Related papers: The Fast M\"obius Transform: An algebraic approach…
The recent explosion of interest in multimodal applications has resulted in a wide selection of datasets and methods for representing and integrating information from different modalities. Despite these empirical advances, there remain…
Spuriousness arises when there is an association between two or more variables in a dataset that are not causally related. In this work, we propose an explainability framework to preemptively disentangle the nature of such spurious…
Mutual Information (MI) is a powerful statistical measure that quantifies shared information between random variables, particularly valuable in high-dimensional data analysis across fields like genomics, natural language processing, and…
Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
Partial Information Decomposition (PID) represents multivariate mutual information via antichain-lattice that aims to specify which source groups can recover which informational components of a target. For three or more sources, widely…
Describing statistical dependencies is foundational to empirical scientific research. For uncovering intricate and possibly non-linear dependencies between a single target variable and several source variables within a system, a principled…
Selecting a minimal feature set that is maximally informative about a target variable is a central task in machine learning and statistics. Information theory provides a powerful framework for formulating feature selection algorithms --…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
One of the key challenges in machine learning is to find interpretable representations of learned functions. The M\"obius transform is essential for this purpose, as its coefficients correspond to unique importance scores for sets of input…
A reaction-coordinate--resolved information-theoretic analysis of chemical reactivity is developed using mutual information and partial information decomposition (PID). Along an intrinsic reaction coordinate (IRC), a local empirical…
Multiscale Proper Orthogonal Decomposition (mPOD) decomposes fluid flows into energy-optimal modes within prescribed frequency bands by combining Proper Orthogonal Decomposition with a multiresolution analysis (MRA). In its classical…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
Partial information decomposition has recently found applications in biological signal processing and machine learning. Despite its impacts, the decomposition was introduced through an informal and heuristic route, and its exact operational…
Partial information decomposition allows the joint mutual information between an output and a set of inputs to be divided into components that are synergistic or shared or unique to each input. We consider five different decompositions and…
We build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection between information geometry and order theory leads to efficient…
Data denoising is a persistent challenge across scientific and engineering domains. Real-world data is frequently corrupted by complex, non-linear noise, rendering traditional rule-based denoising methods inadequate. To overcome these…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
In this paper, we define a new measure of the redundancy of information from a fault tolerance perspective. The partial information decomposition (PID) emerged last decade as a framework for decomposing the multi-source mutual information…