After the pioneering work of the BACON system, the study in the field of scientific discovery has been directed to the discovery of more plausible law equations to represent the first principles underlying objective systems. The state of the art has only succeeded in a weak sense that the soundness, the reproducibility and the mathematical admissibility of the candidates hold within the experimental measurements. The plausibility should be checked for various objects and/or measurements sharing the common first principles, and only the equations having sufficient generality should be retained. In this paper, anovel principle and an algorithm are proposed to predict some mathematically admissible and consistent equation formulae for a newly given set of quantities from the candidate law equations obtained for another set of quantities in advance. The soundness and the reproducibility of the predicted equations are confirmed through the measurements. The law equatio...

Path analysis is a generalization of multiple linear regression that builds models with causal interpretations. It is an exploratory or discovery procedure for finding causal structure in correlational data. Recently, we have applied statistical methods such as path analysis to the problem of building models of AI programs, which are generally complex and poorly understood.

Relational learning algorithms are of special interest to members of the machine learning community; they offer practical methods for extending the representations used in algorithms that solve supervised learning tasks. Five approaches are currently being explored to address issues involved with using relational representations. This paper surveys algorithms embodying these approaches, summarizes their empirical evaluations, highlights their commonalities, and suggests potential directions for future research. Keywords: supervised learning, representation, relational learning 1 Introduction Relational learning algorithms extend the capabilities of propositional or monadic supervised learning algorithms. Supervised learning algorithms input a set of instances, which are described by a set of predictor descriptors and a target descriptor. These algorithms construct a function (i.e., a concept description) that can predict an instance's target descriptor value given its predictor desc...

Both equation discovery and regression methods aim at inducing models of numerical data. While the equation discovery methods are usually evaluated in terms of comprehensibility of the induced model, the emphasis of the regression methods evaluation is on their predictive accuracy. In this paper, we present Ciper, an efficient method for discovery of polynomial equations and empirically evaluate its predictive performance on standard regression tasks. The evaluation shows that polynomials compare favorably to linear and piecewise regression models, induced by the existing state-of-the-art regression methods, in terms of degree of fit and complexity. 1

The problem of how to learn from examples has been studied throughout the history of machine learning, and many successful learning algorithms have been developed. A problem that has received less attention is how to select which algorithm to use for a given learning task. The ability of a chosen algorithm to induce a good generalization depends on how appropriate the model class underlying the algorithm is for the given task. We define an algorithm's model class to be the representation language it uses to express a generalization of the examples. Supervised learning algorithms differ in their underlying model class and in how they search for a good generalization. Given this characterization, it is not surprising that some algorithms find better generalizations for some, but not all tasks. Therefore, in order to find the best generalization for each task, an automated learning system must search for the appropriate model class in addition to searching for the best generalization wit...

The problem of learning qualitative models of physical systems from observations of its behaviour has been addressed by several researchers in recent years. Most current techniques limit themselves to learning a single qualitative differential equation to model the entire system. However, many systems have several qualitative differential equations underlying them. In this paper, we present an approach to learning the models for such systems. Our technique divides the behaviours into segments, each of which can be explained by a single qualitative differential equation. The qualitative model for each segment can be generated using any of the existing techniques for learning a single model. We show the results of applying our technique to several examples and demonstrate that it is effective. Introduction Qualitative reasoning is an elegant approach to studying the behaviour of a physical system without going into as much detail as in a numerical simulation. Model building and model ...

Most conventional law equation discovery systems suchasBACON require experimental environments to acquire their necessary data. The mathematical techniques such as linear system identification and neural network fitting presume the classes of equations to model given observed data sets. The study reported in this paper proposes a novel method to discover an admissible model equation from a given set of observed data, while the equation is ensured to reflect first principles governing the objective system. The power of the proposed method comes from the use of the scale-types of the observed quantities, a mathematical property of identity and quasi-bi-variate fitting to the given data set. Its principles and algorithm are described with moderately complex examples, and its practicality is demonstrated through a real application to psychological and sociological law equation discovery. 1 Introduction The most well known pioneering system to discover scientific law eq...

Building 3D widgets was until now considered to be a costly task performed only by experts: programmers or people who understood complexities of the constraint networks found in the widgets they were constructing, as well as the mathematical details surrounding the operation their widgets were to perform. This paper addresses these problems and presents LOG, an interface for 3D widget construction. LOG is an inference-based 3D widget construction toolkit that facilitates quick and intuitive prototyping of widgets. When using LOG, designing widgets requires absolutely no programming on the user's part or understanding of the constraint networks and mathematical equations involved. Instead, all specification of constraints is done by example, where the users simply presents configurations of the widget they are constructing from defining the geometry of the widget to mapping the widget to an operation. 1 Introduction Building 3D widgets was until now considered to be a costl...

EMERALD 1 is a large-scale system integrating several advanced programs exhibiting different forms of learning or discovery. The system is intended to support teaching and research in the area of machine learning. It enables a user to experiment with the individual programs, run them on various problems, and test the performance of the programs. The problems are defined by a user from a set of predefined visual objects, displayed through color graphics facilities. The current version of the system incorporates the following programs, each displaying the capacity for some simple form of learning or discovery: AQ - learns general rules from examples of correct or incorrect decisions made by experts.

Among the central tasks in the development of expert systems is the formulation, debugging and implementation of a knowledge base. The knowledge encoded in the knowledge base is usually supplied by experts. There are, however, many application domains in which knowledge required by an expert system has to be extracted from facts collected in a data base. In view of the large sizes and the complexity of contemporary data bases in different areas, such as agriculture, medicine, business, etc., determining useful knowledge from them is becoming an increasingly difficult problem. This paper describes a multistrategy "intelligent assistant" for knowledge discovery in large data bases, called INLEN. The system integrates a database, a knowledge base, and machine learning capabilities within a uniform user-oriented framework. The latter capabilities are incorporated into the system in the form of knowledge generation operators (KGOs). These operators can generate diverse kinds of knowledge about the properties and mgularities existing in the dam. For example, they can hypothesize general diagnostic rules from specific cases of diagnosis, optimize the rules according to problem-dependent criteria, determine differences and similarities among groups of facts, propose oew variables, create conceptual classifications, determine equations governing numeric variables and the conditions under which the equations apply, derive statistical properties and use them for qualitative evaluations, etc. The initially implemented system, INLEN-1, is described, and its performance is illustrated by an example.