Tuesday, April 26, 2005

Inference in the Midst of Ignorance

An amazon.com reviewer -- Lyndon S Hibbard -- said of Richard O. Duda, Peter E. Hart & David G. Stork, Pattern Classification (2nd ed., 2000),
Chapter 9 is a particularly interesting review of the recent machine learning research making the point that, absent knowledge of a problem's specific domain, no one classifier is better that any other.
This point, it seems to me, has interesting implications for matters such as handwriting identification -- and also for the question of the nature of uncertain factual inference and statistical inference in general. No? But cf.(?) Judea Pearl, who maintains that all interesting inference involves causality.

Well, I will have to buy the book by Duda et al.

Pattern Recognition, Bayesianism, Fuzzy Logic, Fingerprints etc.

Question: What if anything does the use of pattern recognition to match, e.g., fingerprint specimens have to say about the meaning or interpretation of classifications such as "reasonable and customary care" in legal rules or standards?

To get a flavor of some of the many problems involved in pattern recognition and to see discussion of a variety of possible methods to attack those problems, see (most of us are better-advised to skim) Sonka, [Notes and Slides for] Pattern Recognition Class

A Real Fuzzy (Fuzzified) More-or-Less Actual Fingerprint

See Umut Uludag & Anil Jane, Fuzzy Fingerprint Vault

Intuitive Introduction to Fuzzy Logic, with Examples

See Bart Kosko & Satoru Isaka, Fuzzy Logic

Titillating extracts:

Specimen 1: "When mathematicians lack specific algorithms that dictate how a system should respond to inputs, fuzzy logic can control or describe the system by using "commonsense" rules that refer to indefinite quantities. No known mathematical model can back up a truck-and-trailer rig from a parking lot to a loading dock when the vehicle starts from a random spot. Both humans and fuzzy systems can perform this nonlinear guidance task by using practical but imprecise rules such as 'If the trailer turns a little to the left, then turn it a little to the right.'"

Specimen 2: "Applications for fuzzy logic extend beyond control systems. Recent theorems show that in principle fuzzy logic can be used to model any continuous system, be it based in engineering or physics or biology or economics."

Specimen 3: "At the heart of the difference between classical and fuzzy logic is something Aristotle called the law of the excluded middle. In standard set theory, an object either does or does not belong to a set. There is no middle ground : the number five belongs fully to the set of odd numbers and not at all to the set of even numbers. In such bivalent sets, an object cannot belong to both a set and its complement set or to neither of the sets. This principle preserves the structure of logic and avoids the contradiction of an object that both is and is not a thing at the same time.
Sets that are fuzzy, or multivalent, break the law of the excluded middle- to some degree. Items belong only partially to a fuzzy set. They may also belong to more than one set."

Specimen 4: "A few fuzzy systems manage information rather than devices. With fuzzy logic rules, the Japanese conglomerate Omron oversees five medical data bases in a health management system for large firms. The fuzzy systems use 500 rules to diagnose the health of some 10,000 patients and to draw up personalized plans to help them prevent disease, stay fit and reduce stress."

Zadeh, Fuzzy Sets, Soft Computing, Precisiation, and the Law

Law teachers have not yet come to terms with the conceptual revolution that Professor Lotfi Zadeh launched in 1965 with the publication of his truly seminal and pathbreaking paper, Fuzzy Sets, 8 Information Control pp. 338-353.
  • I was told by a reputable source that this paper is the most-cited scholarly paper of all time.
  • Although it is understandable that law teachers (at least in the occidental world) have yet to wrestle seriously with Zadeh's revolutionary approach -- indeed, it is arguable that even most reputable logicians, mathematicians, and probability theorists have not yet done so in an adequate way --, the time for excuses is running out. It is now time that law teachers grapple with Zadeh's approach to uncertainty; failing that, it is time that they inform themselves of some of the essentials of Zadeh's approach to uncertainty; and, failing even that, it is, at least, high time that U.S. law teachers support a serious effort by the US legal academy to explore the uses of Zadeh's family of theories for law and in the study of law.

    Alas, being at best an amateurish autodidact in mathematics, logic, probability, and related fields, I am ill-equipped to suggest an appropriate starting point for people who wish to learn about soft computing (this is a convenient general label for the family of theories that interest Zadeh) but have no knowledge of set theory or probability theory. However, I suspect that one good starting point for law teachers who do have some familiarity with logic, set theory, and probability might be the latest iteration of Zadeh's recent paper, Toward a Generalized Theory of Uncertainty(GTU) - An Outline (January 20, 2005). If you approach this (detailed outline of a) paper with an open mind -- perhaps with an Eastern or Japanese mind --, you may find many important concepts in this paper, concepts that, in any event, should have particular resonance for law teachers who regularly wrestle with certain forms of uncertainty in law, forms of uncertainty that are often not appreciated by non-lawyers.

    If you already have a good feel for Zadeh's general approach and if you would like a less lengthy introduction to his general theory of uncertainty, you might find it profitable to skim a recent exchange of views on the UAI list about "cointensive precisiation." Two of the posts are by Professor Zadeh; one post is by Tod Levitt (a co-founder of the Association for Uncertainty in Artificial Intelligence); and I contributed a post about some forms of uncertainty that (I think) regularly recur in law. The thread starts here.

    When reading about Zadeh's theories or his papers, it is wise to abandon intellectual and cultural chauvinism. Zadeh's theories generally seem strange to occidental theorists when such theorists first encounter them. But Zadeh's general approach ought not to seem so terribly alien (even initially) to legal theorists, who ought to have, by virtue of their familiarity with certain forms of normative reasoning, an intuitive feel for (i) the notion that some events do not fall clearly either within one category or within one or more another alternative categories but fall instead to some degree both within one category and also, to some degree, within one or more other separate categories or classifications, (ii) the notion that categories (classifications, or sets) themselves have uncertain, or rough, perimeters or boundaries, and (iii) the notion that there are distinct forms of uncertainty, that some of them are semantic, and that not all forms of uncertainty can be pictured, or "captured," adequately by conventional probability theory.

