So, that is my sample data. The column "instable" is the outcome variable,
HR, SAP, MAP etc. is the minute-by-minute raw data. From these I extracted
derived features (using percentiles) and created a training example with the
data from i=1 to i=25 with instable = yes/no and so on...
Thank you.
i instable HR SAP MAP ShockIndex tStamp
1 yes 114,0 87,0 74,0 1,5405405405405406
14.Mrz.10,_11:29:00
2 yes 113,0 89,0 70,0 1,6142857142857143
14.Mrz.10,_11:30:00
3 yes 110,0 145,0 116,0 0,9482758620689655
14.Mrz.10,_11:31:00
4 yes 109,0 202,0 201,0 0,5422885572139303
14.Mrz.10,_11:32:00
5 yes 111,0 207,0 205,0 0,5414634146341464
14.Mrz.10,_11:33:00
6 yes 109,0 209,0 208,0 0,5240384615384616
14.Mrz.10,_11:34:00
7 yes 112,0 144,0 116,0 0,9655172413793104
14.Mrz.10,_11:35:00
8 yes 111,0 112,0 87,0 1,2758620689655173
14.Mrz.10,_11:36:00
9 yes 111,0 105,0 84,0 1,3214285714285714
14.Mrz.10,_11:37:00
10 yes 111,0 102,0 73,0 1,5205479452054795
14.Mrz.10,_11:38:00
11 yes 111,0 103,0 72,0 1,5416666666666667
14.Mrz.10,_11:39:00
12 yes 115,0 94,0 74,0 1,554054054054054
14.Mrz.10,_11:40:00
13 yes 113,0 91,0 67,0 1,6865671641791045
14.Mrz.10,_11:41:00
14 yes 109,0 124,0 101,0 1,0792079207920793
14.Mrz.10,_11:42:00
15 yes 109,0 147,0 123,0 0,8861788617886179
14.Mrz.10,_11:43:00
16 yes 110,0 93,0 69,0 1,5942028985507246
14.Mrz.10,_11:44:00
17 yes 108,0 91,0 74,0 1,4594594594594594
14.Mrz.10,_11:45:00
18 yes 109,0 83,0 69,0 1,5797101449275361
14.Mrz.10,_11:46:00
19 yes 110,0 94,0 70,0 1,5714285714285714
14.Mrz.10,_11:47:00
20 yes 109,0 104,0 73,0 1,4931506849315068
14.Mrz.10,_11:48:00
21 yes 107,0 103,0 68,0 1,5735294117647058
14.Mrz.10,_11:49:00
22 yes 109,0 94,0 69,0 1,5797101449275361
14.Mrz.10,_11:50:00
23 yes 108,0 90,0 66,0 1,6363636363636365
14.Mrz.10,_11:51:00
24 yes 109,0 97,0 73,0 1,4931506849315068
14.Mrz.10,_11:52:00
25 yes 110,0 105,0 73,0 1,5068493150684932
14.Mrz.10,_11:53:00
1 no 84,0 138,0 87,0 0,9655172413793104
22.Dez.10,_04:10:00
2 no 83,0 139,0 87,0 0,9540229885057471
22.Dez.10,_04:11:00
3 no 80,0 142,0 89,0 0,898876404494382
22.Dez.10,_04:12:00
4 no 82,0 142,0 87,0 0,9425287356321839
22.Dez.10,_04:13:00
5 no 81,0 140,0 87,0 0,9310344827586207
22.Dez.10,_04:14:00
6 no 77,0 138,0 85,0 0,9058823529411765
22.Dez.10,_04:15:00
7 no 80,0 143,0 89,0 0,898876404494382
22.Dez.10,_04:16:00
8 no 75,0 139,0 87,0 0,8620689655172413
22.Dez.10,_04:17:00
9 no 79,0 137,0 84,0 0,9404761904761905
22.Dez.10,_04:18:00
10 no 81,0 143,0 89,0 0,9101123595505618
22.Dez.10,_04:19:00
11 no 82,0 142,0 91,0 0,9010989010989011
22.Dez.10,_04:20:00
12 no 80,0 142,0 88,0 0,9090909090909091
22.Dez.10,_04:21:00
13 no 79,0 146,0 90,0 0,8777777777777778
22.Dez.10,_04:22:00
14 no 83,0 151,0 94,0 0,8829787234042553
22.Dez.10,_04:23:00
15 no 78,0 146,0 90,0 0,8666666666666667
22.Dez.10,_04:24:00
