(ML 14.5) Hidden Markov models (HMMs) (part 2)

Definition of a hidden Markov model (HMM). Description of the parameters of an HMM (transition matrix, emission probability distributions, and initial distribution). Illustration of a simple example of a HMM.

Category:

Education

Tags:

• machine learning
• statistics
• math

[Flute121]

By the way but "generated flow" I mean that is also a set of observed and monitored series of flow observed at the outlet of the catchment and not the artificial generating of numbers. Just for clarification. So, flow ~ f(rainfall, soil moisture) .

I don't have soil moisture and I want to know if HMM is a technique to create it?

[mathematicalmonk]

@Flute121 If you can estimate (or guess) the transition matrix and emission probabilities, then based on my understanding of your problem I think the answer is "yes", a HMM could work well.

[Flute121]

Hi, Thanks for the video, was helpful. I have a question: can I used HMM to guess, say, soil moisture time series from rainfall time series. For example, we have time series of rainfall for the past 7 months. Can I used it to develop how the soil moisture time series of the past 7 month was? I would appreciate your advice. Thanks!

[mathematicalmonk]

@Flute121 I'm not an expert on soil moisture and such things, but based on my non-expert understanding, I think it could work well for the problem you described. Here's how I would approach it: take the observed variable X_i to be the rainfall over the course of day i, and take the hidden variable Z_i to be Z_i=(S_i,S_{i+1}) where S_i is the soil moisture at time t=0 (or any consistent time) on day i.

[mathematicalmonk]

@Flute121

(part 2)

By using the *pair* of soil moistures (the moisture at the beginning and end of the day), the conditional independence assumptions make sense.

If you have time series data on soil moisture, you can use that to estimate the transition matrix. And if you have data with the soil moisture at the start and end of the day and the rainfall during those days, you could use that to estimate the emission probabilities.

[mathematicalmonk]

@Flute121

(part 3)

MAP would probably be preferable to MLE for making such estimates. In the absence of such data, another option is to just use your best guess for the transition matrix and emission probabilities.

Sounds like an interesting problem! Have fun!

[tarmizi2005]

I think the character recognition app uses the HMMs haha...but what i'm sure of is that most commercial speech recognition apps uses HMMs.. Neural Networks is another nice choice for pattern recognition tough... nice vid by the way !

[Jacob011]

These videos are splendid, they play in nicely to my whole curriculum.

[ArturoDezaPeru]

I like the way the dude makes ML look fun and entertaining. Your informality rocks!

[fokkinabber]

Thank you very much! Videos 14.1 to 14.5 have been very helpful in making me understand HMMs!

[Flute121]

Thanks for your response. In fact, this is a very common problem. The problem is I have generated flow times series and rainfall time series but I have no soil moisture time series recorded. Now I know the generated flow is a function of rainfall and soil moisture. I wanted to see if HMM is a good way to create a totally unexisting time series of soil moisture. Would this explanation change anything in your advice for me?