This paper analyzes generalization of the classic Rescorla-Wagner (R- W) learning algorithm and studies their relationship to Maximum Like- lihood estimation of causal parameters. We prove that the parameters of two popular causal models, P and P C, can be learnt by the same generalized linear Rescorla-Wagner (GLRW) algorithm provided gener- icity conditions apply. We characterize the fixed points of these GLRW algorithms and calculate the fluctuations about them, assuming that the input is a set of i.i.d. We describe how to determine convergence conditions and calculate conver- gence rates for the GLRW algorithms under these conditions.

We show that linear generalizations of Rescorla-Wagner can perform Maximum Likelihood estimation of the parameters of all generative models for causal reasoning. Our approach involves augmenting variables to deal with conjunctions of causes, similar to the agumented model of Rescorla. Our results involve genericity assumptions on the distributions of causes. If these assumptions are violated, for example for the Cheng causal power theory, then we show that a linear Rescorla-Wagner can estimate the parameters of the model up to a nonlinear transformtion. Moreover, a nonlinear Rescorla-Wagner is able to estimate the parameters directly to within arbitrary accuracy. Previous results can be used to determine convergence and to estimate convergence rates.

We show that linear generalizations of Rescorla-Wagner can perform Maximum Likelihood estimation of the parameters of all generative models for causal reasoning. Our approach involves augmenting variables to deal with conjunctions of causes, similar to the agumented model of Rescorla. Our results involve genericity assumptions on the distributions of causes. If these assumptions are violated, for example for the Cheng causal power theory, then we show that a linear Rescorla-Wagner can estimate the parameters of the model up to a nonlinear transformtion. Moreover, a nonlinear Rescorla-Wagner is able to estimate the parameters directly to within arbitrary accuracy. Previous results can be used to determine convergence and to estimate convergence rates.

Moreover, a nonlinear Rescorla-Wagner is able to estimate the parameters directly to within arbitrary accuracy.