Partial Information Decomposition via Deficiency for Multivariate Gaussians

Bivariate partial information decompositions (PIDs) characterize how the information in a "message" random variable is decomposed between two "constituent" random variables in terms of unique, redundant and synergistic information components. These components are a function of the joint distribution of the three variables, and are typically defined using an optimization over the space of all possible joint distributions. This makes it computationally challenging to compute PIDs in practice and restricts their use to low-dimensional random vectors. To ease this burden, we consider the case of jointly Gaussian random vectors in this paper. This case was previously examined by Barrett (2015), who showed that certain operationally well-motivated PIDs reduce to a closed form expression for scalar messages. Here, we show that Barrett's result does not extend to vector messages in general, and characterize the set of multivariate Gaussian distributions that reduce to closed-form. Then, for all other multivariate Gaussian distributions, we propose a convex optimization framework for approximately computing a specific PID definition based on the statistical concept of deficiency. Using simplifying assumptions specific to the Gaussian case, we provide an efficient algorithm to approximately compute the bivariate PID for multivariate Gaussian variables with tens or even hundreds of dimensions. We also theoretically and empirically justify the goodness of this approximation.Comment: Presented at ISIT 2022. This version has been updated to reflect the final conference publication, including appendices. It also corrects technical errors in Remark 1 and Appendix C, adds a new experiment, and has a substantially improved presentation as well as additional detail in the appendix, compared to the previous arxiv versio

Inferring neural dynamics during burst suppression using a neurophysiology-inspired switching state-space model

Burst suppression is an electroencephalography (EEG) pattern associated with profoundly inactivated brain states characterized by cerebral metabolic depression. Its distinctive feature is alternation between short temporal segments of near-isoelectric inactivity (suppressions) and relatively high-voltage activity (bursts). Prior modeling studies suggest that burst-suppression EEG is a manifestation of two alternating brain states associated with consumption (during a burst) and production (during a suppression) of adenosine triphosphate (ATP). This finding motivates us to infer latent states characterizing alternating brain states and underlying ATP kinetics from instantaneous power of multichannel EEG using a switching state-space model. Our model assumes Gaussian distributed data as a broadcast network manifestation of one of two global brain states. The two brain states are allowed to stochastically alternate with transition probabilities that depend on the instantaneous ATP level, which evolves according to first-order kinetics. The rate constants governing the ATP kinetics are allowed to vary as first-order autoregressive processes. Our latent state estimates are determined from data using a sequential Monte Carlo algorithm. Our neurophysiology-informed model not only provides unsupervised segmentation of multi-channel burst-suppression EEG but can also generate additional insights on the level of brain inactivation during anesthesia.Comment: To appear in the proceedings of the 2020 IEEE Asilomar Conference on Signals, Systems, and Computer

Direct and Indirect Effects -- An Information Theoretic Perspective

Information theoretic (IT) approaches to quantifying causal influences have experienced some popularity in the literature, in both theoretical and applied (e.g. neuroscience and climate science) domains. While these causal measures are desirable in that they are model agnostic and can capture non-linear interactions, they are fundamentally different from common statistical notions of causal influence in that they (1) compare distributions over the effect rather than values of the effect and (2) are defined with respect to random variables representing a cause rather than specific values of a cause. We here present IT measures of direct, indirect, and total causal effects. The proposed measures are unlike existing IT techniques in that they enable measuring causal effects that are defined with respect to specific values of a cause while still offering the flexibility and general applicability of IT techniques. We provide an identifiability result and demonstrate application of the proposed measures in estimating the causal effect of the El Ni\~no-Southern Oscillation on temperature anomalies in the North American Pacific Northwest

