A mixed filter algorithm for cognitive state estimation from simultaneously recorded continuous and binary measures of performance

Abstract

Continuous (reaction times) and binary (correct/incorrect responses) measures of performance are routinely recorded to track the dynamics of a subject's cognitive state during a learning experiment. Current analyses of experimental data from learning studies do not consider the two performance measures together and do not use the concept of the cognitive state formally to design statistical methods. We develop a mixed filter algorithm to estimate the cognitive state modeled as a linear stochastic dynamical system from simultaneously recorded continuous and binary measures of performance. The mixed filter algorithm has the Kalman filter and the more recently developed recursive filtering algorithm for binary processes as special cases. In the analysis of a simulated learning experiment the mixed filter algorithm provided a more accurate and precise estimate of the cognitive state process than either the Kalman or binary filter alone. In the analysis of an actual learning experiment in which a monkey's performance was tracked by its series of reaction times, and correct and incorrect responses, the mixed filter gave a more complete description of the learning NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript process than either the Kalman or binary filter. These results establish the feasibility of estimating cognitive state from simultaneously recorded continuous and binary performance measures and suggest a way to make practical use of concepts from learning theory in the design of statistical methods for the analysis of data from learning experiments.

A Mixed Filter Algorithm for State Estimation from Simultaneously Recorded Continuous-Valued Point Process and Binary Observations

“…Therefore, Kolmogorov-Smirnov (KS) plots can be used to measure agreement between the z i s and the uniform probability density [5] with confidence bounds. b) continuous observations [6] Measuring the amount of time it takes before a monkey correctly/incorrectly performs a task, i.e. the reaction time, also provides us information about learning.…”

“…For trial k, the log of the reaction time, z l and the correct/incorrect trial response m l ∈ {0, 1} have probabilistic relationships with an x l(k) where l(k) ∈ [k(L − 1), k(L)] 2 . More formally, we have the following model for the input/output relationships from x l to the point process [3], [7], continuous [6], and binary [2] valued random variables:…”

“…We develop a parametric model to characterize the cognitive state at millisecond l, given by x l , as a latent variable that evolves according to an AR process: [3], [7], [6], [2]:…”

Bidirectional modulation of human emotional conflict resolution using intracranial stimulation

“…Further, state-space models may allow for more precise mapping of behavior to neural activity, which enables more precise identification of targets for neurostimulation. The power of this state-space modeling approach has been shown in both learning and tests of cognitive flexibility (40,(43)(44)(45)(46)(47).…”

Discrete- and Continuous-Time Probabilistic Models and Algorithms for Inferring Neuronal UP and DOWN States

“…Smith and Brown (2003) extended the standard linear state-space model (SSM) with continuous state and observations to an SSM with a continuous state Markov-modulated point process, and an EM algorithm was developed for the hidden state estimation problem. Later the theory was extended to the SSM with mixed continuous, binary, and point process observations (Coleman & Brown, 2006; Prerau et al, 2008; Eden & Brown, 2008), but the latent process was still limited to the continuous-valued state. In a similar context, Danóczy and Hahnloser (2006) also proposed a two-state HMM for detecting the “singing-like” and “awake-like” states of sleeping songbirds with neural spike trains; their model assumes a continuous-time Markov chain (with the assumption of knowing the exact timing of state transitions), and the sojourn time follows an exponential distribution; in addition, the CIF of the point process was assumed to be discrete in their work.…”