I tried to learn parameters of Hidden Markov Models using jsmile's EM class, and end up having quite different parameters from those from BNT(Bayes Net Toolbox for Matlab), given that I set the initial values of the parameters the same in both toolboxes. The possible reasons I could think of are:
1) the maximum iterations and convergence log-likelihood difference thresholds might be different, which I don't know how to set in jsmile.
2) there might be difference in the inference algorithm. In BNT, I checked that it uses "Online Junction tree inference algorithm for DBNs" with a smoother engine (which "creates an engine which does offline (fixed-interval) smoothing in O(T) space/time"). I am not sure the inference engine used in JSMILE.
3) there might be something wrong with how I prepared the HMM data and network files for jsmile, while I am quite sure the correctness of how I used BNT given that I have used it for over 1 year and have compared the result of it with other tools.
Here is a brief introduction of the network. I am constructing HMMs for inferring students' latent knowledge levels on three skills observing their correct/wrong performance on problems(items). There are in total three skills/knowledge components(KCs)/HMMs. For each one I specified one hidden variable (KC1, KC2, KC3) and an observable(C1, C2, C3), so in total there are 6 variables. In the data file for JSMILE, I created 7 time slices for each variable (6*7 columns). We can observe the observables of multiple HMMs at the same time (slices), but they can also be missing for other time slices. Each HMM is at most observed 4 times (e.g., C1 is observed at the 1st, 3rd, 5th and 7th time slices).
I attach here the two sets of parameters I got from JSMILE vs. BNT, the data file I prepared for JSMILE, and the relevant EM code. Particularly, I am using BNT-SM, a wrapper built based on BNT specialized for doing student modeling, i.e., using HMMs to infer students' latent knowledge levels. I already make sure the initial network passed to JSMILE has parameters the same as the initial parameters used for BNT.
EM code:
Code: Select all
public static void learnParameters(String networkFile, String dataFile, String learnedNetworkFile, Integer nbSlices) {
System.out.println("\nLearing parameters ...");
DataSet ds = new DataSet();
System.out.println("Reading data file " + dataFile);
ds.readFile(dataFile, "*");
Network net = new Network();
net.readFile(networkFile);
System.out.println("Reading network file " + networkFile);
DataMatch[] matching = null;
boolean dbn = (networkFile.contains("hmm") || networkFile.contains("wkt")) ? true : false;
if (dbn) {//here is the part for learning HMMs
assert nbSlices != null;
int nbVars = net.getAllNodeIds().length;//doesn't consider the timeslices
ArrayList<Integer> varsArray = new ArrayList<Integer>();
int[] nodes = net.getAllNodes();
for (int i = 0; i < nbVars; i++) {
int node = nodes[i];
String nodeId = net.getNodeId(node);
if (nodeId.contains("KC")) { //record hidden variables in varsArray so that we could match columns in the data file later
System.out.println("vars[" + varsArray.size() + "]: node=" + node + ", id=" + nodeId);
varsArray.add(node);
}
}
for (int i = 0; i < nbVars; i++) {
int node = nodes[i];
String nodeId = net.getNodeId(node);
if (!nodeId.contains("KC")) { //record observed variables in varsArray so that we could match columns in the data file later
System.out.println("vars[" + varsArray.size() + "]: node=" + node + ", nodeId=" + nodeId);
varsArray.add(node);
}
}
Integer[] vars = varsArray.toArray(new Integer[varsArray.size()]);
int nbColumns = nbVars * nbSlices;
// for matching the columns in the dataset, nodes in the network, and the time slices
matching = new DataMatch[nbColumns];
int i = 0;
for (i = 0; i < nbColumns; i++) {
System.out.println("\tMatching column " + i + " with vars[" + i / nbSlices + "] with node=" + vars[i / nbSlices] + " timeslice " + i % nbSlices);
matching[i] = new DataMatch(i, vars[i / nbSlices], i % nbSlices);
/* e.g., nbSlices = 7:
* 0-6 column in the data matches the variable 0 time slice 0-6;
* 7-13 .... 1...0-6
*/
}
} else {
matching = ds.matchNetwork(net);
}
final EM em = new EM();
em.setRandomizeParameters(false);
System.out.println("Starting learning em...");
em.learn(ds, net, matching);
net.writeFile(learnedNetworkFile);
System.out.println("Output to " + learnedNetworkFile);
}I'd appreciate if you could give me some clues how I can resolve the difference so that I could decide whether I could replace BNT with JSMILE, because JSMILE really has faster speed than BNT :D
Thank you so much,
Yun
Intelligent Systems Program
University of Pittsburgh