"In both models, there's an unobserved state that changes over time according to relatively simple rules, and you get indirect information about that state every so often. In Kalman filters, you assume the unobserved state is Gaussian-ish and it moves continuously according to linear-ish dynamics (depending on which flavor of Kalman filter is being used). In HMMs, you assume the hidden state is one of a few classes, and the movement among these states uses a discrete Markov chain. In my experience, the algorithms are often pretty different for these two cases, but the underlying idea is very similar." - THISISDAVE
-- HMM vs LSTM/RNN:
"Some state-of-the-art industrial speech recognition [0] is transitioning from HMM-DNN systems to "CTC" (connectionist temporal classification), i.e., basically LSTMs. Kaldi is working on "nnet3" which moves to CTC, as well. Speech was one of the places where HMMs were _huge_, so that's kind of a big deal." -PRACCU
"HMMs are only a small subset of generative models that offers quite little expressiveness in exchange for efficient learning and inference." - NEXTOS
"IMO, anything that be done with an HMM can now be done with an RNN. The only advantage that an HMM might have is that training it might be faster using cheaper computational resources. But if you have the $$$ to get yourself a GPU or two, this computational advantage disappears for HMMs." - SHERJILOZAIR
Sometimes I wish I could quit my job for a few years and just catch up on all of the math I'd like to know. There is an amazing amount of stuff to learn that I just have no clue about and ultimately is much more interesting than yet another HR tool.
My advice is to just start a side programming project where you have to learn the concept. I think it's a much, much faster way of learning, to have to implement the technique, than to go through textbooks and exercises. I don't think most people who aren't career mathematicians will truly understand linear algebra until they write a few Matrix and Vector libraries in support of some other thing they are deeply interested in building.
Seconded. The slightly better option, if you can get away with it, is working it into a project at work (rather than a side project) so you can devote a few of your fresh-brained 9-5 hours to it each week and not feel too guilty.
I've done this, learning advanced orbital mechanics on my spare time. But I manage to put in 1-3 hours a week, about one week per month at most and it's been almost half a year since the last time I was able to put my mind into it.
It's not like I don't have the time, it's the fact that I'm way too tired after work to do any substantial amount of learning. I think I could manage something that's much easier, say learning some languages or learning how to knit. But learning math, physics, etc just requires more than I have to give after work.
That said, I managed to get a firm understanding of orbital mechanics up to a level where I could probably ace all the tests for freshman-level courses at an aerospace university and I did all of it on Saturday afternoons (but it took me 5 years to do so).
I have carved out 1 hour in my morning before work to do things that I consider important. It's not quite enough time. I'm going to try to improve it to 1.5 hours. But either way, it means the best of my brain goes to me. Sometimes I give it to my employer, but not always. Most likely, you don't need the best of your brainpower to do your day-to-day work.
This is a great technique. I have a 2.5 hour morning routine, I do before I head to the office.
You'll often hear about famous writers, hollywood-writers, etc. doing this type of technique of doing their best creative work before the chaos of the day sets in.
In my study project, I learned thoroughly how to solve different two body problems (initial value, boundary value, closest approach) and wrote a C library [0] that's got all the orbital mechanics code you need to write your own Kerbal Space Program clone (but I don't intend to do that). During the process, I read 3-4 books and an inch thick pile of research papers.
If you'd like to start looking at three-body problems, you might be interested in studying the Kozai-Lidov mechanism. It's a really fascinating subject, so much so that I did my dissertation on it! Here's a really good paper (one of my all time favorites) to get you started: https://arxiv.org/abs/1309.5244
Kalman filters (unless you get into really esoteric modifications) are just one tool and are related to stochastic processes. It's more like learning an algorithm than learning a whole field of math.
