experience in Government, in business and in University, I have to say that Universities are the most status-conscious of the three institutions, and the one where good, original ideas from low-status people are given the shortest-shrift, if they are heard at all. So be prepared to be ignored.If you are coming to a PhD straight from undergraduate studies, you will not find many changes in the way you are treated by academic or other staff. However, if you have any prior working experience at all, you will find life as a PhD student a great shock. You may have commanded empires, thousands may have quaked at your words, but this will count for absolutely nothing in a university. You will be treated as if you were a blank piece of paper, to be inscribed on by the faculty, and only rarely will you find anyone interested in what you may have done before enrolling in the PhD. I think part of the reason for this is that most academics — having no experience of the world beyond their walls — think that only their problems contain intellectual challenges, and look down on those in business and Government. How little they know!Related to this is the bias which most academics have for beliefs over actions. Perhaps it is a result of the nature of the modern research university where the culture is primarily a written one, rather than being verbal or tactile; in the main, written outputs (such as books and journal articles) are preferred over non-written outputs (such as developing complex software). Certainly, there are many important activities in modern society requiring great intelligence and advanced skills which are not, and could not be, taught through lectures and reading (for example: playing the piano; forecasting demand for high-tech products; managing software development projects). All of these activities are learnt on the job, not in formal education.Another part of the reason is that most universities, being state-funded or funded by generous endowments, do not face the ever-present threat of extinction which even large companies in most markets face. How else to explain the fact that Universities so often treat their next generation of leaders with apathy, disrespect and cynicism, in ways which no company would survive very long doing.

  A PhD is perhaps the last remnant of a feudal relationship in the modern world. The only way to deal with this, in my opinion, is to maintain your self-respect and self-esteem, despite the insults thrown at you (wittingly or not) by the system. Stand your ground, give no quarter, and believe in yourself.

Third, it is very hard to evaluate a decision to undertake a PhD. Because most of us only do one PhD in our lives, we have no control group to compare our PhD with another. Moreover, even after you have finished, and successfully obtained your PhD, you may not be able to tell whether it was a good program or not. It may have been a painful and frustrating exercise, but that may be true of both good and bad programs. The program may produce lots of prize-winning graduates, but that may be feature of the people attracted to enter it, rather than anything they received while doing the PhD.

Deciding to do a PhD and deciding which PhD program to enter are therefore decisions we make and carry-through under great uncertainty. In particular, prior to doing the PhD, you will not be in a position to know what will be your own reactions to the experience, what the possible outcomes will be, or your own valuations of these outcomes. (It is odd that classical decision theory – developed by academic economists – should be so useless for such a common and important decision. Yet another failing of economics!) The first thing you can do is talk to as many people as possible about their experiences as PhD students (both successful and failed), or as PhD supervisors, before you make your decision. Here are some guides which I have found useful, and you may gain something from them:

• David Chapman (Editor) [1988]: How to Do Research at the MIT AI Lab. AI Working Paper 316. MIT. 
• Alan Bundy, Ben du Boulay, Jim Howe and Gordon Plotkin [1985]: The Researcher’s Bible, a guide produced by AI and CS people at Edinburgh University. 
• Some guides produced by the Computer Science Department at Carnegie-Mellon University.

The second thing to do, before you start your PhD, is to list all the challenges you expect to encounter in the course of the program, and to identify possible reactions to these. Most PhD students get depressed at one or more points in their studies, often at the immense amount of reading they feel they have to do. To counter this depression, you need to identify strategies to deal with it, such as tackling some non-reading PhD activity (e.g., building a software simulator) or engaging in something not associated with your PhD (e.g., taking a holiday). Of course, you won’t know in advance all the challenges you are likely to face, nor the best strategies for surmounting or coping with them. But thinking about these in advance of starting forces you to reflect on the path you are embarking on. Thirdly, it is useful in my experience to keep a diary of your experiences, and of your reactions to them, as you proceed through the program. Writing a regular diary forces you to reflect on your experiences, and thereby distances you somewhat from them. I think it the best antidote to depression.

Some general advice I give to PhD students:

It is my belief that one crucial skill which a PhD student should acquire in the course of his or her degree is the ability to identify a feasible research problem. Therefore, I believe very strongly that the supervisor should not choose the problem for the student, but instead allow the student to identify a problem for him or herself. I realize that this is not the usual practice in all academic disciplines, especially mathematics, where the supervisor usually assigns a problem to each student. I think this practice condescending, and inappropriate in computer science and AI.Accordingly, as the problem may only be identified gradually, the precise details of the research may only emerge in the course of the PhD itself. Emergence is a phenomenon with which all reseachers in AI should be familiar. This means that the actual work undertaken during the PhD may appear to repeat on itself, or to diverge in new directions, or appear in other ways to be undirected. Nothing is undirected, if viewed from the right perspective. Part of the task of a PhD is to find the right perspective with which to view the work undertaken.