16 no 80,0 143,0 89,0 0,898876404494382
22.Dez.10,_04:25:00
17 no 81,0 143,0 88,0 0,9204545454545454
22.Dez.10,_04:26:00
18 no 79,0 143,0 88,0 0,8977272727272727
22.Dez.10,_04:27:00
19 no 85,0 145,0 90,0 0,9444444444444444
22.Dez.10,_04:28:00
20 no 82,0 138,0 88,0 0,9318181818181818
22.Dez.10,_04:29:00
21 no 81,0 146,0 91,0 0,8901098901098901
22.Dez.10,_04:30:00
22 no 83,0 135,0 86,0 0,9651162790697675
22.Dez.10,_04:31:00
23 no 80,0 143,0 89,0 0,898876404494382
22.Dez.10,_04:32:00
24 no 85,0 141,0 88,0 0,9659090909090909
22.Dez.10,_04:33:00
25 no 88,0 135,0 88,0 1,0 22.Dez.10,_04:34:00
Am 24.07.2011 21:15, schrieb Ted Dunning:
I remember this problem.
Is it possible for you to post some sample data?
On Sun, Jul 24, 2011 at 12:08 PM, Svetlomir Kasabov<
[email protected]> wrote:
Hello again and thanks for the replies of both of you, I really apreciate
them. The most important think is, that you try helping and how you do
this
is irrelevant :). I didn't feel angry/insulted.
Yes, X1 and X2 are two independent hidden sequences, like
BP -- BP -- BP (Blood Pressure)
HR -- HR -- HR (Heart Rate)
And I want to train the model to predict the probability of giving a drug
Y
to a patient (for example, with this sequence)
Y=0 -- Y=0 -- Y=1
I already tried this with logistic regression, but ended with poor
results
(probably because of my small example set). Logistic regression has also
no
built-in time series and that's why Imust analyze the X's changes using
percentiles and then train the logistic model with these percentiles. In
this way I reduce the dimensions to only one. That's why I thought that
the
HMM can do this for me 'out of the box', staying in the dimension of 2,
if
they allow to have two hidden chains, like this:
http://t3.gstatic.com/images?****q=tbn:ANd9GcR8pu4bSm-**MSyg3Pj0-**<http://t3.gstatic.com/images?**q=tbn:ANd9GcR8pu4bSm-MSyg3Pj0-**>
aTyi8FaqUOy4U2bcKJBTBYKKvgAhyw****6P<http://t3.gstatic.com/**
images?q=tbn:ANd9GcR8pu4bSm-**MSyg3Pj0-**aTyi8FaqUOy4U2bcKJBTBYKKvgAhyw*
*6P<http://t3.gstatic.com/images?q=tbn:ANd9GcR8pu4bSm-MSyg3Pj0-aTyi8FaqUOy4U2bcKJBTBYKKvgAhyw6P>
or 'coupled' HMMs.
I am not very experienced with the HMMs, but will read further the
literature and Mahout's API :).
Maybe reducing the dimensions is not that bad idea? I've read that we can
do it with PCA (Principle Components Analysis). Is there a Ḿahout code
for
this somewhere?
Thanks a lot once again,
Svetlomir.
Am 24.07.2011 20:46, schrieb Ted Dunning:
My impression (and Svetlomir should correct me) is that the intent was
to
use two HMM's on separate inputs and then use the decoded state
sequences
from those as inputs to a third HMM.
If that is the question, then I think that Mahout's HMM's are
sufficiently
object-ish that this should work. Obviously, it will take multiple
training
passes to train each separate model.
