For these systems, a common issue is the difficulty of collecting sufficiently refined timescale data.

For these systems, a common issue is the difficulty of collecting sufficiently refined timescale data.

Identifying the underlying reason for a failing dynamic process or otherwise anomalous observation is a fundamental challenge, yet has numerous industrial applications. Identifying the failure-causing sub-system using causal inference, one can ask the question: "Would the observed failure also occur, if we had replaced the behaviour of a sub-system at a certain point in time with its normal behaviour?" To this end, a formal description of behaviour of the full system is needed in which such counterfactual questions can be answered. However, existing causal methods for root cause identification are typically limited to static settings and focusing on additive external influences causing failures rather than structural influences. In this paper, we address these problems by modelling the dynamic causal system using a Residual Neural Network and deriving corresponding counterfactual distributions over trajectories. We show quantitatively that more root causes are identified when an intervention is performed on the structural equation and the external influence, compared to an intervention on the external influence only. By employing an efficient approximation to a corresponding Shapley value, we also obtain a ranking between the different subsystems at different points in time being responsible for an observed failure, which is applicable in settings with large number of variables. We illustrate the effectiveness of the proposed method on a benchmark dynamic system as well as on a real world river dataset.

Inferring causal structures from time series data is the central interest of many scientific inquiries. A major barrier to such inference is the problem of subsampling, i.e., the frequency of measurement is much lower than that of causal influence. To overcome this problem, numerous methods have been proposed, yet either was limited to the linear case or failed to achieve identifiability. In this paper, we propose a constraint-based algorithm that can identify the entire causal structure from subsampled time series, without any parametric constraint. Our observation is that the challenge of subsampling arises mainly from hidden variables at the unobserved time steps. Meanwhile, every hidden variable has an observed proxy, which is essentially itself at some observable time in the future, benefiting from the temporal structure. Based on these, we can leverage the proxies to remove the bias induced by the hidden variables and hence achieve identifiability. Following this intuition, we propose a proxy-based causal discovery algorithm. Our algorithm is nonparametric and can achieve full causal identification. Theoretical advantages are reflected in synthetic and real-world experiments.

This study addresses the issue of balancing graph summarization and graph change detection. Graph summarization compresses large-scale graphs into a smaller scale. However, the question remains: To what extent should the original graph be compressed? This problem is solved from the perspective of graph change detection, aiming to detect statistically significant changes using a stream of summary graphs. If the compression rate is extremely high, important changes can be ignored, whereas if the compression rate is extremely low, false alarms may increase with more memory. This implies that there is a trade-off between compression rate in graph summarization and accuracy in change detection. We propose a novel quantitative methodology to balance this trade-off to simultaneously realize reliable graph summarization and change detection. We introduce a probabilistic structure of hierarchical latent variable model into a graph, thereby designing a parameterized summary graph on the basis of the minimum description length principle. The parameter specifying the summary graph is then optimized so that the accuracy of change detection is guaranteed to suppress Type I error probability (probability of raising false alarms) to be less than a given confidence level. First, we provide a theoretical framework for connecting graph summarization with change detection. Then, we empirically demonstrate its effectiveness on synthetic and real datasets.

In recent years, a growing number of method and application works have adapted and applied the causal-graphical-model framework to time series data. Many of these works employ time-resolved causal graphs that extend infinitely into the past and future and whose edges are repetitive in time, thereby reflecting the assumption of stationary causal relationships. However, most results and algorithms from the causal-graphical-model framework are not designed for infinite graphs. In this work, we develop a method for projecting infinite time series graphs with repetitive edges to marginal graphical models on a finite time window. These finite marginal graphs provide the answers to $m$-separation queries with respect to the infinite graph, a task that was previously unresolved. Moreover, we argue that these marginal graphs are useful for causal discovery and causal effect estimation in time series, effectively enabling to apply results developed for finite graphs to the infinite graphs. The projection procedure relies on finding common ancestors in the to-be-projected graph and is, by itself, not new. However, the projection procedure has not yet been algorithmically implemented for time series graphs since in these infinite graphs there can be infinite sets of paths that might give rise to common ancestors. We solve the search over these possibly infinite sets of paths by an intriguing combination of path-finding techniques for finite directed graphs and solution theory for linear Diophantine equations. By providing an algorithm that carries out the projection, our paper makes an important step towards a theoretically-grounded and method-agnostic generalization of a range of causal inference methods and results to time series.

We address in this study the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new temporal mutual information measure defined on a window-based representation of time series. We then show how this measure relates to an entropy reduction principle that can be seen as a special case of the Probabilistic Raising Principle. We finally combine these two ingredients in a PC-like algorithm to construct the summary causal graph. This algorithm is evaluated on several datasets that shows both its efficacy and efficiency.

Lying at the core of human intelligence, relational thinking is characterized by initially relying on innumerable unconscious percepts pertaining to relations between new sensory signals and prior knowledge, consequently becoming a recognizable concept or object through coupling and transformation of these percepts. Such mental processes are difficult to model in real-world problems such as in conversational automatic speech recognition (ASR), as the percepts (if they are modelled as graphs indicating relationships among utterances) are supposed to be innumerable and not directly observable. In this paper, we present a Bayesian nonparametric deep learning method called deep graph random process (DGP) that can generate an infinite number of probabilistic graphs representing percepts. We further provide a closed-form solution for coupling and transformation of these percept graphs for acoustic modeling. Our approach is able to successfully infer relations among utterances without using any relational data during training. Experimental evaluations on ASR tasks including CHiME-2 and CHiME-5 demonstrate the effectiveness and benefits of our method.

The continuing development of Semantic Web technologies and the increasing user adoption in the recent years have accelerated the progress incorporating explicit semantics with data on the Web. With the rapidly growing RDF (Resource Description Framework) data on the Semantic Web, processing large semantic graph data have become more challenging. Constructing a summary graph structure from the raw RDF can help obtain semantic type relations and reduce the computational complexity for graph processing purposes. In this paper, we addressed the problem of graph summarization in RDF graphs, and we proposed an approach for building summary graph structures automatically from RDF graph data. Moreover, we introduced a measure to help discover optimum class dissimilarity thresholds and an effective method to discover the type classes automatically. In future work, we plan to investigate further improvement options on the scalability of the proposed method.

Due to the dynamic nature of biological systems, biological networks underlying temporal process such as the development of {\it Drosophila melanogaster} can exhibit significant topological changes to facilitate dynamic regulatory functions. Thus it is essential to develop methodologies that capture the temporal evolution of networks, which make it possible to study the driving forces underlying dynamic rewiring of gene regulation circuity, and to predict future network structures. Using a new machine learning method called Tesla, which builds on a novel temporal logistic regression technique, we report the first successful genome-wide reverse-engineering of the latent sequence of temporally rewiring gene networks over more than 4000 genes during the life cycle of \textit{Drosophila melanogaster}, given longitudinal gene expression measurements and even when a single snapshot of such measurement resulted from each (time-specific) network is available. Our methods offer the first glimpse of time-specific snapshots and temporal evolution patterns of gene networks in a living organism during its full developmental course. The recovered networks with this unprecedented resolution chart the onset and duration of many gene interactions which are missed by typical static network analysis, and are suggestive of a wide array of other temporal behaviors of the gene network over time not noticed before.