Qualitative System Identification from Imperfect Data

Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as differential equations. Quantitative modelling works best when the structure of the model (i.e., the form of the equations) is known; and the primary concern is one of estimating the values of the parameters in the model. For complex biological systems, the model-structure is rarely known and the modeler has to deal with both model-identification and parameter-estimation. In this paper we are concerned with providing automated assistance to the first of these problems. Specifically, we examine the identification by machine of the structural relationships between experimentally observed variables. These relationship will be expressed in the form of qualitative abstractions of a quantitative model. Such qualitative models may not only provide clues to the precise quantitative model, but also assist in understanding the essence of that model. Our position in this paper is that background knowledge incorporating system modelling principles can be used to constrain effectively the set of good qualitative models. Utilising the model-identification framework provided by Inductive Logic Programming (ILP) we present empirical support for this position using a series of increasingly complex artificial datasets. The results are obtained with qualitative and quantitative data subject to varying amounts of noise and different degrees of sparsity. The results also point to the presence of a set of qualitative states, which we term kernel subsets, that may be necessary for a qualitative model-learner to learn correct models. We demonstrate scalability of the method to biological system modelling by identification of the glycolysis metabolic pathway from data

kLog: A Language for Logical and Relational Learning with Kernels

We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials

Structure and Properties of Traces for Functional Programs

The tracer Hat records in a detailed trace the computation of a program written in the lazy functional language Haskell. The trace can then be viewed in various ways to support program comprehension and debugging. The trace was named the augmented redex trail. Its structure was inspired by standard graph rewriting implementations of functional languages. Here we describe a model of the trace that captures its essential properties and allows formal reasoning. The trace is a graph constructed by graph rewriting but goes beyond simple term graphs. Although the trace is a graph whose structure is independent of any rewriting strategy, we define the trace inductively, thus giving us a powerful method for proving its properties