Human Memory Search as Initial-Visit Emitting Random Walk
Imagine a random walk that outputs a state only when visiting it for the first time. The observed output is therefore a repeat-censored version of the underlying walk, and consists of a permutation of the states or a prefix of it. We call this model initial-visit emitting random walk (INVITE). Prior work has shown that the random walks with such a repeat-censoring mechanism explain well human behavior in memory search tasks, which is of great interest in both the study of human cognition and various clinical applications. However, parameter estimation in IN-VITE is challenging, because naive likelihood computation by marginalizing over infinitely many hidden random walk trajectories is intractable. In this paper, we propose the first efficient maximum likelihood estimate (MLE) for INVITE by decomposing the censored output into a series of absorbing random walks. We also prove theoretical properties of the MLE including identifiability and consistency. We show that INVITE outperforms several existing methods on real-world human response data from memory search tasks.
An initial-visit emitting random walk is a random walk that emits an output only when visiting a state for the first time. Previous researchers have used these walks to model human behavior data on memory search tasks (e.g., name as many animals as you can). The contributions of this paper are that it proposes a new and efficient way of computing a likelihood function for the model, it proves that the resulting maximum likelihood estimates are consistent, it presents a way of estimating parameter values using a regularized likelihood function, and it shows, via computer simulation, that the proposed parameter estimation procedure performs better than alternatives on a toy task and on real-world data collected (by others) in experiments with people.I should start by stating that this paper relies on areas of mathematics that I know nothing about.That said, I have a mixed opinion of this paper. On the one hand, the proposed way of computing a likelihood for the model seems extremely clever and a clear technical advance over previous efforts. In addition, the paper is very well-written. On the other hand, the paper is likely to appeal to a very small segment of the NIPS community. Initial-visit emitting random walks would seem to have limited applicability. Indeed, to my knowledge, they have only been studied by psychologists with interests in mathematical models of semantic memory search (a surprisingly small sub-community). In addition, the point of using these random walks is that they reveal something interesting about human memory search. However, although the current paper provides an improvement in fitting parameter values for these walks, it does not demonstrate any payoff in terms of revealing new information about human memory search. That is, the paper demonstrates improved parameter estimation but no payoff from these improved parameter estimates.But, but, but...perhaps I'm being too harsh. Maybe someone else will be able to use the parameter estimation procedure proposed here to learn something new about human memory search. I hope so.