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We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict…
Since its introduction in 2011, the partial information decomposition (PID) has triggered an explosion of interest in the field of multivariate information theory and the study of emergent, higher-order ("synergistic") interactions in…
Feature selection can efficiently identify the most informative features with respect to the target feature used in training. However, state-of-the-art vector-based methods are unable to encapsulate the relationships between feature samples…
The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique,…
An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates…
The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Software architecture optimization aims to enhance non-functional attributes like performance and reliability while meeting functional requirements. Multi-objective optimization employs metaheuristic search techniques, such as genetic…
User models play an important role in interaction design, supporting automation of interaction design choices. In order to do so, model parameters must be estimated from user data. While very large amounts of user data are sometimes…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current…
The interactions between parameters, model structure, and outputs can determine what inferences, predictions, and control strategies are possible for a given system. Parameter space reduction and parameter estimation---and, more generally,…
Information theory is a powerful tool to express principles to drive autonomous systems because it is domain invariant and allows for an intuitive interpretation. This paper studies the use of the predictive information (PI), also called…
We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of M\"obius inversion.…
Quantifying relationships between components of a complex system is critical to understanding the rich network of interactions that characterize the behavior of the system. Traditional methods for detecting pairwise dependence of time…
A central challenge in analyzing multivariate interactions within complex systems is to decompose how multiple inputs jointly determine an output. Existing approaches generally operate on observed probability distributions and can conflate…
The concept of autonomy is fundamental for understanding biological organization and the evolutionary transitions of living systems. Understanding how a system constitutes itself as an individual, cohesive, self-organized entity is a…
We develop a tractable and flexible approach for incorporating side information into dynamic optimization under uncertainty. The proposed framework uses predictive machine learning methods (such as $k$-nearest neighbors, kernel regression,…
Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…