Information Flows in Causal Networks

“These and other features distinguish this ‘‘intrinsic’’ notion of information from the ‘‘extrinsic’’, Shannon notion (see Text S3; cf. [21–23] for related approaches to information and causation in networks).”

“…the a posteriori repertoire by forcibly intervening in the system and imposing each state in the a priori repertoire, thus we implement a perturbational approach [1,2,4,6]; see also [8,9] which apply perturbations to measure the average interaction between subsets for general distributions.”

“, [31,32]) will ultimately be needed to provide a truly causal description of sensorimotor and neural networks.”

“The assumption of conditional independence distinguishes IIT’s causal analysis from standard information-theoretic analyses of information flow [13,31] and corresponds to an assumption that variables are “physical” units in the sense that they are irreducible within and can be observed and manipulated independently.”

“On the one hand, the study of the information flows in such a system gives important insights into the operation of the agent-environment system (Ay and Wennekers 2003; Lungarella and Sporns 2006; Ay and Polani 2008).”

“However, now that causal interventional measures and measures of information transfer can be clearly distinguished (Ay and Polani, 2008; Lizier and Prokopenko, 2010) it seems no longer warranted to map causal interactions to information transfer in a one-to-one manner.”

“…ways (e.g. using stimuli or direct intervention) and can predict the outcome of each manipulation for another other part of the system (e.g. the neurophysiological responses) in the form of probabilities we say that the manipulation was causal to the outcome (see [1,2] for a more formal account).”

“There also exists an alternative perturbation-based candidate that captures information flow from the perspective of causality rather than prediction [8].”

“Moreover, measures of information flow [5, 17] which are able to measure the overall amount of causal information flow, still struggle with over-determination (i.”

“3 Information flow After arguing that transfer entropy does not properly capture the strength of the impact of interventions, [10] proposes to define causal strength using Pearl’s do calculus [1].”

“This approach is inspired by the framework of causal interventions [72,73], in which causal effects are measured by counter-factually intervening on one part of a system and then measuring the resulting changes in other parts of the system.”

“When we speak about causal effect, we specifically consider the interventionist notion of causality in the sense of Pearl (2000) and the notion of causal information flow based upon it (Ay and Polani 2008).”

“This has far reaching consequences for the interpretation of the two measures: The intervention inherent in Strong’s method places it somewhat closer to causal measures such as Ay and Polani’s causal information flow [47], whereas intervention-free TE has a clear interpretation as the information transfered in relatio…”

“The fundamental reason for this is that information transfer relies on causal interactions, but non-zero transfer entropy can occur without direct causal links, and causal interactions do not necessarily lead to non-zero information transfer (Ay and Polani, 2008; Lizier and Prokopenko, 2010; Chicharro and Ledberg, 201…”

“In fact, a causal measure that is intimately related to TE, but employs Pearl’s ’do-formalism’ [56] for interventions, has been proposed by Ay and Polani [3].”

“…relationships and explore how the causal variables affect the predicted labels, the information theory, especially the idea of “information flow” [47], is improved and applied to measure the causal information among those core features, which can Authorized licensed use limited to the terms of…”

“In this way, the analysis captures how a mechanism in a state constrains a purview without being biased by whether certain states arise more frequently than others in the dynamical evolution of the system [3,4,11,16].”

“Others have outlined similar metrics, such as the information-theoretic causal power in 2005 [11] and the information flow in 2008 [12], which was renamed “causal specificity” in 2015 [13].”

“32 The motivation for such models can be, for instance, to describe a causal network (Ay and Polani, 2008; 33 Friston, 1994) or to model the directed information flow in the system (Vicente et al.”

“…an asymptote (in terms of each information bit’s contribution to the reduction of uncertainty), the theoretical costs of producing/decoding new information continues to accelerate, leading to the prediction that economically, communication systems have severe constraints (Ay & Polani, 2008).”

“Information flow was proposed as a measure for causal information flow by Ay and Polani [25], and it is important to realise a crucial difference between (1) transfer entropy and (2) information flow.”

“However, the idea of considering a post-interventional mutual information is similar to the one formalized in [35,36] using Pearl’s interventional calculus.”

“Other recent works in mathematics and computer science have brought information theory together with causal modeling to study information processing in complex systems ðAy and Polani 2008; Lizier and Prokopenko 2010Þ.”

“2 Maroney [25] argues that while a logically irreversible transformation of information does generate this amount of heat, it can in fact be accomplished by a thermodynamically reversible mechanism. thermodynamic interpretation of transfer entropy somewhat separately from the body of work relating57 Boltzmann and Shan…”

“We use this interchangeably with the terminology ‘information transfer’ and ‘information processing’, this is not the same concept of information flow as proposed by Ay & Polani, which is a measure of causation [23].”

“For a more general consideration, empowerment needs to be formulated using the perception-action loop and information flow formalism from [5,9,41] based on the framework of Causal Bayesian Networks [42].”

“For example, these questions might be better cast in terms of causal structure rather than as ‘informational’ in the Shannon sense (Ay and Poloni, 2007).”

“This also implies that the methods of Pearl [40] and its generalizations [41] give no insight on structure in these distributions.”

“dynamical evolution. This is because a discrete dynamical system 6 and the mechanisms of its elements are only specified fully by the transition probabilities of all possible system states (Eqn. 1) (Ay and Polani, 2008; Oizumi et al., 2014). For example, element E in Fig. 5C, an XNOR, can only be distinguished from th…”

“…that causal information of this sort is relevant for explanation (see also, Pacer et al., 2013), then alternatives to Kolmogorov Complexity that represent causal information (such as causal information flow, see Ay & Polani, 2008) may need to be developed to fully describe these relationships.”

