Related papers: A Differential Equation Approach to the Most-Infor…
We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…
We study the problem of conditional expectations in free random variables and provide closed formulas for the conditional expectation of resolvents of arbitrary non-commutative polynomials in free random variables onto the subalgebra of an…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
We discuss some conjectural inequalities that are related to singular integrals, martingales, quasiconformal mappings, and the calculus of variations. Specifically, we present evidence for a conjecture of Iwaniec concerning the best…
We consider the Courtade-Kumar most informative Boolean function conjecture for balanced functions, as well as a conjecture by Li and M\'edard that dictatorship functions also maximize the $L^\alpha$ norm of $T_pf$ for $1\leq\alpha\leq2$…
We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The…
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…
Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…
Evolving Boolean functions with specific properties is an interesting optimization problem since, depending on the combination of properties and Boolean function size, the problem can range from very simple to (almost) impossible to solve.…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
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…
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of…
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…
The ability of information processing in biologically motivated Boolean networks is of interest in recent information theoretic research. One measure to quantify this ability is the well known mutual information. Using Fourier analysis we…
The Courtade-Kumar conjecture posits that dictatorship functions maximize the mutual information between the function's output and a noisy version of its input over the Boolean hypercube. We present two significant advancements related to…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
In classic papers, Zellner demonstrated that Bayesian inference could be derived as the solution to an information theoretic functional. Below we derive a generalized form of this functional as a variational lower bound of a predictive…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
We consider debiased inference on finite-dimensional functionals of infinite-dimensional least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not…