Etiology of Burst Suppression EEG Patterns

Burst-suppression electroencephalography (EEG) patterns of electrical activity, characterized by intermittent high-power broad-spectrum oscillations alternating with isoelectricity, have long been observed in the human brain during general anesthesia, hypothermia, coma and early infantile encephalopathy. Recently, commonalities between conditions associated with burst-suppression patterns have led to new insights into the origin of burst-suppression EEG patterns, their effects on the brain, and their use as a therapeutic tool for protection against deleterious neural states. These insights have been further supported by advances in mechanistic modeling of burst suppression. In this Perspective, we review the origins of burst-suppression patterns and use recent insights to weigh evidence in the controversy regarding the extent to which burst-suppression patterns observed during profound anesthetic-induced brain inactivation are associated with adverse clinical outcomes. Whether the clinical intent is to avoid or maintain the brain in a state producing burst-suppression patterns, monitoring and controlling neural activity presents a technical challenge. We discuss recent advances that enable monitoring and control of burst suppression

Gastric Alimetry® test interpretation in gastroduodenal disorders : review and recommendations

Chronic gastroduodenal symptoms are prevalent worldwide, and there is a need for new diagnostic and treatment approaches. Several overlapping processes may contribute to these symptoms, including gastric dysmotility, hypersensitivity, gut–brain axis disorders, gastric outflow resistance, and duodenal inflammation. Gastric Alimetry® (Alimetry, New Zealand) is a non-invasive test for evaluating gastric function that combines body surface gastric mapping (high-resolution electrophysiology) with validated symptom profiling. Together, these complementary data streams enable important new clinical insights into gastric disorders and their symptom correlations, with emerging therapeutic implications. A comprehensive database has been established, currently comprising > 2000 Gastric Alimetry tests, including both controls and patients with various gastroduodenal disorders. From studies employing this database, this paper presents a systematic methodology for Gastric Alimetry test interpretation, together with an extensive supporting literature review. Reporting is grouped into four sections: Test Quality, Spectral Analysis, Symptoms, and Conclusions. This review compiles, assesses, and evaluates each of these aspects of test assessment, with discussion of relevant evidence, example cases, limitations, and areas for future work. The resultant interpretation methodology is recommended for use in clinical practice and research to assist clinicians in their use of Gastric Alimetry as a diagnostic aid and is expected to continue to evolve with further development

Information Theoretic Measures and Estimators of Specific Causal Influences

The need to measure causal influences between random variables or processes in complex networks arises throughout academic disciplines. In four parts, we here develop techniques for measuring and estimating causal influences using tools from information theory, with the explicit goal of providing context for how information theoretic perspectives on causal influence fit within the vast and interdisciplinary body of work studying causality. Throughout the dissertation, we demonstrate the utility of the proposed methods with applications to physiologic, economic, and climatological datasets. Beginning with a focus on time series, we present a modularized approach to finding the maximum a posteriori estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g., group sparsity) and/or non-Gaussian measurement models (e.g., point process observation models used in neuroscience). Importantly, this framework can be leveraged in the estimation of the latent parameters specifying the probability distribution of a time series, which is a fundamental step in the estimation of causal influences between time series. Second, we study the conditions under which directed information, a popular information theoretic notion of causal influence between time series, can be estimated without bias. While the assumptions made by estimators of directed information are often presented explicitly, a characterization of when we can expect these assumptions to hold is lacking. Using the concept of d-separation from Bayesian networks, we present sufficient and almost everywhere necessary conditions for which proposed estimators can be implemented without bias. We further introduce a notion of partial directed information, which can be used to bound the bias under a milder set of assumptions. Third, we present a sample path dependent measure of causal influence between time series. The proposed measure is a random sequence, a realization of which enables identification of specific patterns that give rise to high levels of causal influence. We demonstrate how sequential prediction theory may be leveraged to estimate the proposed causal measure and introduce a notion of regret for assessing the performance of such estimators which we subsequently bound. Finally, we extend our focus to general causal graphs and show that information theoretic measures of causal influence are fundamentally different from mainstream (e.g. statistical) notions in that they (1) compare distributions over the effect rather than values of the effect and (2) are defined with respect to random variables representing a cause rather than specific values of a cause. We leverage perspectives from the statistical causality literature to present a novel information theoretic framework for measuring direct, indirect, and total causal effects in natural complex networks. In addition to endowing information theoretic approaches with an enhanced "resolution," the proposed framework uniquely elucidates the relationship between the information theoretic and statistical perspectives on causality