HiddenMarkovModel | A simple library for representing an HMM
kandi X-RAY | HiddenMarkovModel Summary
kandi X-RAY | HiddenMarkovModel Summary
A simple library for representing an HMM.
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QUESTION
Using the great TensorFlow Hidden Markov Model library, it is straightforward to model the following Dynamic Bayesian Network:
where Hi is the probability variable that represents the HMM and Si is the probability variable that represents observations.
What if I'd like to make H depend on yet another HMM (Hierarchical HMM) or simply other probability variable like this:
The HiddenMarkovModel
definition in TensorFlow looks like the following:
ANSWER
Answered 2021-Feb-21 at 19:02The TFP HiddenMarkovModel
implements message passing algorithms for chain-structured graphs, so it can't natively handle the graph in which the C
s are additional latent variables. I can think of a few approaches:
Fold the
C
s into the hidden stateH
, blowing up the state size. (that is, ifH
took values in1, ..., N
andC
took values in1, ..., M
, the new combined state would take values in1, ..., NM
).Model the chain conditioned on values for the
C
s that are set by some approximate inference algorithm. For example, if the Cs are continuous, you could fit them using gradient-based VI or MCMC:
QUESTION
I'm a little inexperienced about Hidden Markov Model. If I want to make a model of HMM for online handwriting recognition (which means handwriting recognition of letter that user draw live on device instead of recognizing image of letter), how is the parameter model? Like what are the:
- hidden states,
- observations,
- initial state probabilities,
- state transition probabilities,
- emission probabilities?
What I have right now maybe the observations, which is the array of { x, y, timestamp } that is each dot that I record from the user's finger movement on the tablet.
The system will only record/train/recognize one number at a time. Which means I have 10 (0 to 9) states???? Or 10 classification results?? From various website like this, I found that hidden states usually in form of "sequences", instead of one single state like that. What is the states then in this case?
...ANSWER
Answered 2020-Nov-11 at 05:46HMMs work well with temporal data, but it may be a suboptimal fit for this problem.
As you've identified, the observations {x, y, timestamp} are temporal in nature. As a result, it is best cast as the emissions of the HMM, while reserving the digits as states of the HMM.
- Explicitly, if numbers (0 to 9) are encoded as hidden states, then for a 100 x 100 "image", the emission can be one of 10000 possible pixels coordinates.
- The model predicts a digit state at every timestamp (on-line). The output is a non-unique pixel location. This is cumbersome but not impossible to encode (you'd just have a huge emission matrix).
- The initial state probabilities of which digit to start can be a uniform distribution (1/10). More cleverly, you can invoke Benford's law to approximate the frequency of digits appearing in text and distribute your starting probability accordingly.
- State transition and emission probabilities are tricky. One strategy is to train your HMM using the Baum-Welch (a variation of Expectation-Maximization) algorithm to iteratively and agnostically estimate parameters for your transition and emission matrices. The training data would be known digits with pixel locations registered across time.
Casting the problem the other way is less natural because of this lack of temporal fit, but not impossible.
- You can also make 10000 possible states aligning to the pixels, while having 10 emissions (0-9).
- However, most commonly used algorithms for HMMs have run times quadratically related to number of states ( ie. Viterbi algorithm for the most likely valid hidden states runs O(n_emissions * n_states^2)). You are incentivized to keep the number of hidden states low.
Unsolicited suggestions
Maybe what you might be looking for are Kalman filters, which may be a more elegant way to develop this on-line digit recognition (outside of CNNs which appear to the most effective) using this time-series format.
You may also want to look at structured perceptrons, if your emissions are multivariate (ie. x, y) and independent. Here, I believe x, y coordinates should be correlated and should be respected as such.
QUESTION
I am following this tutorial:
in it it has code that references and uses a HiddenMarkovModel class in tfp. the code that does this in the tutorial is here:
...ANSWER
Answered 2019-Feb-11 at 17:10The current stable version, 0.5, was released a while ago. The API docs match that version. We are in the process of preparing 0.6 for release, which has HMM. In the mean time you can install tfp-nightly instead, to get the latest goodness. You should then be sure to uninstall the one you have (pip uninstall tensorflow-probability
) and similarly install tf-nightly in place of TensorFlow stable. HTH! Thanks for using tfp!
QUESTION
I'm running the pomegranate HMM (http://pomegranate.readthedocs.io/en/latest/HiddenMarkovModel.html) on my data, and I load the results into a Pandas DF, and define the idealized intensity as the median of all the points in that state: df["hmm_idealized"] = df.groupby(["hmm_state"],as_index = False)["Raw"].transform("median")
. Sample data:
ANSWER
Answered 2018-May-03 at 09:39It looks like you just need to define a sorted HMM state like this:
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