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We investigate the task of retrieving information from compositional distributed representations formed by Hyperdimensional Computing/Vector Symbolic Architectures and present novel techniques which achieve new information rate bounds.…
We study multivariate problems like function approximation, numerical integration, global optimization and dispersion. We obtain new results on the information complexity $n(\varepsilon,d)$ of these problems. The information complexity is…
We study lower bounds on the worst-case error of numerical integration in tensor product spaces. As reference we use the $N$-th minimal error of linear rules that use $N$ function values. The information complexity is the minimal number $N$…
The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…
The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of interest $\theta$ is reduced on average by collecting relevant…
In this paper we pose the question: After gathering N data points, at what value of the control parameter should the next measurement be done? We propose an on-line algorithm which samples optimally by maximizing the gain in information on…
We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely upon sampling large numbers of training…
The aim of this work is to verify the new entropic and information inequalities for non-composite systems using experimental $5 \times 5$ density matrix of the qudit state, measured by the tomographic method in a multi-level superconducting…
Dey and Xin (J.Appl.Comput.Top., 2022, arXiv:1904.03766) describe an algorithm to decompose finitely presented multiparameter persistence modules using a matrix reduction algorithm. Their algorithm only works for modules whose generators…
In this paper, we investigate the problem of optimization multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction…
The body morphology plays an important role in the way information is perceived and processed by an agent. We address an information theory (IT) account on how the precision of sensors, the accuracy of motors, their placement, the body…
We present $\texttt{Maxent}$, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
We consider the problem of finding an informative path through a graph, given initial and terminal nodes and a given maximum path length. We assume that a linear noise corrupted measurement is taken at each node of an underlying unknown…
This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…
To alleviate the expensive human labeling, semi-supervised semantic segmentation employs a few labeled images and an abundant of unlabeled images to predict the pixel-level label map with the same size. Previous methods often adopt…
The authors have recently defined the R\'enyi information dimension rate $d(\{X_t\})$ of a stationary stochastic process $\{X_t,\,t\in\mathbb{Z}\}$ as the entropy rate of the uniformly-quantized process divided by minus the logarithm of the…
We use density evolution to optimize the parameters of binary product codes (PCs) decoded based on the recently introduced iterative bounded distance decoding with scaled reliability. We show that binary PCs with component codes of 3-bit…
Multipartite entanglement is a crucial resource for a wide range of quantum information processing tasks, including quantum metrology, quantum computing, and quantum communication. The verification of multipartite entanglement, along with…
X3 is a lossless optimizing dictionary-based data compressor. The algorithm uses a combination of a dictionary, context modeling, and arithmetic coding. Optimization adds the ability to find the most appropriate parameters for each file.…