Finding a good structure for the Dynamic Trees Bayesian Networks
Today I have a chance to talk with Sudir and Shalom @ CNEL after our ITL class
The discussion was about finding a good structure for a DTs using ITL unsupervised learning. Shalom and I discussed about Sinisa’s work, using wavelets as features in DTs, how to make a different scale images that still have some correlation between the same pixels in the different scales.
- How to incorporate ITL unsupervised clustering into the Dynamic Trees Bayesian Networks. First I read the paper from Jenssen, the paper is very easy to understand and gives very clear idea of how we can use the ITL for making DAG unsupervisedly. However, the work is pretty much heuristic and computationally expensive since we have to tune the sigma and we have to find the direction of force for each point in the space which takes very long time. As Sudir’s work is more convenient since it gives a closed-form update rules for each point, therefore, I will use his segmentation method to build the structure. For this work, the only parameter we will have to play with is sigma; smaller sigma gives more number of clusters. On the other hand, bigger sigma gives smaller number of clusters. Consequently we will use the small sigma at the leaf nodes and big sigma at the root node.
- We may use the wavelets coefficients as features for finding DTs structure. There are 2 classic papers to read: 1) “Wavelet-based statistical signal processing using hidden Markov models” (1998) by Crouse, M.S. Nowak, R.D. Baraniuk, R.G. and 2) “Approximating discrete probability distributions with dependence trees” (1968) Chow, C.; Liu, C.
- We can make observations in each scale by using wavelet decompose the image into several scale, then we might be able to reconnect the links.
- We can also make observations in each scale by using Gaussian blur, resample (Sinisa’s work) applied to the image, then find some relationship between the upper-scale pixels and the lower-scale pixels. However, using Gaussian blur may not be a powerful method because it does not show much about the relationship across the scale, whereas, the wavelets and resampling might do a good job on that.
- If we really want to make a multi-scale image by bluring, we will have to design a blur function such that it will boost or remain the relationship between the across-scale pixels. How can we design such a blur function? Of course it might be an adaptive one!!!