scholarly journals Information Guided Exploration of Scalar Values and Isocontours in Ensemble Datasets

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 540 ◽  
Author(s):  
Subhashis Hazarika ◽  
Ayan Biswas ◽  
Soumya Dutta ◽  
Han-Wei Shen
Keyword(s):  
Weather Forecasting ◽  
Conditional Entropy ◽  
Specific Information ◽  
Theoretic Approach ◽  
Information Theoretic ◽  
Information Measures ◽  
New Information ◽  
Real World Datasets ◽  
The Individual ◽  
Information Theoretic Approach

Uncertainty of scalar values in an ensemble dataset is often represented by the collection of their corresponding isocontours. Various techniques such as contour-boxplot, contour variability plot, glyphs and probabilistic marching-cubes have been proposed to analyze and visualize ensemble isocontours. All these techniques assume that a scalar value of interest is already known to the user. Not much work has been done in guiding users to select the scalar values for such uncertainty analysis. Moreover, analyzing and visualizing a large collection of ensemble isocontours for a selected scalar value has its own challenges. Interpreting the visualizations of such large collections of isocontours is also a difficult task. In this work, we propose a new information-theoretic approach towards addressing these issues. Using specific information measures that estimate the predictability and surprise of specific scalar values, we evaluate the overall uncertainty associated with all the scalar values in an ensemble system. This helps the scientist to understand the effects of uncertainty on different data features. To understand in finer details the contribution of individual members towards the uncertainty of the ensemble isocontours of a selected scalar value, we propose a conditional entropy based algorithm to quantify the individual contributions. This can help simplify analysis and visualization for systems with more members by identifying the members contributing the most towards overall uncertainty. We demonstrate the efficacy of our method by applying it on real-world datasets from material sciences, weather forecasting and ocean simulation experiments.

scholarly journals Renyi and Tsallis formulations of noise-disturbance trade-off relations

2016 ◽  
Vol 16 (3&4) ◽  
pp. 313-331
Author(s):  
Alexey E. Rastegin
Keyword(s):  
Probability Distributions ◽  
Conditional Entropy ◽  
Uncertainty Relations ◽  
Theoretic Approach ◽  
Trade Off ◽  
Information Theoretic ◽  
Entropic Uncertainty Relations ◽  
Related Information ◽  
Information Theoretic Measures ◽  
Information Theoretic Approach

We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R´enyi and Tsallis entropies. Related information-theoretic measures of noise and disturbance are introduced. These definitions are based on the concept of conditional entropy. To motivate introduced measures, some important properties of the conditional R´enyi and Tsallis entropies are discussed. There exist several formulations of entropic uncertainty relations for a pair of observables. Trade-off relations for noise and disturbance are derived on the base of known formulations of such a kind.

scholarly journals On the Anonymity Risk of Time-Varying User Profiles

2017 ◽  
Author(s):  
Silvia Puglisi ◽  
Jordi Forné ◽  
David Rebollo-Monedero
Keyword(s):  
User Profile ◽  
User Preferences ◽  
Third Party ◽  
Theoretic Approach ◽  
Time Varying ◽  
User Profiles ◽  
Information Theoretic ◽  
New Information ◽  
On Line ◽  
Information Theoretic Approach

Websites and applications use personalisation services to profile their users, collect their patterns and activities and eventually use this data to provide tailored suggestions. User preferences and social interactions are therefore aggregated and analysed. Every time a user publishes a new post or creates a link with another entity, either another user, or some on-line resource, new information is added to the user profile. Exposing private data does not only reveal information about single users' preferences, increasing their privacy risk, but can expose more about their network that single actors intended. This mechanism is self-evident on \emph{social networks} where users receive suggestions based on their friends' activity. We propose an information theoretic approach to measure the differential update of the anonymity risk for time-varying user profiles. This expresses how privacy is affected when new content is posted and how much third party services get to know about the users when a new activity is shared. We use real Facebook data to show how our model can be applied on a real world scenario.

Quantifying Stimulus Discriminability: A Comparison of Information Theory and Ideal Observer Analysis

2005 ◽  
Vol 17 (4) ◽  
pp. 741-778 ◽  
Author(s):  
Eric E. Thomson ◽  
William B. Kristan
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Conditional Entropy ◽  
Ideal Observer ◽  
Upper And Lower Bounds ◽  
Specific Information ◽  
Information Theoretic ◽  
Information Measures ◽  
Improved Performance ◽  
Ideal Observer Analysis

Performance in sensory discrimination tasks is commonly quantified using either information theory or ideal observer analysis. These two quantitative frameworks are often assumed to be equivalent. For example, higher mutual information is said to correspond to improved performance of an ideal observer in a stimulus estimation task. To the contrary, drawing on and extending previous results, we show that five information-theoretic quantities (entropy, response-conditional entropy, specific information, equivocation, and mutual information) violate this assumption. More positively, we show how these information measures can be used to calculate upper and lower bounds on ideal observer performance, and vice versa. The results show that the mathematical resources of ideal observer analysis are preferable to information theory for evaluating performance in a stimulus discrimination task. We also discuss the applicability of information theory to questions that ideal observer analysis cannot address.

scholarly journals SIMIT: Subjectively Interesting Motifs in Time Series

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 566 ◽  
Author(s):  
Junning Deng ◽  
Jefrey Lijffijt ◽  
Bo Kang ◽  
Tijl De Bie
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Synthetic Data ◽  
Series Data ◽  
Theoretic Approach ◽  
Information Theoretic ◽  
Novel Approach ◽  
Approximate Form ◽  
Real World Datasets ◽  
Information Theoretic Approach

Numerical time series data are pervasive, originating from sources as diverse as wearable devices, medical equipment, to sensors in industrial plants. In many cases, time series contain interesting information in terms of subsequences that recur in approximate form, so-called motifs. Major open challenges in this area include how one can formalize the interestingness of such motifs and how the most interesting ones can be found. We introduce a novel approach that tackles these issues. We formalize the notion of such subsequence patterns in an intuitive manner and present an information-theoretic approach for quantifying their interestingness with respect to any prior expectation a user may have about the time series. The resulting interestingness measure is thus a subjective measure, enabling a user to find motifs that are truly interesting to them. Although finding the best motif appears computationally intractable, we develop relaxations and a branch-and-bound approach implemented in a constraint programming solver. As shown in experiments on synthetic data and two real-world datasets, this enables us to mine interesting patterns in small or mid-sized time series.

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