1
$\begingroup$

Say we've previously used a neural network or some other classifier C with $N$ training samples $I:=\{I_1,...I_N\}$ (that has a sequence or context, but is ignored by C) the, belonging to $K$ classes. Assume, for some reason (probably some training problem or declaring classes), C is confused and doesn't perform well. The way we assign a class using C to each test data $I$ is: $class(I):= arg max _{ {1 \leq j \leq K} } p_j(I)$, where $p_j(I)$ is the probability estimate of $I$ corresponding to the $j$-th class, given by C.

Now, on top of this previous classifier C, I'd like to use a Hidden Markov Model (HMM) to "correct" the mistakes made by the previous context-free classifier C, by taking into account the contextual/sequential information not used by C.

Hence let in my HMM, the hidden state $Z_i$ denote the true class of the $i$-th sample $I_i$, and $X_i$ be the predicted class by C. My question is: how could we use the probabilistic information $cl(I):= arg max _{ {1 \leq j \leq K} } p_j(I)$ to train this HMM? I understand that the confusion matrix of C can be used to define the emission prob. of the HMM, but how do we define the transition and start/prior prob.? I'm tempted to define the start/prior prob. vector as $\pi:=(p_1(x_1), ..., p_K(x_1))$. But I may be wrong. This is my main question.

A follow up question: One can define an HMM in the above way (using confusion matrix and the prob. information from C); call the resulting parameter set $\Theta_0$. But after doing so, is it advisable to estimate the parameters to best fit the data $I$ used for C, while initializing a parameter set with the values mentioned in the previous paragraph?

$\endgroup$
3
  • $\begingroup$ Why can you not make the original classifier aware of the context? E.g. use a CNN with a window of time, or an RNN? $\endgroup$
    – kbrose
    Apr 20, 2018 at 14:16
  • $\begingroup$ @kbrose: I'm kind of new to the subject, but I've been instructed to use neighborhood information of the samples; samples are retail products in supermarkets, and the contexts are not time, but the for a product P(t,s), the neighborhood consisting of all P(t+/- 1, s+/-1). $\endgroup$
    – Sus_Q
    Apr 20, 2018 at 14:22
  • $\begingroup$ Ok, so a CNN with filter widths of 3? $\endgroup$
    – kbrose
    Apr 20, 2018 at 23:10

1 Answer 1

0
$\begingroup$

As far i know u can't saything about hidden class, hidden class value at time t is 'some intermediate values of weighted values of all hidden classes'.

see the point- 2) hidden state sequence in blog- https://machinelearningstories.blogspot.com/2017/02/hidden-markov-model-session-1.html

so ur statement-

"Hence let in my HMM, the hidden state Zi denote the true class of the i-th sample Ii, and Xi be the predicted class by C- is incorrect.

How can u compare hidden class value with actual, u could have compared emission value and actual.

You can try ensembling of HMM and Cs. I wonder how exactly you trying to use parameters from classification problem to time series/sequence (HMM).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.