Transcriptomics response of SK-N-AS cells to methamidophos (an acetylcholine esterase inhibitor) exposure was measured at 10 time points between 0.5 and 48 h. The data was analyzed using a combination of traditional statistical methods and novel machine learning algorithms for detecting anomalous behavior and infer causal relations between time profiles. We identified several processes that appeared to be upregulated in cells treated with methamidophos including: unfolded protein response, response to cAMP, calcium ion response, and cell-cell signaling. The data confirmed the expected consequence of acetylcholine buildup. In addition, transcripts with potentially key roles were identified and causal networks relating these transcripts were inferred using two different computational methods: Siamese convolutional networks and time warp causal inference. Two types of anomaly detection algorithms, one based on Autoencoders and the other one based on Generative Adversarial Networks (GANs), were applied to narrow down the set of relevant transcripts.

In spite of the rapidly increasing number of applications of machine learning in various domains, a principled and systematic approach to the incorporation of domain knowledge in the engineering process is still lacking and ad hoc solutions that are difficult to validate are still the norm in practice, which is of growing concern not only in mission-critical applications. In this note, we introduce Probabilistic Approximate Logic (PALO) as a logic based on the notion of mean approximate probability to overcome conceptual and computational difficulties inherent to strictly probabilistic logics. The logic is approximate in several dimensions. Logical independence assumptions are used to obtain approximate probabilities, but by averaging over many instances of formulas a useful estimate of mean probability with known confidence can usually be obtained. To enable efficient computational inference, the logic has a continuous semantics that reflects only a subset of the structural properties of classical logic, but this imprecision can be partly compensated by richer theories obtained by classical inference or other means. Computational inference, which refers to the construction of models and validation of logical properties, is based on Stochastic Gradient Descent (SGD) and Markov Chain Monte Carlo (MCMC) techniques and hence another dimension where approximations are involved. We also present the Logical Imagination Engine (LIME), a prototypical implementation of PALO based on TensorFlow. Albeit not limited to the biological domain, we illustrate its operation in a quite substantial bioinformatics machine learning application concerned with network synthesis and analysis in a recent DARPA project.

There is an abundance of complex dynamic systems that are critical to our daily lives and our society but that are hardly understood, and even with today's possibilities to sense and collect large amounts of experimental data, they are so complex and continuously evolving that it is unlikely that their dynamics will ever be understood in full detail. Nevertheless, through computational tools we can try to make the best possible use of the current technologies and available data. We believe that the most useful models will have to take into account the imbalance between system complexity and available data in the context of limited knowledge or multiple hypotheses. The complex system of biological cells is a prime example of such a system that is studied in systems biology and has motivated the methods presented in this paper. They were developed as part of the DARPA Rapid Threat Assessment (RTA) program, which is concerned with understanding of the mechanism of action (MoA) of toxins or drugs affecting human cells. Using a combination of Gaussian processes and abstract network modeling, we present three fundamentally different machine-learning-based approaches to learn causal relations and synthesize causal networks from high-dimensional time series data. While other types of data are available and have been analyzed and integrated in our RTA work, we focus on transcriptomics (that is gene expression) data obtained from high-throughput microarray experiments in this paper to illustrate capabilities and limitations of our algorithms. Our algorithms make different but overall relatively few biological assumptions, so that they are applicable to other types of biological data and potentially even to other complex systems that exhibit high dimensionality but are not of biological nature.