Research can be very frightening. In formal subjects such as computer science, we are trying to put together a jigsaw puzzle, but a puzzle where we do not know in advance what the picture is on the jigsaw. Also, the pieces are not given to us in advance — we usually have to find them, or even have to construct them ourselves. Moreover, once we complete the puzzle we may discover that the picture it displays is not the one we thought we were constructing. We may even find that our efforts result in a jigsaw without any picture at all. This is indeed scary, and I liken it to finding one’s way across a deep canyon one has never been in before in thick fog. Why do we do it? Well, partly because we imagine the view from the other side of the canyon is so beautiful, partly because we want to be first to reach the other side, and partly because the adrenalin rush as we stumble down and back up the canyon is addictive. Doing a PhD successfully involves finding that source of adrenalin and using it to motivate us through three hard years of mountaineering.

I view the literature search as a survey of a landscape: you want to find what’s in the landscape, and where it is. Most of the survey is simply so you know what’s where, and so that you can find it again, if you need to. Some of the material you will read will turn out to be extremely important to your research topic, but you won’t know this in advance of reading it, and you may not even know it until you are near the end of your PhD. Only when you come to final write-up will you be forced to identify, formally and precisely, what your research is really about, and so ideally your literature search should only be done at the end. But, of course, you need to do it at the beginning in order to know what is where. This tension is an example of activities which appear to be undirected (reading everything more than once), but which in reality are essential.

Try not to be depressed by all the reading in front of you at the beginning. If you persist through this, then by about 18 months or so after you start, you will awake one morning to find you now know what is important to your topic and what not. You will then find you need to do very little reading until you come near the end.

Finally, it seems customary in guidebooks for PhDs to have some statement about this being the best experience of one’s life, or about research being a noble and elevated calling. I think such statements are misleading. PhDs are a feudal anachronism, an example of Karl Marx’s definition of tradition being the accumulated errors of past generations. They are required in order to get a job as an academic, or as a researcher in many advanced research labs. They serve no purpose that I can see which would not be served by other, less humbling and less psychologically-intrusive means of learning how to do research. The best you can hope for, in my experience, is to find a supervisor and a topic with whom you are sympatico, and try your best to get the damn thing over with as soon as possible. Real life in a real world awaits you, after all.

If you have any comments on these notes, I would very much welcome hearing from you.

Some time back, I wrote about the painting of spirit-dreamtime maps by Australian aboriginal communities as proof of their relationship to specific places:  Only people with traditional rights to the specific place would have the necessary dreamtime knowledge needed to make the painting, an argument whose compelling force has been recognized by Australian courts.  These paintings are a form of map, showing (some of) the spirit relationships of the specific place.  The argument they make is a very interesting one, along the lines of: 

What I am saying is true, by virtue of the mere fact that I am saying it, since only someone having the truth would be able to make such an utterance (ie, the painting).

Another example of this type of argument is given by Rory Stewart, in his account of his walk across Afghanistan.   Stewart does not carry a paper map of the country he is walking through, lest he be thought a foreign spy (p. 211).   Instead, he learns and memorizes a list of the villages and their headmen, in the order he plans to walk through them.  Like the aboriginal dreamtime paintings, mere knowledge of this list provides proof of his right to be in the area.  Like the paintings, the list is a type of map of the territory, a different way of knowing.  And also like the paintings, possession of this knowledge leads others, when they learn of the possession, to act differently towards the possessor.  Here’s Stewart on his map (p. 213):

It was less accurate the further you were from the speaker’s home . . .  But I was able to add details from villages along the way, till I could chant the stages from memory.

Day one:  Commandant Maududi in Badgah.  Day two:  Abdul Rauf Ghafuri in Daulatyar.  Day three:  Bushire Khan in Sang-izard.  Day four:  Mir Ali Hussein Beg of Katlish.  Day five: Haji Nasir-i-Yazdani Beg of Qala-eNau.  Day six:  Seyyed Kerbalahi of Siar Chisme . . .

I recited and followed this song-of-the-places-in-between as a map.  I chanted it even after I had left the villages, using the list as credentials.  Almost everyone recognized the names, even from a hundred kilometres away.  Being able to chant it made me half belong:  it reassured hosts who were not sure whether to take me in and it suggested to anyone who thought of attacking me that I was linked to powerful names. (page 213) 

Because AI is (or should be) about ways of knowing and doing in the world, it therefore has close links to the social sciences, particularly anthropology, and to the humanities.

