Benjamin M. Gyori

Charles Tapley Hoyt, Max Berrendorf, Mikhail Galkin et al. · deepmind, harvard

The link prediction task on knowledge graphs without explicit negative triples in the training data motivates the usage of rank-based metrics. Here, we review existing rank-based metrics and propose desiderata for improved metrics to address lack of interpretability and comparability of existing metrics to datasets of different sizes and properties. We introduce a simple theoretical framework for rank-based metrics upon which we investigate two avenues for improvements to existing metrics via alternative aggregation functions and concepts from probability theory. We finally propose several new rank-based metrics that are more easily interpreted and compared accompanied by a demonstration of their usage in a benchmarking of knowledge graph embedding models.

Benedek Rozemberczki, Charles Tapley Hoyt, Anna Gogleva et al.

In this paper, we introduce ChemicalX, a PyTorch-based deep learning library designed for providing a range of state of the art models to solve the drug pair scoring task. The primary objective of the library is to make deep drug pair scoring models accessible to machine learning researchers and practitioners in a streamlined framework.The design of ChemicalX reuses existing high level model training utilities, geometric deep learning, and deep chemistry layers from the PyTorch ecosystem. Our system provides neural network layers, custom pair scoring architectures, data loaders, and batch iterators for end users. We showcase these features with example code snippets and case studies to highlight the characteristics of ChemicalX. A range of experiments on real world drug-drug interaction, polypharmacy side effect, and combination synergy prediction tasks demonstrate that the models available in ChemicalX are effective at solving the pair scoring task. Finally, we show that ChemicalX could be used to train and score machine learning models on large drug pair datasets with hundreds of thousands of compounds on commodity hardware.

Benjamin M. Gyori, Bing Liu, Soumya Paul et al.

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability $1$. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximately- that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings.

Benjamin M. Gyori, Daniel Paulin, Sucheendra K. Palaniappan

The construction and formal verification of dynamical models is important in engineering, biology and other disciplines. We focus on non-linear models containing a set of parameters governing their dynamics. The value of these parameters is often unknown and not directly observable through measurements, which are themselves noisy. When treating parameters as random variables, one can constrain their distribution by conditioning on observations and thereby constructing a posterior probability distribution. We aim to perform model verification with respect to this posterior. The main difficulty in performing verification on a model under the posterior distribution is that in general, it is difficult to obtain \emph{independent} samples from the posterior, especially for non-linear dynamical models. Standard statistical model checking methods require independent realizations of the system and are therefore not applicable in this context. We propose a Markov chain Monte Carlo based statistical model checking framework, which produces a sequence of dependent random realizations of the model dynamics over the parameter posterior. Using this sequence of samples, we use statistical hypothesis tests to verify whether the model satisfies a bounded temporal logic property with a certain probability. We use sample size bounds tailored to the setting of dependent samples for fixed sample size and sequential tests. We apply our method to a case-study from the domain of systems biology, to a model of the JAK-STAT biochemical pathway. The pathway is modeled as a system of non-linear ODEs containing a set of unknown parameters. Noisy, indirect observations of the system state are available from an experiment. The results show that the proposed method enables probabilistic verification with respect to the parameter posterior with specified error bounds.