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.

Charles Tapley Hoyt, Craig Bakker, Richard J. Callahan et al.

We present the $Y_0$ Python package, which implements causal identification algorithms that apply interventional, counterfactual, and transportability queries to data from (randomized) controlled trials, observational studies, or mixtures thereof. $Y_0$ focuses on the qualitative investigation of causation, helping researchers determine whether a causal relationship can be estimated from available data before attempting to estimate how strong that relationship is. Furthermore, $Y_0$ provides guidance on how to transform the causal query into a symbolic estimand that can be non-parametrically estimated from the available data. $Y_0$ provides a domain-specific language for representing causal queries and estimands as symbolic probabilistic expressions, tools for representing causal graphical models with unobserved confounders, such as acyclic directed mixed graphs (ADMGs), and implementations of numerous identification algorithms from the recent causal inference literature. The $Y_0$ source code can be found under the MIT License at https://github.com/y0-causal-inference/y0 and it can be installed with pip install y0.

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.