Expectation Maximization in Deep Probabilistic Logic Programming

Probabilistic Logic Programming (PLP) combines logic and probability for representing and reasoning over domains with uncertainty. Hierarchical probability Logic Programming (HPLP) is a recent language of PLP whose clauses are hierarchically organized forming a deep neural network or arithmetic circuit. Inference in HPLP is done by circuit evaluation and learning is therefore cheaper than any generic PLP language. We present in this paper an Expectation Maximization algorithm, called Expectation Maximization Parameter learning for HIerarchical Probabilistic Logic programs (EMPHIL), for learning HPLP parameters. The algorithm converts an arithmetic circuit into a Bayesian network and performs the belief propagation algorithm over the corresponding factor graph

A Comparison of MCMC Sampling for Probabilistic Logic Programming

Markov Chain Monte Carlo (MCMC) methods are a class of algorithms used to perform approximate inference in probabilistic models. When direct sampling from a probability distribution is difficult, MCMC algorithms provide accurate results by constructing a Markov chain that gradually approximates the desired distribution. In this paper we describe and compare the performances of two MCMC sampling algorithms, Gibbs sampling and Metropolis Hastings sampling, with rejection sampling for probabilistic logic programs. In particular, we analyse the relation between execution time and number of samples and how fast each algorithm converges

Dense-core senile plaques in the Flemish variant of Alzheimer's disease are vasocentric

Alzheimer's disease (AD) is characterized by deposition of beta-amyloid (Abeta) in diffuse and senile plaques, and variably in vessels. Mutations in the Abeta-encoding region of the amyloid precursor protein (APP) gene are frequently associated with very severe forms of vascular Abeta deposition, sometimes also accompanied by AD pathology. We earlier described a Flemish APP (A692G) mutation causing a form of early-onset AD with a prominent cerebral amyloid angiopathy and unusually large senile plaque cores. The pathogenic basis of Flemish AD is unknown. By image and mass spectrometric Abeta analyses, we demonstrated that in contrast to other familial AD cases with predominant brain Abeta42, Flemish AD patients predominantly deposit Abeta40. On serial histological section analysis we further showed that the neuritic senile plaques in APP692 brains were centered on vessels. Of a total of 2400 senile plaque cores studied from various brain regions from three patients, 68% enclosed a vessel, whereas the remainder were associated with vascular walls. These observations were confirmed by electron

Probabilistic (logic) programming concepts

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position and survey state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been considered for over 20 years

Influence of 1α, 25-dihydroxyvitamin D3 [1, 25(OH)2D3] on the expression of Sox 9 and the transient receptor potential vanilloid 5/6 ion channels in equine articular chondrocytes

Background Sox 9 is a major marker of chondrocyte differentiation. When chondrocytes are cultured in vitro they progressively de-differentiate and this is associated with a decline in Sox 9 expression. The active form of vitamin D, 1, 25 (OH)2D3 has been shown to be protective of cartilage in both humans and animals. In this study equine articular chondrocytes were grown in culture and the effects of 1, 25 (OH)2D3 upon Sox 9 expression examined. The expression of the transient receptor potential vanilloid (TRPV) ion channels 5 and 6 in equine chondrocytes in vitro, we have previously shown, is inversely correlated with de-differentiation. The expression of these channels in response to 1, 25 (OH)2D3 administration was therefore also examined. Results The active form of vitamin D (1, 25 (OH)2D3) when administered to cultured equine chondrocytes at two different concentrations significantly increased the expression of Sox 9 at both. In contrast 1, 25 (OH)2D3 had no significant effect upon the expression of either TRPV 5 or 6 at either the protein or the mRNA level. Conclusions The increased expression of Sox 9, in equine articular chondrocytes in vitro, in response to the active form of vitamin D suggests that this compound could be utilized to inhibit the progressive de-differentiation that is normally observed in these cells. It is also supportive of previous studies indicating that 1α, 25-dihydroxyvitamin D3 can have a protective effect upon cartilage in animals in vivo. The previously observed correlation between the degree of differentiation and the expression levels of TRPV 5/6 had suggested that these ion channels may have a direct involvement in, or be modulated by, the differentiation process in vitro. The data in the present study do not support this