The Naive Discrimination Learning (NDL) approach is based on the Rescorla-Wagner learning theory (Rescorla & Wagner, 1972), which assumes that learners attempt to predict an outcome based on available cues. The association strength between an outcome and a set of cues increases if they often associate with one another. Alternatively, if a set of cues do not often associate with a certain outcome. Their association strength is weaker.
For example, when an infant keeps hearing “five” being pronounced as [faɪv], the association strength from the [faɪv] to the lexical outcome “five” gets stronger and stronger. At the same time, if the possible pronunciation [faːv] for “five” is rarely heard by the infant. The association strength from [faːv] to “five” is then weaker. For infants whose L1 system is not stable, the association strength between the outcome and its possible cues (e.g., pronunciations) are constantly updating depending on the type and the amount of language input. Rescorla and Wagner formulated such process into the following equations:
\[V_i^{t+1} = V_i^t+{\Delta}V_i^t,\]
The association strength at time t + 1 is equal to its previous association strength at time t modified by some change change in association strength \({\Delta}V_i^t\), which is defined as
\[\mathbf{\Delta}{V_i^t} = \begin{cases} 0 & if _{ABSENT} (C_i,t)\\ {\alpha}_i{\beta}_1({\lambda}-\sum_{present(C_j,t)}V_j) & if _{PRESENT} (C_j,t) \& _{PRESENT} (O,t),\\ {\alpha}_i{\beta}_2({\lambda}-\sum_{present(C_j,t)}V_j) & if _{PRESENT} (C_j,t) \& _{ABSENT} (O,t),\\ \end{cases}\]
Standard settings for the parameters are λ = 1, α1 = α2 = 0.1, β1 = β2 = 0.1. If a cue is not present in the input, its association strength is not changed. When the cue is present, the change in association strength depends on whether or not the outcome is present. Association strengths are increased when cue and outcome co-occur, and decreased when the cue occurs without the outcome. Furthermore, when more cues are present simultaneously, adjustments are more conservative. In this case, we can speak of cue competition. (Baayen, R. H. ,2011)To approximate assoication strength between cues and outcomes in the stable state (i.e. adults), Danks (2003) assumes \(V_i^{t+1} = V_i^t\), and proposes the following equilibrium equation \[Pr (O|C_j)-\sum_{j=0}^n Pr(C_j|C_i)V_j=0\]
The ndl package in R implements learning and classification models based on the Rescorla-Wagner equations and their equilibrium equations. I used this package for the current project.
Watch the following video for a short tutorial on the NDL approach and the ndl package.
Retrieved from https://www.youtube.com/watch?v=ee3p4canV8k