Related papers: Partial Information Decomposition of Boolean Funct…
We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. This framework enables us to express an indirect…
When a machine-learning algorithm makes biased decisions, it can be helpful to understand the sources of disparity to explain why the bias exists. Towards this, we examine the problem of quantifying the contribution of each individual…
A Boolean network (BN) with $n$ components is a discrete dynamical system described by the successive iterations of a function $f:\{0,1\}^n \to \{0,1\}^n$. This model finds applications in biology, where fixed points play a central role.…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
By means of partial fraction method, we investigate the decomposition of rational functions. Several striking identities on harmonic numbers and generalized Apery numbers will be established, including the binomial-harmonic number identity…
The information decomposition problem requires an additive decomposition of the mutual information between the input and target variables into nonnegative terms. The recently introduced solution to this problem, Information Attribution,…
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…
An important issue during an engineering design process is to develop an understanding which design parameters have the most influence on the performance. Especially in the context of optimization approaches this knowledge is crucial in…
Despite the impressive performance of biological and artificial networks, an intuitive understanding of how their local learning dynamics contribute to network-level task solutions remains a challenge to this date. Efforts to bring learning…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
The Bayesian and Akaike information criteria aim at finding a good balance between under- and over-fitting. They are extensively used every day by practitioners. Yet we contend they suffer from at least two afflictions: their penalty…
This paper explores algorithms for processing probabilistic and deterministic information when the former is represented as a belief network and the latter as a set of boolean clauses. The motivating tasks are 1. evaluating beliefs networks…
This paper characterizes the values of partial regression coefficients, defined as projection coefficients onto the space spanned by explanatory variables, for random variables generated by linear structural equation models using graphical…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
Bayesian optimization (BO) has proven to be an effective paradigm for the global optimization of expensive-to-sample systems. One of the main advantages of BO is its use of Gaussian processes (GPs) to characterize model uncertainty which…
In this paper we study a basic and natural question about Fourier analysis of Boolean functions, which has applications to the study of Matching Vector based Private Information Retrieval (PIR) schemes. For integers m and r, define a delta…
Scientists and practitioners increasingly rely on machine learning to model data and draw conclusions. Compared to statistical modeling approaches, machine learning makes fewer explicit assumptions about data structures, such as linearity.…
The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…
Since the early 1900s, numerous research efforts have been devoted to developing quantitative solutions to stochastic mechanical systems. In general, the problem is perceived as solved when a complete or partial probabilistic description on…
The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures…