Paper: Type-safe, Polyvariadic Event Correlation

The pivotal role that event correlation technology plays in todays applications has lead to the emergence of different families of event correlation approaches with a multitude of specialized correlation semantics, including computation models that support the composition and extension of different semantics. However, type-safe embeddings of extensible and composable event patterns into statically-typed general-purpose programming languages have not been systematically explored so far. Event correlation technology has often adopted well-known and intuitive notations from database queries, for which approaches to type-safe embedding do exist. However, we argue in the paper that these approaches, which are essentially descendants of the work on monadic comprehensions, are not well-suited for event correlations and, thus, cannot without further ado be reused/re-purposed for embedding event patterns. To close this gap we propose PolyJoin, a novel approach to type-safe embedding for fully polyvariadic event patterns with polymorphic correlation semantics. Our approach is based on a tagless final encoding with uncurried higher-order abstract syntax (HOAS) representation of event patterns with n variables, for arbitrary $n \in \mathbb{N}$. Thus, our embedding is defined in terms of the host language without code generation and exploits the host language type system to model and type check the type system of the pattern language. Hence, by construction it impossible to define ill-typed patterns. We show that it is possible to have a purely library-level embedding of event patterns, in the familiar join query notation, which is not restricted to monads. PolyJoin is practical, type-safe and extensible. An implementation of it in pure multicore OCaml is readily usable.

Paper: Precision annealing Monte Carlo methods for statistical data assimilation and machine learning

In statistical data assimilation (SDA) and supervised machine learning (ML), we wish to transfer information from observations to a model of the processes underlying those observations. For SDA, the model consists of a set of differential equations that describe the dynamics of a physical system. For ML, the model is usually constructed using other strategies. In this paper, we develop a systematic formulation based on Monte Carlo sampling to achieve such information transfer. Following the derivation of an appropriate target distribution, we present the formulation based on the standard Metropolis-Hasting (MH) procedure and the Hamiltonian Monte Carlo (HMC) method for performing the high dimensional integrals that appear. To the extensive literature on MH and HMC, we add (1) an annealing method using a hyperparameter that governs the precision of the model to identify and explore the highest probability regions of phase space dominating those integrals, and (2) a strategy for initializing the state space search. The efficacy of the proposed formulation is demonstrated using a nonlinear dynamical model with chaotic solutions widely used in geophysics.

Library: Local Gaussian Process Model for Large-Scale Dynamic Computer Experiments (DynamicGP)

Fits localized GP model for dynamic computer experiments via singular value decomposition of the response matrix Y for large N (the number of observations) using the algorithm proposed by Zhang et al. (2018) . The current version only supports 64-bit architecture.

Paper: Foundations for conditional probability

We analyze several formalizations of conditional probability and find a new one that encompasses all. Our main result is that a preference relation on random quantities called a plausible preorder induces a coherent conditional expectation; and vice versa, that every coherent function can be extended to a conditional expectation induced by a plausible preorder. The advantages of our approach include a convenient justification of probability laws by the properties of plausible preorders, independence on probability interpretations, or the ability to extend conditional probability to any nonzero condition. In particular, if C is a nonzero condition and \Prob is coherent, then it can be extended so that \Prob(0|C)=0, \Prob(C|C)=1 and \Prob(1|C)=1, no matter whether \Prob(C) is zero or whether it is defined.

Paper: Uncertainty and causal emergence in complex networks

The connectivity of a network conveys information about the dependencies between nodes. We show that this information can be analyzed by measuring the uncertainty (and certainty) contained in paths along nodes and links in a network. Specifically, we derive from first principles a measure known as effective information and describe its behavior in common network models. Networks with higher effective information contain more information within the dependencies between nodes. We show how subgraphs of nodes can be grouped into macro-nodes, reducing the size of a network while increasing its effective information, a phenomenon known as causal emergence. We find that causal emergence is common in simulated and real networks across biological, social, informational, and technological domains. Ultimately, these results show that the emergence of higher scales in networks can be directly assessed, and that these higher scales offer a way to create certainty out of uncertainty.

Paper: Quantifying Confounding Bias in Neuroimaging Datasets with Causal Inference

Neuroimaging datasets keep growing in size to address increasingly complex medical questions. However, even the largest datasets today alone are too small for training complex machine learning models. A potential solution is to increase sample size by pooling scans from several datasets. In this work, we combine 12,207 MRI scans from 15 studies and show that simple pooling is often ill-advised due to introducing various types of biases in the training data. First, we systematically define these biases. Second, we detect bias by experimentally showing that scans can be correctly assigned to their respective dataset with 73.3% accuracy. Finally, we propose to tell causal from confounding factors by quantifying the extent of confounding and causality in a single dataset using causal inference. We achieve this by finding the simplest graphical model in terms of Kolmogorov complexity. As Kolmogorov complexity is not directly computable, we employ the minimum description length to approximate it. We empirically show that our approach is able to estimate plausible causal relationships from real neuroimaging data.