Stochastic computation of dominant eigenvalue and the law of total variance

Oja´s neuron is extended to find the dominant eigenvalue alongside the computation of the dominant eigenvector. This is achieved through a stochastic gradient descent learning rule that computes the second moment of the neuron output. The effectiveness of this family of learning rules is further demonstrated in a network that verifies the law of total variance. The inputs are generated by a doubly stochastic process, and conditional means and variances are accurately computed and propagated in the network. The law of total variance has been recently used in the analysis of biological experiments to explain neural processes.