Related papers: Generalized redundancies for time series analysis

The use of deep neural networks to make high risk decisions creates a need for global and local explanations so that users and experts have confidence in the modeling algorithms. We introduce a novel technique to find global and local…

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…

We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability…

Since its introduction, the transformer has shifted the development trajectory away from traditional models (e.g., RNN, MLP) in time series forecasting, which is attributed to its ability to capture global dependencies within temporal…

Detecting structure in noisy time series is a difficult task. One intuitive feature is the notion of trend. From theoretical hints and using simulated time series, we empirically investigate the efficiency of standard recurrent neural…

A nonlinear generalisation of Schrodinger's equation is obtained using information-theoretic arguments. The nonlinearities are controlled by an intrinsic length scale and involve derivatives to all orders thus making the equation mildly…

An information theory description of finite systems explicitly evolving in time is presented for classical as well as quantum mechanics. We impose a variational principle on the Shannon entropy at a given time while the constraints are set…

We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…

These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…

Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably…

We present a general approach for studying autoregressive categorical time series models with dependence of infinite order and defined conditional on an exogenous covariate process. To this end, we adapt a coupling approach, developed in…

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…

Time series data can be subject to changes in the underlying process that generates them and, because of these changes, models built on old samples can become obsolete or perform poorly. In this work, we present a way to incorporate…

Correlation remains to be one of the most widely used statistical tools for assessing the strength of relationships between data series. This paper presents a novel compositional correlation method for detecting linear and nonlinear…

Temporal graphs model relationships among entities over time. Recent studies applied temporal graphs to abstract complex systems such as continuous communication among participants of social networks. Often, the amount of data is larger…

Here we present a novel approach to statistical analysis of financial time series. The approach is based on $n$-grams frequency dictionaries derived from the quantized market data. Such dictionaries are studied by evaluating their…

This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition). It aims to provide students…

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer…

A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…

Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have…