References:

Seymour Papert [1988]: One AI or Many? Daedalus, 117 (1) (Winter 1988):  1-14.

Rory Stewart [2004]: The Places in Between. London, UK:  Picador, pp. 211-214.

Technorati Tags: Seymour Papert, Artificial Intelligence, dreamtime, Rory Stewart

In the primordial ooze of Internet content several hundred million seconds ago (1993), fewer than 100 Web sites inhabited the planet. Early clans of information seekers hunted for data among the far larger populations of text-only Gopher sites and FTP file-sharing servers. This was the world in the years before Google.

Even in this primitive Internet world, the need for more accessible interfaces to growing data collections had already been recognized. The National Science Foundation led the multi-agency Digital Library Initiative (DLI) that, in 1994, made its first six awards. One of those awards supported a Stanford University project led by professors Hector Garcia-Molina and Terry Winograd.

None of the early DLI proposals – submitted before the World Wide Web experienced its Cambrian explosion – explicitly included research into the Web. However, by the time DLI funding began, the information landscape had changed.

In 1994, some of the first Web search tools crawled out of the Internet sea. Two Stanford students started Yahoo!, a manually constructed “table of contents” for Web sites. Other early search engines emerged, such as Lycos and WebCrawler, and began automatically indexing Web pages, focusing on keyword-based techniques to rank search results.

Around the same time, one of the graduate students funded under the NSF-supported DLI project at Stanford took an interest in the Web as a “collection.” The student was Larry Page.

Page uncovered the missing links, so to speak, in Web page ranking. His evolutionary leap was to recognize that the act of linking one page to another required conscious effort, which in turn was evidence of human judgment about the link’s destination. Individually, each link was a simple but effective tool. But collectively, millions of these links provided a key adaptation for the natural selection of search results.

Page was soon joined by Sergey Brin, another Stanford graduate student working on the DLI project. (Brin was supported by an NSF Graduate Student Fellowship.) Together, Page and Brin constructed an ambitious prototype in their Stanford student offices. The equipment for the prototype, called BackRub, was funded by the DLI project and other industrial contributions.

The prototype used well-established technology to crawl from page to page by following links. However, in addition to compiling a standard text index, the prototype also mapped out a vast family tree that reflected the Web links among pages.

To calculate rankings from this family tree, the pair developed the PageRank method. In short, the method ranks a particular Web page highly if many other highly ranked Web pages link to it. Those other page’s rankings, in turn, depend on the pages that link to them. Such logic could spiral out of control, but PageRank eventually stops because, as a rule, the more distantly related a page is, the less it contributes to the final rank of its descendants.

Page and Brin wrote an initial paper on their ideas and the theoretical underpinnings of PageRank and tested the fitness of the ranking approach on live Web data — initially a test set of 24 million pages. PageRank survives as one of the main components of today’s Google search service.

By late 1997, as the Dot-Com Era began to flourish, the BackRub approach proved to be sound, expandable and popular. By the end of the Early DLI Age in 1998, Page and Brin obtained funding that allowed them to move their growing hardware facility from the Stanford campus into a friend’s garage and to incorporate Google, Inc.

Technorati Tags: DARPA, Google, National Science Foundation

Academic publishers Springer have just released a new book on Argumentation in Artificial Intelligence.  From the blurb:

This volume is a systematic, expansive presentation of the major achievements in the intersection between two fields of inquiry: Argumentation Theory and Artificial Intelligence. Contributions from international researchers who have helped shape this dynamic area offer a progressive development of intuitions, ideas and techniques, from philosophical backgrounds, to abstract argument systems, to computing arguments, to the appearance of applications producing innovative results. Each chapter features extensive examples to ensure that readers develop the right intuitions before they move from one topic to another.

 In particular, the book exhibits an overview of key concepts in Argumentation Theory and of formal models of Argumentation in AI. After laying a strong foundation by covering the fundamentals of argumentation and formal argument modeling, the book expands its focus to more specialized topics, such as algorithmic issues, argumentation in multi-agent systems, and strategic aspects of argumentation. Finally, as a coda, the book explores some practical applications of argumentation in AI and applications of AI in argumentation.”

References:

Previous posts on argumentation can be found here.

Iyad Rahwan and Guillermo R. Simari (Editors) [2009]:  Argumentation in Artificial Intelligence.  Berlin, Germa ny Springer.

Technorati Tags: Argumentation, Artificial Intelligence, multi-agent systems

(Photo:  Gisella Somentino).