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Register a new userInference of Causal Information Flow in Collective Animal Behavior
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Understanding and even defining what constitutes animal interactions remains a challenging problem. Correlational tools may be inappropriate for detecting communication between a set of many agents exhibiting nonlinear behavior. A different approach is to define coordinated motions in terms of an information theoretic channel of direct causal information flow. In this work, we consider time series data obtained by an experimental protocol of optical tracking of the insect species Chironomus riparius. The data constitute reconstructed 3-D spatial trajectories of the insects flight trajectories and kinematics. We present an application of the optimal causation entropy (oCSE) principle to identify direct causal relationships or information channels among the insects. The collection of channels inferred by oCSE describes a network of information flow within the swarm. We find that information channels with a long spatial range are more common than expected under the assumption that causal information flows should be spatially localized. The tools developed herein are general and applicable to the inference and study of intercommunication networks in a wide variety of natural settings.
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Causal inference is perhaps one of the most fundamental concepts in science, beginning originally from the works of some of the ancient philosophers, through today, but also weaved strongly in current work from statisticians, machine learning experts, and scientists from many other fields. This paper takes the perspective of information flow, which includes the Nobel prize winning work on Granger-causality, and the recently highly popular transfer entropy, these being probabilistic in nature. Our main contribution will be to develop analysis tools that will allow a geometric interpretation of information flow as a causal inference indicated by positive transfer entropy. We will describe the effective dimensionality of an underlying manifold as projected into the outcome space that summarizes information flow. Therefore contrasting the probabilistic and geometric perspectives, we will introduce a new measure of causal inference based on the fractal correlation dimension conditionally applied to competing explanations of future forecasts, which we will write $GeoC_{yrightarrow x}$. This avoids some of the boundedness issues that we show exist for the transfer entropy, $T_{yrightarrow x}$. We will highlight our discussions with data developed from synthetic models of successively more complex nature: then include the H{e}non map example, and finally a real physiological example relating breathing and heart rate function. Keywords: Causal Inference; Transfer Entropy; Differential Entropy; Correlation Dimension; Pinskers Inequality; Frobenius-Perron operator.
With new advancements in technology, it is now possible to collect data for a variety of different metrics describing tumor growth, including tumor volume, composition, and vascularity, among others. For any proposed model of tumor growth and treatment, we observe large variability among individual patients parameter values, particularly those relating to treatment response; thus, exploiting the use of these various metrics for model calibration can be helpful to infer such patient-specific parameters both accurately and early, so that treatment protocols can be adjusted mid-course for maximum efficacy. However, taking measurements can be costly and invasive, limiting clinicians to a sparse collection schedule. As such, the determination of optimal times and metrics for which to collect data in order to best inform proper treatment protocols could be of great assistance to clinicians. In this investigation, we employ a Bayesian information-theoretic calibration protocol for experimental design in order to identify the optimal times at which to collect data for informing treatment parameters. Within this procedure, data collection times are chosen sequentially to maximize the reduction in parameter uncertainty with each added measurement, ensuring that a budget of $n$ high-fidelity experimental measurements results in maximum information gain about the low-fidelity model parameter values. In addition to investigating the optimal temporal pattern for data collection, we also develop a framework for deciding which metrics should be utilized at each data collection point. We illustrate this framework with a variety of toy examples, each utilizing a radiotherapy treatment regimen. For each scenario, we analyze the dependence of the predictive power of the low-fidelity model upon the measurement budget.
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearls celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational one. In this framework, the primitive causal relations are encoded as functional dependencies in a Structural Causal Model (SCM), which are generally mapped into a Directed Acyclic Graph (DAG) in the absence of cycles. In this paper, by contrast, we capture causality without reference to graphs or functional dependencies, but with information fields and Witsenhausens intrinsic model. The three rules of do-calculus reduce to a unique sufficient condition for conditional independence, the topological separation, which presents interesting theoretical and practical advantages over the d-separation. With this unique rule, we can deal with systems that cannot be represented with DAGs, for instance systems with cycles and/or spurious edges. We treat an example that cannot be handled-to the extent of our knowledge-with the tools of the current literature. We also explain why, in the presence of cycles, the theory of causal inference might require different tools, depending on whether the random variables are discrete or continuous.
Video analysis is currently the main non-intrusive method for the study of collective behavior. However, 3D-to-2D projection leads to overlapping of observed objects. The situation is further complicated by the absence of stall shapes for the majority of living objects. Fortunately, living objects often possess a certain symmetry which was used as a basis for morphological fingerprinting. This technique allowed us to record forms of symmetrical objects in a pose-invariant way. When combined with image skeletonization, this gives a robust, nonlinear, optimization-free, and fast method for detection of overlapping objects, even without any rigid pattern. This novel method was verified on fish (European bass, Dicentrarchus labrax, and tiger barbs, Puntius tetrazona) swimming in a reasonably small tank, which forced them to exhibit a large variety of shapes. Compared with manual detection, the correct number of objects was determined for up to almost $90 %$ of overlaps, and the mean Dice-Sorensen coefficient was around $0.83$. This implies that this method is feasible in real-life applications such as toxicity testing.
From philosophers of ancient times to modern economists, biologists and other researchers are engaged in revealing causal relations. The most challenging problem is inferring the type of the causal relationship: whether it is uni- or bi-directional or only apparent - implied by a hidden common cause only. Modern technology provides us tools to record data from complex systems such as the ecosystem of our planet or the human brain, but understanding their functioning needs detection and distinction of causal relationships of the system components without interventions. Here we present a new method, which distinguishes and assigns probabilities to the presence of all the possible causal relations between two or more time series from dynamical systems. The new method is validated on synthetic datasets and applied to EEG (electroencephalographic) data recorded in epileptic patients. Given the universality of our method, it may find application in many fields of science.
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