First-order logic learning in artificial neural networks

Artificial Neural Networks have previously been applied in neuro-symbolic learning to learn ground logic program rules. However, there are few results of learning relations using neuro-symbolic learning. This paper presents the system PAN, which can learn relations. The inputs to PAN are one or more atoms, representing the conditions of a logic rule, and the output is the conclusion of the rule. The symbolic inputs may include functional terms of arbitrary depth and arity, and the output may include terms constructed from the input functors. Symbolic inputs are encoded as an integer using an invertible encoding function, which is used in reverse to extract the output terms. The main advance of this system is a convention to allow construction of Artificial Neural Networks able to learn rules with the same power of expression as first order definite clauses. The system is tested on three examples and the results are discussed

Fast relational learning using bottom clause propositionalization with artificial neural networks

Relational learning can be described as the task of learning first-order logic rules from examples. It has enabled a number of new machine learning applications, e.g. graph mining and link analysis. Inductive Logic Programming (ILP) performs relational learning either directly by manipulating first-order rules or through propositionalization, which translates the relational task into an attribute-value learning task by representing subsets of relations as features. In this paper, we introduce a fast method and system for relational learning based on a novel propositionalization called Bottom Clause Propositionalization (BCP). Bottom clauses are boundaries in the hypothesis search space used by ILP systems Progol and Aleph. Bottom clauses carry semantic meaning and can be mapped directly onto numerical vectors, simplifying the feature extraction process. We have integrated BCP with a well-known neural-symbolic system, C-IL2P, to perform learning from numerical vectors. C-IL2P uses background knowledge in the form of propositional logic programs to build a neural network. The integrated system, which we call CILP++, handles first-order logic knowledge and is available for download from Sourceforge. We have evaluated CILP++ on seven ILP datasets, comparing results with Aleph and a well-known propositionalization method, RSD. The results show that CILP++ can achieve accuracy comparable to Aleph, while being generally faster, BCP achieved statistically significant improvement in accuracy in comparison with RSD when running with a neural network, but BCP and RSD perform similarly when running with C4.5. We have also extended CILP++ to include a statistical feature selection method, mRMR, with preliminary results indicating that a reduction of more than 90 % of features can be achieved with a small loss of accuracy

Novel loci for adiponectin levels and their influence on type 2 diabetes and metabolic traits: A multi-ethnic meta-analysis of 45,891 individuals

Circulating levels of adiponectin, a hormone produced predominantly by adipocytes, are highly heritable and are inversely associated with type 2 diabetes mellitus (T2D) and other metabolic traits. We conducted a meta-analysis of genome-wide association studies in 39,883 individuals of European ancestry to identify genes associated with metabolic disease. We identified 8 novel loci associated with adiponectin levels and confirmed 2 previously reported loci (P = 4.5×10−8- 1.2 ×10−43). Using a novel method to combine data across ethnicities (N = 4,232 African Americans, N = 1,776 Asians, and N = 29,347 Europeans), we identified two additional novel loci. Expression analyses of 436 human adipocyte samples revealed that mRNA levels of 18 genes at candidate regions were associated with adiponectin concentrations after accounting for multiple testing (p<3×10−4). We next developed a multi-SNP genotypic risk score to test the association of adiponectin decreasing risk alleles on metabolic traits and diseases using consortia-level meta-analytic data. This risk score was associated with increased risk of T2D (p = 4.3×10−3, n = 22,044), increased triglycerides (p = 2.6×10−14, n = 93,440), increased waist-to-hip ratio (p = 1.8×10−5, n = 77,167), increased glucose two hours post oral glucose tolerance testing (p = 4.4×10−3, n = 15,234), increased fasting insulin (p = 0.015, n = 48,238), but with lower in HDL- cholesterol concentrations (p = 4.5×10−13, n = 96,748) and decreased BMI (p = 1.4×10−4, n = 121,335). These findings identify novel genetic determinants of adiponectin levels, which, taken together, influence risk of T2D and markers of insulin resistance

Genome-wide association identifies nine common variants associated with fasting proinsulin levels and provides new insights into the pathophysiology of type 2 diabetes

OBJECTIVE - Proinsulin is a precursor of mature insulin and C-peptide. Higher circulating proinsulin levels are associated with impaired b-cell function, raised glucose levels, insulin resistance, and type 2 diabetes (T2D). Studies of the insulin processing pathway could provide new insights about T2D pathophysiology. RESEARCH DESIGN AND METHODS - We have conducted a meta-analysis of genome-wide association tests of ;2.5 million genotyped or imputed single nucleotide polymorphisms (SNPs) and fasting proinsulin levels in 10,701 nondiabetic adults of European ancestry, with follow-up of 23 loci in up to 16,378 individuals, using additive genetic models adjusted for age, sex, fasting insulin, and study-specific covariates. RESULTS - Nine SNPs at eight loci were associated with proinsulin levels (P < 5 × 10-8). Two loci (LARP6 and SGSM2) have not been previously related to metabolic traits, one (MADD) has been associated with fasting glucose, one (PCSK1) has been implicated in obesity, and four (TCF7L2, SLC30A8, VPS13C/ C2CD4A/B, and ARAP1, formerly CENTD2) increase T2D risk. The proinsulin-raising allele of ARAP1 was associated with a lower fasting glucose (P = 1.7 3 10-4), improved b-cell function (P = 1.1 × 10-5), and lower risk of T2D (odds ratio 0.88; P = 7.8 × 10-6). Notably, PCSK1 encodes the protein prohormone convertase 1/3, the first enzyme in the insulin processing pathway. A genotype score composed of the nine proinsulin-raising alleles was not associated with coronary disease in two large case-control datasets. CONCLUSIONS - We have identified nine genetic variants associated with fasting proinsulin. Our findings illuminate the biology underlying glucose homeostasis and T2D development in humans and argue against a direct role of proinsulin in coronary artery disease pathogenesis