Related papers: Entropy of Difference
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown…
We evaluated the impact of changing the observation scale over the entropy measures for text descriptions. MIDI coded Music, computer code and two human natural languages were studied at the scale of characters, words, and at the…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike…
Estimating the p-th frequency moment of data stream is a very heavily studied problem. The problem is actually trivial when p = 1, assuming the strict Turnstile model. The sample complexity of our proposed algorithm is essentially O(1) near…
Patch-based transformers have emerged as efficient and improved long-horizon modeling architectures for time series modeling. Yet, existing approaches rely on temporally-agnostic patch construction, where arbitrary starting positions and…
This paper presents a new period finding method based on conditional entropy that is both efficient and accurate. We demonstrate its applicability on simulated and real data. We find that it has comparable performance to other…
EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a…
As a new method for detecting change-points in high-resolution time series, we apply Maximum Mean Discrepancy to the distributions of ordinal patterns in different parts of a time series. The main advantage of this approach is its…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
We propose a method for computing the transfer entropy between time series using Ulam's approximation of the Perron-Frobenius (transfer) operator associated with the map generating the dynamics. Our method differs from standard transfer…
The aim of this paper is to study certain properties of the Kullback-Leibler distance between two positive integer numbers or between two ideals. We present some results related the entropy of a positive integer number and the divergence of…
A surrogate data analysis is presented, which is based on the fluctuations of the ``entropy'' $S$ defined in the natural time-domain [Phys. Rev. E {\bf 68}, 031106, 2003]. This entropy is not a static one as, for example, the Shannon…
We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In random dynamical system, this indicator coincides with the rate K of divergence of…
Anomalies are strange data points; they usually represent an unusual occurrence. Anomaly detection is presented from the perspective of Wireless sensor networks. Different approaches have been taken in the past, as we will see, not only to…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
Understanding the confidence with which a machine learning model classifies an input datum is an important, and perhaps under-investigated, concept. In this paper, we propose a new calibration metric, the Entropic Calibration Difference…
We study the problem of estimating the Earth Mover's Distance (EMD) between probability distributions when given access only to samples. We give closeness testers and additive-error estimators over domains in $[0, \Delta]^d$, with sample…
This thesis applies entropy as a model independent measure to address three research questions concerning financial time series. In the first study we apply transfer entropy to drawdowns and drawups in foreign exchange rates, to study their…
Experimental designs are tools which can dramatically reduce the number of simulations required by time-consuming computer codes. Because we don't know the true relation between the response and inputs, designs should allow one to fit a…