Related papers: Lossless Compression and Complexity of Chaotic Seq…
We live in a data-driven era that involves the generation, collection and processing of a massive amount of data. This data often contains valuable intellectual property and sensitive user information that must be safeguarded. There is a…
We introduce a new class of measurement matrices for compressed sensing, using low order summaries over binary sequences of a given length. We prove recovery guarantees for three reconstruction algorithms using the proposed measurements,…
We investigate symbolic sequences and in particular information carriers as e.g. books and DNA--strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is…
Graphical data is comprised of a graph with marks on its edges and vertices. The mark indicates the value of some attribute associated to the respective edge or vertex. Examples of such data arise in social networks, molecular and systems…
Algorithms for rare event complex systems simulations are proposed. Compressed Sensing (CS) has {\it revolutionized} our understanding of limits in signal recovery and has forced us to re-define Shannon-Nyquist sampling theorem for sparse…
Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn),…
We study a new model-free algorithm to compute $\varepsilon$-optimal policies for average reward Markov decision processes, in the weakly communicating case. Given a generative model, our procedure combines a recursive sampling technique…
Implicit Neural Representations (INRs) are increasingly recognized as a versatile data modality for representing discretized signals, offering benefits such as infinite query resolution and reduced storage requirements. Existing signal…
The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…
We leverage the powerful lossy image compression algorithm BPG to build a lossless image compression system. Specifically, the original image is first decomposed into the lossy reconstruction obtained after compressing it with BPG and the…
Lossless and near-lossless image compression is of paramount importance to professional users in many technical fields, such as medicine, remote sensing, precision engineering and scientific research. But despite rapidly growing research…
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…
Noiseless compressive sensing is a two-steps setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on $\lone$ regularization, provides an efficient and…
Deep learning (DL) models, despite their remarkable success, remain vulnerable to small input perturbations that can cause erroneous outputs, motivating the recent proposal of probabilistic robustness (PR) as a complementary alternative to…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…
Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of…
We have recently established a strong connection between the Tent map (also known as Generalized Luroth Series or GLS which is a chaotic, ergodic and lebesgue measure preserving non-linear dynamical system) and Arithmetic coding which is a…
We propose a method for lossy image compression based on recurrent, convolutional neural networks that outperforms BPG (4:2:0 ), WebP, JPEG2000, and JPEG as measured by MS-SSIM. We introduce three improvements over previous research that…
Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we…