Quantifying the Predictability of Visual Scanpaths Using Active Information Storage

Abstract

Entropy-based measures are an important tool for studying human gaze behavior under various conditions. In particular, gaze transition entropy (GTE) is a popular method to quantify the predictability of a visual scanpath as the entropy of transitions between fixations and has been shown to correlate with changes in task demand or changes in observer state. Measuring scanpath predictability is thus a promising approach to identifying viewers’ cognitive states in behavioral experiments or gaze-based applications. However, GTE does not account for temporal dependencies beyond two consecutive fixations and may thus underestimate the actual predictability of the current fixation given past gaze behavior. Instead, we propose to quantify scanpath predictability by estimating the active information storage (AIS), which can account for dependencies spanning multiple fixations. AIS is calculated as the mutual information between a processes’ multivariate past state and its next value. It is thus able to measure how much information a sequence of past fixations provides about the next fixation, hence covering a longer temporal horizon. Applying the proposed approach, we were able to distinguish between induced observer states based on estimated AIS, providing first evidence that AIS may be used in the inference of user states to improve human–machine interaction.

Information theoretic evidence for layer- and frequency-specific changes in cortical information processing under anesthesia

“…We assume that a stochastic process Y recorded from a system (e.g cortical or layers sites), can be treated as a realizations y t of random variables Y t that form a random process Y = {Y 1 ..., Y t , ..., Y N }, describing the system dynamics. Then, AIS is defined as the (differential) mutual information between the future of a signal and its immediate past state [3,7,22]:…”

“…We assume that a stochastic process 𝒴 recorded from a system (e.g cortical or layers sites), can be treated as a realizations y t of random variables Y t that form a random process Y = { Y 1 …, Y t , …, Y N }, describing the system dynamics. Then, AIS is defined as the (differential) mutual information between the future of a signal and its immediate past state [3, 7, 22]: where Y is a random process with present value Y t , and past state , with δ i = i Δ t , where Δ t is the sampling interval of the process observation, and δ 1 ≤ δ i ≤ δ k . Y <t is a vector of random variables chosen from Y from the past of the current time point t .…”

Information theoretic evidence for layer- and frequency-specific changes in cortical information processing under anesthesia

“…We assume that a stochastic process Y recorded from a system (e.g cortical or layers sites), can be treated as a realizations y t of random variables Y t that form a random process Y ¼ fY 1 :::; Y t ; :::; Y N g, describing the system dynamics. Then, AIS is defined as the (differential) mutual information between the future of a signal and its immediate past state [3,7,24]:…”

“…We assume that a stochastic process recorded from a system (e.g cortical or layers sites), can be treated as a realizations y t of random variables Y t that form a random process , describing the system dynamics. Then, AIS is defined as the (differential) mutual information between the future of a signal and its immediate past state [ 3 , 7 , 24 ]: where Y is a random process with present value Y t , and past state , with δ i = i Δ t , where Δ t is the sampling interval of the process observation, and δ 1 ≤ δ i ≤ δ k . Y < t is a vector of random variables chosen from the process from the past of the current time point t .…”