“Importantly, this predictive information flow may or may not account for the causal information flow affecting the source and the destination (Ay and Polani 2008; Lizier and Prokopenko 2010)—however it does typically indicate presence of causality, either within the considered pair or from some common cause.”

“…by the history of the other process, but where the present state of each process is conditionally independent of the history of the other [96, 97] (e.g. one can have zero TE when a real causal connection exists, for instance, the system x t = y t − 1 , y t = x t − 1 , x 1 = 0 and y 1 =…”

“As noted by Ay and Polani [475], Bayesian networks have temporal structure; the nodes can be partitioned into sets such that if a node ∈ + A V t 1 then there exists a node ∈ B V t with an edge from B to A .”

“To address this issue, we leverage recent work on information-theoretic measures of causal influence [1].”

“X and Y mutually and deterministically cause one another through a copy operation ( Ay and Polani, 2011 ; Peters et al., 2017 ): X ( t ) copies Y ( t − 1) and vice versa.”

“A measure of “information flow” (IF) that accurately captures casual effects has been proposed by Ay and Polani [42], where causality is detected by using a measure similar to TE that replaces observational conditioning on the probability distributions (as used in TE) with interventional conditioning [40].”

“Empowerment is formalized as the maximal potential causal flow [29] from an agent’s actuators to an agent’s sensors at a later point in time.”

“Fig. 1(b)). The random variables C, A, W, and Srefer to the controller, actuator signals, world and sensor signals, and the directed edges re ect causal dependencies between the random variables (see [20, 21, 18]). Everything that is extrinsic is captured in the variable W, whereas S, C, and Aare intrinsic to the syst…”

“On the other hand, another line of thought leads to defining causal as “must have caused” which requires active interventions [44], [45] that are often impractical for the data analysis of large complex systems.”

“Additionally, to demonstrate the effect of reduced source entropy on transfer entropy, we estimated transfer entropy on simulated data with a constant coupling between processes, but a varying source entropy.”

“This interventional approach can be incorporated to the framework by adopting interventional information-theoretic measures suited to quantify causal effects (Ay and Polani, 2008; Lizier and Prokopenko, 2010; Chicharro and Ledberg, 2012b).”

““if I change the value of the source, to what extent does that alter the value of the target?” [74, 2, 56].”

“This formalism is used in a causal measure called information flow (Ay and Polani 2008), which is also based on the cMI.”

“1142/S0219525908001465 Blahut, R. (1972). Computation of channel capacity and rate-distortion functions. IEEE Trans. Info. Theory 18, 460–473. doi:10.1109/TIT.1972. 1054855 Boden, M., Bryson, J., Caldwell, D., Dautenhahn, K., Edwards, L., Kember, S., et al. (2011). “Principles of robotics,” in The United Kingdoms Engi…”

“It is a conditional mutual information [22], being the average information in the source yn about the next state of the destination xn+1 that was not already contained in the destination’s past x (k) n”

“…2001b) ✓ Excess Information (Crutchfield and Feldman, 2003; Feldman and Crutchfield, 2003) ✓ Effective Information (Hoel et al., 2013; Hoel, 2017) × Information Flow (Ay and Polani, 2008) × Partial Information Decomposition (Williams and Beer, 2010) × Evidence of Integration (Biehl et al., 2016)”

“Interventional methods are needed to supplement purely observational ones in order to distinguish information transfer from spurious correlations [13,1].”

“Another popular set of approaches in information and network sciences to study the causal relationships between subsystems are interventional methods [44,45].”

“In this way, our approach is more closely related to proposed measures of causal information flow [44,54], but evaluated in a state-dependent manner, as the information specified by the subset in its current state about its causes and effects (see also [55]).”

“This is more informal language than the technical meaning of “information flow” as formulated by Ay and Polani, which is a measure of causal flows [43].”

“Moreover, in general correlation and causation are hard to disentangle without causal interventions [59, 122, 123].”

“Rather than using traditional measures of information such as mutual information, CET uses causal information flow [Ay and Polani, 2008] to decide how the tree will grow.”

“2 ] 4 , 2 , 1 [ ], 4 , 2 , 1 [ 2 ] 2 [ ], 2 [ 2 ] 4 , 2 [ ], 4 , 2 [ 2 ] 2 , 1 [ ], 2 , 1 [ 2 ] 4 , 2 :, 1 [ ], 4 , 2 , 1 [ 3 2 ] 2 [ ], 2 [ 1 2 ] 4 , 2 [ ], 4 , 2 [ 2 2 ] 2 , 1 [ ], 2 , 1 [ 2 2”

“Combined with the notion of intervention, this also leads to measures of causal information flows [4].”

“Additionally, MSA can incorporate metrics and concepts that are already developed to infer causal structure in networks [38].”

“, perturbing the candidate cause variable to investigate its direct influence on the response variable [20, 21].”

“These include the transfer entropy (Schreiber, 2000; Lizier, 2014), which assumes a dynamical systems framework and that the system consists of identifiable components which can be tracked through time, and the causal information flow (Ay and Polani, 2008), which is defined in terms of general causal Bayesian networks…”

“131:14 X. Li et al. — Causal: The causal-based methods employ a range of techniques, such as information-theoretic measures of causal influence and Individual Causal Effects ( ICEs ) [81, 89], to measure causal effects of input features on prediction results.”