a computerized matchmaker that is capable of learning

4
Computing 11, 69--72 (1973) by Springer-Verlag 1973 A Computerized Matchmaker That is Capable of Learning* By N. V. Findler** and E. Goit, Buffalo (Received December 15, I972) Abstract -- Zusammenfassung A Computerized Matchmaker that is Capable of Learning. This paper describes a self-adaptive, learning system which, beyond the humorous task environment presently placed into, can be made use of in a variety of personality tests. Possible applications range from market research studies to quasi- optimum game playing programs. It is hoped that Women's Libbers wilt recognizethe tongue-in-cheek approach, Phase I of the learning program MATER aims at discovering the terms of the evaluation function to be patterned and computes the weights of importance of its features approximately. Phase II adjusts further these weights, if needed, to match those of the subject imitated. Ein lernf~ihiger maschineller Heiratsvermittler. Dieser Artikel beschreibt ein selbststeuerndesLern- system,welches-- auger in diesemheiteren Aufgabengebiet - - i n einerVielzahlvon Pers6nlichkeitstesten verwendet werden kann. M6gliche Anwendungen reichen von Marktforschung bis zu quasi-optimalen Spiel-Programmen. Es ist zu hoffen, dab die Frauenemanzipations-Bewegung diese etwas ironisch wirkende Stellungnahme anerkennen wird. Phase I des Lernprogramms MATER zielt auf die Aufdeckungder Terme der Auswertungsfunktion und berechnet ann~ihernd die Gewichte der Bedeutung ihrer Merkmale. Phase II berichtigt, wenn notwendig, im weiteren Verlauf diese Gewichte, um sie den imitierten Subjekten anzupassen. 1. The Role of a Matchmaker A young man's taste is determined to a rather large extent by his upbringing (parents' and teachers' influence) and by his social environment (friends, living conditions, local customs, advertisements, information media, etc.). No matter how well-formed his scale of values and preference ranking are, most people find it difficult to verbalize their taste in a precise, reproducible way. It is also true that the criteria and values of selection change with time as a consequence of new experiences and new influences. The present project attempts to automate the process through which an interviewer can find out a person's taste in general. Let us assume that an old-fashioned matchmaker has a photo and the personal description of a finite number of potential brides lined up in his filling system. His role is to find out what a young man likes within the shortest possible time 1 * The work reported here was partially supported by the National Science Foundation Grant GJ-65g. ** Professor FrYDLER'Saddress during the 1972/73 academic year is: Institute of Numerical Mathematics, Technical University of Vienna, Karlsplatz 13, A- 1040 Vienna, Austria. The matchmaker's time is at premium slnce he has to satisfy many customers.

Upload: n-v-findler

Post on 10-Jul-2016

214 views

Category:

Documents


2 download

TRANSCRIPT

C o m p u t i n g 11, 69 - -72 (1973) �9 by Springer-Verlag 1973

A Computerized Matchmaker That is Capable of Learning* By

N . V. F indler** a n d E. Goit , Buffalo

(Received December 15, I972)

Abstract - - Zusammenfassung

A Computerized Matchmaker that is Capable of Learning. This paper describes a self-adaptive, learning system which, beyond the humorous task environment presently placed into, can be made use of in a variety of personality tests. Possible applications range from market research studies to quasi- optimum game playing programs. It is hoped that Women's Libbers wilt recognize the tongue-in-cheek approach,

Phase I of the learning program MATER aims at discovering the terms of the evaluation function to be patterned and computes the weights of importance of its features approximately. Phase II adjusts further these weights, if needed, to match those of the subject imitated.

Ein lernf~ihiger maschineller Heiratsvermittler. Dieser Artikel beschreibt ein selbststeuerndes Lern- system, welches-- auger in diesem heiteren Aufgabengebiet - - in einer Vielzahl von Pers6nlichkeitstesten verwendet werden kann. M6gliche Anwendungen reichen von Marktforschung bis zu quasi-optimalen Spiel-Programmen. Es ist zu hoffen, dab die Frauenemanzipations-Bewegung diese etwas ironisch wirkende Stellungnahme anerkennen wird.

Phase I des Lernprogramms MATER zielt auf die Aufdeckung der Terme der Auswertungsfunktion und berechnet ann~ihernd die Gewichte der Bedeutung ihrer Merkmale. Phase II berichtigt, wenn notwendig, im weiteren Verlauf diese Gewichte, um sie den imitierten Subjekten anzupassen.

1. T h e R o l e o f a M a t c h m a k e r

A young man ' s taste is de termined to a rather large extent by his upbr ing ing (parents ' and teachers' influence) and by his social e nv i r onme n t (friends, living condi t ions, local customs, advert isements, in format ion media, etc.). N o mat ter how well-formed his scale of values and preference r ank ing are, most people find it difficult to verbalize their taste in a precise, reproducible way. It is also true that the criteria and values of selection change with t ime as a consequence of new experiences and new influences. The present project a t tempts to au tomate the process through which an interviewer can find out a person 's taste in general.

Let us assume that an old-fashioned ma tchmaker has a photo and the personal descr ipt ion of a finite n u m b e r of potent ia l brides l ined up in his filling system. His role is to find out what a young man likes within the shortest possible time 1

* The work reported here was partially supported by the National Science Foundation Grant GJ-65g.

** Professor FrYDLER'S address during the 1972/73 academic year is: Institute of Numerical Mathematics, Technical University of Vienna, Karlsplatz 13, A- 1040 Vienna, Austria.

The matchmaker's time is at premium slnce he has to satisfy many customers.

70 N.V. FINDLER and E. GoIT:

by presenting to him the characteristics of small sets of optimally chosen girls and, after this multistage selection process, pick a bride that suits him best.

