1. Homework 2
Let us simulate the savings experiment of Kojima et al. (2004) assuming that the learner models the hidden state of the world with a 3x1 vector that takes on a slow, medium, and fast time scales. As before, we assume that the learner makes the following assumptions:
1. The world has many hidden states. What I observe is a linear combination of these states.
2. The hidden states change from trial to trial. Some change slowly, others change fast.
3. The states that change fast have larger noise than states that change slow. A
The learner’s model of the world

2. Homework 2 (continued)
To simulate the Kojima et al. (2004) experiment, we will provide the learner with data y(n) that initially is at zero, then jumps up to 1, then is brought down to -1 until the learner’s estimate is back to zero, and then we check for savings by bringing y(n) back up to 1 (see below).
Using the Kalman filter approach, simulate the learner’s performance using the initial conditions given in the last slide.
Plot the y and yhat as a function of trial number. (yhat in a given trial is the current estimate of w times x). Is there savings?
Plot w1, w2, and w3.
Plot the diagonal elements of the uncertainty matrix. By end of training, which hidden state has the highest uncertainty?
The data the experimenter provides to the learner: