Worth Reading

Stephen Della Pietra, Vincent Della Pietra, John Lafferty. Inducing Features of Random Fields. PAMI. 1997

This paper is quite theoretic and uses several important theorems of Mathematical Analysis. Well written and very readable.

page 4. Proof of proposition 1 and proposition 2 is not so straightforward as declared in the paper. So I just work it through step by step and here is the scanned version of my manuscript.
It's interesting to see in proposition 2 that the problem can be simplified into Bernoulii model.

Is there anyway that we can share our comments for papers?


Appendix I DUALITY. Lemma 4


4.b Auxiliary functions, Lemma3. One should notice the following theorem in Analysis:
For any compact set S and a sequence A in S, A must have a cluster point in S.

In proof of Proposition 5: because the sequence q^k belong to Q, so its cluster point must belong to the closure of Q.

Since Improved iterative Scaling algorithm is based on a bound function A(r,q), I strongly doubt that they could find an even better boundary function and further improve the convergence speed for the algorithm and I doubt that this problem could have already been solved somewhere in the optimization context.