2. The Technique of Evaluation

Suppose each female has N features, which a man may like, dislike or be neutrai about. The importance to a particular man of a feature can be quantified by weighting factor cz, i = 1 . . . . N. A large positive value means strong liking, a large negative value strong disliking. The feature variable, itself, may assume the values 1 or 0, depending on whether the lady in question possesses it or not, respectively.

The computer program MATER is designed to find out the "evaluation function" of the man, i.e., which features and with what weights appear in it. Consistency of taste is assumed, although a "reasonable" noise level should cause no problem other than enlengthening the convergence process.

We shall assume that evaluation functions are linear. This means that each feature and its effect are independent of all the others - - a simplifying but conceptually not indispensable assumption. The "attraction" by a lady to a man is, therefore, equal to the scalar product of the weight vector and the feature vector,

C.F.---Cl . f l + c 2 . f 2 + . . . + c , . f , , .

3. The Program 'Mater'

The following inputs are specified for the program in a given task environment:

(a) A list of all possible features and categories. Each feature belongs to a category with either several of one single feature. In the former case, one and only one of the features in the category may assume the value 1. In the latter case, the single feature can be given the value 0 or 1.

(b) Data base consisting of M potential brides each with N features. MATER transforms this into a M x N matrix. The (J, K) element is 1 if the J-th girl has the K-th feature; otherwise it is 0.

(c) The young man may, but need not, specify a list of features absolutely necessary to occur or not to occur.

Since presently we have no interactive mode of computation, the questioning- responding activity is simulated by the program. Not much change is, however, needed to convert the system into a conversational type of operation.

The Phase 1 learning program sets up a tentative preference matrix, possibly using the above described input information of type (c). It then presents pairs of girls together with their features for preference selection. The members of these pairs are selected systematically in order to complete the preference matrix as quickly as possible. We note here an interesting information theoretic problem, which we have not yet investigated closely. To minimize the number of decisions to be made for the completion of the preference matrix, the optimum number of girls presented each time is not two. The question is: how many and

A Computerized Matchmaker that is Capable of Learning 71

which girls should be selected for presentation at each stage with the given set of girls ?

The program then normalizes and unitizes the features. We describe this technique here briefly. A more detailed discussion, including some proofs, can be found in (SLAGLE, 1971) or, particularly, in (NILSSON, 1965).

For most procedures for solving the (m, n) evaluation problem, that is to find the C vector that is quasi-optimum, it is desirable to normalize the features. In the following, m is the sample size and n is the number of features. Let xij be the i-th sample value of the j-th feature; ~j the average over all samples of the absolute value of xij, that is

J=mi l l x jl.

These are not normalized since it is not true that ~ l=~a . . . . . ~ . We can redefine the features as

With these, for all j, it is already true that

• mi=l

One must, of course, remember that the coefficients obtained for the normalized features, c}, must be divided by ~j to get the solutions for the original features,

The next step is to unitize the vectors 2~, that is to replace them by unit vectors pointing in the same direction in order to make C independent of the magnitudes of 2~,

Cfi = Xi/I 2 i I.

The MATER program then computes a tentative ~: vector by summing up the Ui vectors

Cry. i=1

This procedure, although very simple and plausible, does not always compute optimum coefficients. One of the other advantages of this method can also be noted, namely it is rotationally invariant.

The program would test the quality of the solution obtained so far by comparing the "young man's preferences" with its own. In case of discrepancies between the two, it enters the Phase II learning program. This consists of a relaxa- tion procedure which corrects each component of G one by one. The inclement, positive or negative, in c~ is proportional to 12~1 and inversely proportional to n. This method always converges to a unique C vector, as can be proven, whenever the set of Xi is linearly separable.

Our results indicate that, depending on the data base, Phase I learning ended up with poor or mediocre weighting factors when compared to those of the

72 N.V. FINDLER and E. GOlT: A Computerized Matchmaker that is Capable of Learning

subject to be imitated. However, Phase II learning was always able to arrive at a unique opt imum C vector. In a characteristic run, 16 girls were described by 14 features in 5 categories (m = 16, n = 14). After Phase I, MATER found that about one-third of its paired preferences differ from those of the subject. The subsequent Phase II learning process, therefore, adjusted altogether eight weight- ing factors in three iterations.

4. Possible Applications

It is obvious that in an interactive mode of operation, this program can be used to administer and evaluate a variety of personality tests. An interesting area of application is the task environment used to discover the so-called utility function of individuals. Market researchers, for example, could easily pinpoint the features and their importance of competing products. Historical decisions in international affairs could be reduced to a, hopefully consistent, evaluation function of individual nations. The abilities of candidates for executive positions could be tested when the consequences of decisions to be made are known from past history. Finally, game playing programs could be made to imitate the playing style of experts by following the moves described in book games (SAMUEL, 1958; FINDLER, 1960).

References

[1] FINDLER, N. V. : On the game "Dama" which can played on a digital computer. The Computer Journal 3, 4 0 4 4 (1960).

[2] NiLssoY, N. J. : Learning Machines. New York: McGraw-Hill. 1965. [3] SAMUEL, A. L. : Some studies in machine learning using the game of Checkers. IBM J. Res. Dev. 3,

216--229 (1959). [4] SLAGLE, J.R.: Artificial Intelligence - - The Heuristic Programming Approach. New York:

McGraw-Hill. 1971.

Prof. N. V. Findler and Mr. E. Goit

Department of Computer Science State University of New York at Buffalo

Buffalo, N. Y., U. S. A.

"Gee] my.first computer date/ I wonder what he'll be like?"

(With permission by Modern Data, Framingham, Mass., U. S. A.)