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

Learning to Synthesize a 4D RGBD Light Field from a Single Image

We present a machine learning algorithm that takes as input a 2D RGB image and synthesizes a 4D RGBD light field (color and depth of the scene in each ray direction). For training, we introduce the largest public light field dataset, consisting of over 3300 plenoptic camera light fields of scenes containing flowers and plants. Our synthesis pipeline consists of a convolutional neural network (CNN) that estimates scene geometry, a stage that renders a Lambertian light field using that geometry, and a second CNN that predicts occluded rays and non-Lambertian effects. Our algorithm builds on recent view synthesis methods, but is unique in predicting RGBD for each light field ray and improving unsupervised single image depth estimation by enforcing consistency of ray depths that should intersect the same scene point. Please see our supplementary video at https://youtu.be/yLCvWoQLnmsComment: International Conference on Computer Vision (ICCV) 201

Numerical reasoning with an ILP system capable of lazy evaluation and customised search

Using problem-speci®c background knowledge, computer programs developed within theframework of Inductive Logic Programming (ILP) have been used to construct restricted®rst-order logic solutions to scienti®c problems. However, their approach to the analysis ofdata with substantial numerical content has been largely limited to constructing clauses that:(a) provide qualitative descriptions (high'', low'' etc.) of the values of response variables;and (b) contain simple inequalities restricting the ranges of predictor variables. This has precludedthe application of such techniques to scienti®c and engineering problems requiring amore sophisticated approach. A number of specialised methods have been suggested to remedythis. In contrast, we have chosen to take advantage of the fact that the existing theoreticalframework for ILP places very few restrictions of the nature of the background knowledge.We describe two issues of implementation that make it possible to use background predicatesthat implement well-established statistical and numerical analysis procedures. Any improvementsin analytical sophistication that result are evaluated empirically using arti®cial andreal-life data. Experiments utilising arti®cial data are concerned with extracting constraintsfor response variables in the text-book problem of balancing a pole on a cart. They illustratethe use of clausal de®nitions of arithmetic and trigonometric functions, inequalities, multiplelinear regression, and numerical derivatives. A non-trivial problem concerning the predictionof mutagenic activity of nitroaromatic molecules is also examined. In this case, expert chemistshave been unable to devise a model for explaining the data. The result demonstrates the combineduse by an ILP program of logical and numerical capabilities to achieve an analysis thatincludes linear modelling, clustering and classi®cation. In all experiments, the predictions obtainedcompare favourably against benchmarks set by more traditional methods of quantitativemethods, namely, regression and neural-network

Preliminary screening of osteoporosis and osteopenia in middle aged urban women from Hyderabad (INDIA) using calcaneal QUS

Background: Osteoporosis is a major public health problem, associated with substantial morbidity and socio-economic burden. An early detection can help in reducing the fracture rates and overall socio-economic burden in such patients. The present study was carried out to screen the bone status (osteopenia and osteoporosis) above the age of 25 years in urban women population in this region.Methods: A hospital based study was carried out in 316 women by calculating T-scores utilizing calcaneal QUS as diagnostic tool.Results: The result suggested that a substantial female population had oesteopenia and osteoporosis after the age of 45 years. The incidence of osteoporosis was (20.25%) and osteopenia (36.79%) with maximum number of both osteoporosis and osteopenic women recorded in the age group of (55-64 years). After the age of 65 years, there was an almost 100% incidence of either osteopenia or osteoporosis, indicating that it increases with age and in postmenopausal period, thereby suggesting lack of estrogenic activity might be responsible for this increasing trend. Religion, caste and diet had an influence on the outcome of osteopenic and osteoporosis score in present study, but still it has to be substantiated by conducting larger randomized clinical trials in future.Conclusions: A substantial female population was screened for osteoporosis and osteopenia using calcaneal QUS method utilizing same WHO T score criteria that otherwise shall remain undiagnosed and face the complications and menace of osteoporosis.

Knowledge-based Analogical Reasoning in Neuro-symbolic Latent Spaces

Analogical Reasoning problems challenge both connectionist and symbolic AI systems as these entail a combination of background knowledge, reasoning and pattern recognition. While symbolic systems ingest explicit domain knowledge and perform deductive reasoning, they are sensitive to noise and require inputs be mapped to preset symbolic features. Connectionist systems on the other hand can directly ingest rich input spaces such as images, text or speech and recognize pattern even with noisy inputs. However, connectionist models struggle to include explicit domain knowledge for deductive reasoning. In this paper, we propose a framework that combines the pattern recognition abilities of neural networks with symbolic reasoning and background knowledge for solving a class of Analogical Reasoning problems where the set of attributes and possible relations across them are known apriori. We take inspiration from the 'neural algorithmic reasoning' approach [DeepMind 2020] and use problem-specific background knowledge by (i) learning a distributed representation based on a symbolic model of the problem (ii) training neural-network transformations reflective of the relations involved in the problem and finally (iii) training a neural network encoder from images to the distributed representation in (i). These three elements enable us to perform search-based reasoning using neural networks as elementary functions manipulating distributed representations. We test this on visual analogy problems in RAVENs Progressive Matrices, and achieve accuracy competitive with human performance and, in certain cases, superior to initial end-to-end neural-network based approaches. While recent neural models trained at scale yield SOTA, our novel neuro-symbolic reasoning approach is a promising direction for this problem, and is arguably more general, especially for problems where domain knowledge is available.Comment: 13 pages, 4 figures, Accepted at 16th International Workshop on Neural-Symbolic Learning and Reasoning as part of the 2nd International Joint Conference on Learning & Reasoning (IJCLR 2022