I don't like TikZ very much, since I always found it difficult to use. I realy like IPE, a good vector graphics editor that can do bezier curves. In addition, it saves as a pdf or eps, and can even (I believe) be converted to TikZ code via an add-on.
This is great.
I also want to suggest IPE as another option for making graphics and diagrams. IPE is extremely lightweight and easy to use, and you can insert LaTeX source. For anything complicated I use Inkscape; for anything simple I use IPE.
Ipe uses stylesheets to define what presets are available in the UI. If you don't want to stick to the defaults (which work well for use in papers) you should make a new stylesheet with your own values and include that in your documents though Edit > Stylesheets.
Excellently explained. Here are my thoughts on how you can make it even better!
Add diagrams! I recommend IPE to do this
> What should the parameters of a HMM be given a training sequence of observations ?
Add a comma after 'be'.
Add a sentence around this: "With the understanding of what a HMM is, we can pose three meaningful questions:" saying something like "A HMM is therefore defined by the two matrices, A and B, and whenever I say 'HMM' in future, I mean those two matrices." Or maybe change "We will denote a particular HMM as lambda." to "We will denote a particular HMM (i.e. the matrices A and B) as lambda."
Is there any reason you change from S to Q?
Move the motivation further up.
Diagrams!!!
Anyway, good job.