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With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…

The covariance matrix is a foundation in numerous statistical and machine-learning applications such as Principle Component Analysis, Correlation Heatmap, etc. However, missing values within datasets present a formidable obstacle to…

The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…

Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of…

First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…

We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…

We aim at predicting a complete and high-resolution depth map from incomplete, sparse and noisy depth measurements. Existing methods handle this problem either by exploiting various regularizations on the depth maps directly or resorting to…

Correlation Plenoptic Imaging (CPI) is a novel technological imaging modality enabling to overcome drawbacks of standard plenoptic devices, while preserving their advantages. However, a major challenge in view of real-time application of…

Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…

Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…

Generating high-performance code for diverse hardware and application domains is challenging. Functional array programming languages with patterns like map and reduce have been successfully combined with term rewriting to define and explore…

A hallmark of object-oriented programming is the ability to perform computation through a set of interacting objects. A common manifestation of this style is the notion of a package, which groups a set of commonly used classes together. A…

Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a $d$-dimensional domain. The application of the inverse operator…

Saturation is considered the state-of-the-art method for computing fixpoints with decision diagrams. We present a relatively simple decision diagram operation called REACH that also computes fixpoints. In contrast to saturation, it does not…

In this submission, we explore the use of equality saturation to optimize concurrent computations. A concurrent environment gives rise to new optimization opportunities, like extracting a common concurrent subcomputation. To our knowledge,…

This paper presents a method to explain how the information of each input variable is gradually discarded during the forward propagation in a deep neural network (DNN), which provides new perspectives to explain DNNs. We define two types of…

We consider the Demand Strip Packing problem (DSP), in which we are given a set of jobs, each specified by a processing time and a demand. The task is to schedule all jobs such that they are finished before some deadline $D$ while…

Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…

Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…