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We introduce a temporal feature encoding architecture called Time Series Representation Model (TSRM) for multivariate time series forecasting and imputation. The architecture is structured around CNN-based representation layers, each…
A general overview of the existing difference ring theory for symbolic summation is given. Special emphasis is put on the user interface: the translation and back translation of the corresponding representations within the term algebra and…
Data engineering pipelines are essential - albeit costly - components of predictive analytics frameworks requiring significant engineering time and domain expertise for carrying out tasks such as data ingestion, preprocessing, feature…
Time-series representation learning is a fundamental task for time-series analysis. While significant progress has been made to achieve accurate representations for downstream applications, the learned representations often lack…
Due to the importance of the lower bounding distances and the attractiveness of symbolic representations, the family of symbolic aggregate approximations (SAX) has been used extensively for encoding time series data. However, typical…
We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…
In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times…
This paper presents a novel framework for decentralized monitoring of Linear Temporal Logic (LTL), under the situation where processes are synchronous, uniform (i.e. all processes are peers), and the formula is represented as a tableau. The…
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of…
In time-series analysis, many recent works seek to provide a unified view and representation for time-series across multiple domains, leading to the development of foundation models for time-series data. Despite diverse modeling techniques,…
The ability to detect anomalies in time series is considered highly valuable in numerous application domains. The sequential nature of time series objects is responsible for an additional feature complexity, ultimately requiring specialized…
A recently proposed history formalism is used to define temporal entanglement in quantum systems, and compute its entropy. The procedure is based on the time-reduction of the history density operator, and allows a symmetrical treatment of…
Time series analysis remains a major challenge due to its sparse characteristics, high dimensionality, and inconsistent data quality. Recent advancements in transformer-based techniques have enhanced capabilities in forecasting and…
Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures,…
Algebraic statistics is a recently evolving field, where one would treat statistical models as algebraic objects and thereby use tools from computational commutative algebra and algebraic geometry in the analysis and computation of…
The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…
In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel…
In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
This paper endeavors to learn time-varying graphs by using structured temporal priors that assume underlying relations between arbitrary two graphs in the graph sequence. Different from many existing chain structure based methods in which…