Causal Consistency of Structural Equation Models

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.Comment: equal contribution between Rubenstein and Weichwald; accepted manuscrip

Principal Patterns on Graphs: Discovering Coherent Structures in Datasets

Graphs are now ubiquitous in almost every field of research. Recently, new research areas devoted to the analysis of graphs and data associated to their vertices have emerged. Focusing on dynamical processes, we propose a fast, robust and scalable framework for retrieving and analyzing recurring patterns of activity on graphs. Our method relies on a novel type of multilayer graph that encodes the spreading or propagation of events between successive time steps. We demonstrate the versatility of our method by applying it on three different real-world examples. Firstly, we study how rumor spreads on a social network. Secondly, we reveal congestion patterns of pedestrians in a train station. Finally, we show how patterns of audio playlists can be used in a recommender system. In each example, relevant information previously hidden in the data is extracted in a very efficient manner, emphasizing the scalability of our method. With a parallel implementation scaling linearly with the size of the dataset, our framework easily handles millions of nodes on a single commodity server

ExplainIt! -- A declarative root-cause analysis engine for time series data (extended version)

We present ExplainIt!, a declarative, unsupervised root-cause analysis engine that uses time series monitoring data from large complex systems such as data centres. ExplainIt! empowers operators to succinctly specify a large number of causal hypotheses to search for causes of interesting events. ExplainIt! then ranks these hypotheses, reducing the number of causal dependencies from hundreds of thousands to a handful for human understanding. We show how a declarative language, such as SQL, can be effective in declaratively enumerating hypotheses that probe the structure of an unknown probabilistic graphical causal model of the underlying system. Our thesis is that databases are in a unique position to enable users to rapidly explore the possible causal mechanisms in data collected from diverse sources. We empirically demonstrate how ExplainIt! had helped us resolve over 30 performance issues in a commercial product since late 2014, of which we discuss a few cases in detail.Comment: SIGMOD Industry Track 201

Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation

The applicability of the so-called truncated Wigner approximation (-W) is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. Firstly, what class of multitime averages the -W approximates, and, secondly, how to proceed if the average in question does not belong to this class. To answer the first question we develop an (in principle, exact) path-integral approach in phase-space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The -W equations emerge as an approximation within this path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages Kubo's renowned formula relating the linear response function to two-time commutators suffices. The -W is trivially generalised to the response properties of the system allowing one to calculate approximate time-normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.Comment: 20 pages, 6 figure

Perspectives on the Neuroscience of Cognition and Consciousness

The origin and current use of the concepts of computation, representation and information in Neuroscience are examined and conceptual flaws are identified which vitiate their usefulness for addressing problems of the neural basis of Cognition and Consciousness. In contrast, a convergence of views is presented to support the characterization of the Nervous System as a complex dynamical system operating in the metastable regime, and capable of evolving to configurations and transitions in phase space with potential relevance for Cognition and Consciousness

Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system's behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages, and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively), and provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv requirements; write first author for higher-resolution version