    If these intuitions do not move you, you should at least ponder the fact that fuzzy set theory and its affiliates have an enormously wide range of real-world applications. They work! Given this, one should hesitate before calling soft computing nonsense. Soft computing may or may not turn out to be the best way to portray or grapple with uncertainty or with uncertainties of various kinds. But one thing is practically certain:

    The "soft" way of thinking about uncertainty that Zadeh initiated in 1965 is not nonsense. It is, instead, a profoundly important new way of thinking about uncertainty. Even if this new way of thinking is not the final answer to the problem or phenomenon of uncertainty, this new way of thinking is an important stepping-stone to a more comprehensive conception of the nature of uncertainty.

    Monday, April 25, 2005

    Brian Leiter and the Reproduction of Willy Lomanhood

    While surfing the internet the other day I encountered web pages about a person I knew many years ago, while I was still in college. This person went on to a renowned doctoral program at an illustrious university. Very shortly thereafter she published a book that made a big splash in her field and sold very well to the general public. Her book was favorably noted by the New York Times. Passages from it are now found among collections of famous quotations. And then, to all intents and purposes, this person disappeared. As far as I can determine, she has published nary another word.

    This morning (during my spring break) I was listening to WNYC, the local public radio station. I heard a snippet of an interview with Scott A. Sandage. He was discussing his new book Born Losers: A History of Failure in America (Harvard University Press 2005). See the informative review in the Washington Post. Talk in the interview briefly (and inevitably, I suppose) led to mention of Willy Loman. A few moments later Sandage said that he had not tried to study attitudes toward success and failure elsewhere in the world but that anecdotal evidence suggested to him that in at least some parts of the world attitudes toward success and failure differ markedly from those in the United States. He said that when he was still working on his book and mentioned the topic of his book -- failure -- to Americans, the response would usually be an embarrassed silence, but that when he mentioned the topic of his book -- failure -- to Europeans and other non-Americans, his partners in conversation would immediately start grilling him about why Americans are so obsessed with success.

    Thoughts about my vanished friend and about the book Born Losers put me in mind of Brian Leiter.

    Brian Leiter of the University of Texas maintains a ranking system of American law schools. He also ranks philosophy departments now and then. He also ranks various programs in law schools. He also uses alternative metrics to produce a variety of alternative rankings of American law schools.

    Now this business -- the business of ranking law schools, law school programs, and philosophy departments -- is, I suppose, not an unnatural avocation. But Leiter does more than rank various educational institutions and programs. He also reports, in detail, the movement of faculty members -- and rumors of faculty moves -- among American law schools. He has been at it for years now.

    Leiter is preoccupied with hierarchy -- but not in the way that Duncan Kennedy once was. Leiter's reports on lateral faculty moves are generally limited to law schools (and, for all I know, philosophy departments) that he apparently considers either elite or above average. The reports often have a breathless quality. For example:

    Report 1: "A number of top schools, including Texas, were in the 'hunt' for this scholarly couple this past year!" (Leiter Reports, April 14, 2005)

    Report 2: "This marks the first time since roughly the late 1980s that there has been any lateral movement between the two New York schools, and the first time (ever, to my knowledge) that NYU has dislodged a senior faculty member from Columbia. That's a big coup for NYU, ..." (Leiter Reports, April 5, 2005)

    I suspect that many of my fellow law teachers share my reaction to Leiter's reports about faculty moves (often to-and-fro) in the American law school world. Leiter's reports about such matters strike me as mildly repellent; they strike me as the equivalent of a gossip column; they seem to amount to chit chat about the doings of the law school world's equivalent of the rich and famous. But, despite my better judgment and instincts, I find that, exactly like a moth to fire, I am occasionally drawn to Leiter's chatter.

    I teach at a reasonably-good law school. I also fancy that my standing in my field is reasonably good. Yet I find that I am invariably depressed after I look at the most recent edition of Leiter's reports of law school rankings and faculty movement among law schools; indeed, I invariably feel that I am Willy Loman redux.

    At the risk of personal embarrassment, the scorn of my colleagues, and impairment of my standing (if any) in the legal profession at large, I wish to say this: Brian Leiter's reports are not good for the soul. And perhaps they are not good for legal education. Oh, well, shucks: I retract the last suggestion. I can't really say that his reports positively harm American legal education; I haven't done a rigorous economic analysis of the costs and benefits of his "reports" (and I never will). But of this much I am reasonably sure: Brian Leiter's law school faculty gossip column is an example an unhealthy obsession with "success" (in this case, of the academic variety).

    Work in your own gardens, folks (law teachers, I mean, and the rest of you too!). Think less about what your neighbors do and think. Yes, you are entitled to seek just compensation for your labors; and, yes, you must eat and some of you have families to feed. But keep in mind that there is a large grain of truth in the notion that good work is its own reward. So, while it's tough medicine and probably hard to swallow, here is my prescription: Try to keep Brian Leiter -- or, in any event, his reports of law faculty moves -- out of your minds. I will try to do likewise. If we succeed, perhaps we will -- as a group, on the whole -- live better and enjoy our wonderful work more. Let's try to keep the number of Willy Lomans on law school faculties to a minimum.

    There! I have that off my chest. Now I can get back to Evidence.

  • N.B. Honestly! I don't know why that Leiter guy never mentions my name!