On Sun, Jul 24, 2011 at 11:25 AM, Dhruv<[email protected]> wrote:
Svetlomir and Ted -- I was not trying to be rude, sorry if I came
across
that way because of my exuberance. I apologize.
I was eager to help and may have acted too fast and misunderstood the
question, so I turn to both of you for a little clarification.
I'm confused whether the X's refer to the hidden states, or training
instances. Since the hidden sequence is always a Markov Chain in HMMs,
I
assumed that Svetlomir meant that X1 and X2 were two separate hidden
state
sequences because Markov Chain was explicitly mentioned in his original
question. To quote:
-----------
X1----X1----X1----...X1 (Markov Chain for input parameter 1 =>
monitoring
X1's changes over time)
X2----X2----X2----...X2 (Markov Chain for intput parameter 2 =>
monitoring
X2's changes over time)
-----------
Further, since X1 and X2 were not slated to have any relationship with
each
other and since they were the observations of two different parameters,
I
construed that X1 and X2 represented two separate hidden state
sequences.
I
gathered that the hidden state sequences X1 and X2 are drawn from two
disjoint hidden vocabulary sets. The user wants to discover the model
on
some training set and then, to the trained model, feed Y for decoding
to
arrive at the most likely sequence of states, X1 and X2 which emitted
Y.
In my answer, I continued with this line saying that in one training,
you
can't arrive at two separate models for X1 and X2 which contain the
requisite distributions which can be used for decoding, say sequences
of
X1
to have produced Y or sequence of X2 to have produced Y. Hence, I
suggested
having only one set for the hidden states, combining X1s and X2s and
then
train the model on it. Given the domain of application, this may or may
not
make sense, hence I was doubtful of formulating the problem as HMM and
suggested alternatives.
However:
If X's are two separate input sequences for training, then yes, the
current
implementation is capable of training the HMM. If Y is the output, then
one
can decode, after training, the sequence of hidden states which most
likely
produced Y.
For the output probability question, my answer was to use the trained
model's HmmModel.getEmissionMatrix.****get(hiddenState, emittedState)
method to
compute the output probability for a particular hidden state. I believe
this
is not what the user wanted?
Dhruv
On Sun, Jul 24, 2011 at 12:56 PM, Ted Dunning<[email protected]>
wrote:
On Sun, Jul 24, 2011 at 7:52 AM, Dhruv<[email protected]> wrote:
... If you look into the *definition* of HMM, the hidden sequence is
drawn
from
only one set. The hidden sequence's transitions can be expressed as a
joint
probability p(s0, s1). Similarly the observed sequence has a joint
distribution with the hidden sequence such as p(y0, s1) and so on.
I think gentler language might be a good idea here. The question
was
not
at
all unreasonable.
The hidden state transitions follow the Markov memorylessness
property
and
hence form a Markov Chain.
In your case, you are trying to model your problem assuming that
there
are
two underlying state sequences affecting the observed output. This
doesn't
fit into the HMM's definition and you probably want something else.
Actually, what the original poster wanted is quite sensible. While
the
output sequence is due to a single input sequence, that input sequence
is
not observable. As such, we have a noisy channel problem where we
want
to
estimate something about that original sequence. The point of the
Markov
model is that it defines a distribution of output sequence given an
input
sequence (and model). This distribution can be inverted so that given
a
particular output sequence, we can estimate the probability
distribution
of
input sequences conditional on the output.
The typical decoding algorithm for HMM's estimates only the maximum
likelihood input sequence but this does not negate the fact that we
have
a
distribution. There are alternative decoding algorithms that allow a
set
of
high probability sequences to be estimated or allow a partial
probability
lattice to be output that allows alternative sequences to be probed.
If you do want to fit your problem into the HMM framework, you need to
condense the X1 and X2 sequences into a single set and then condition
the
Ys
on it.
Not at all.
3. Can we get output probabilities from the HMM for a concrete state?
Yes, after training, you can retrieve any of the trained model's
distributions as a Mahout Matrix type and use get(row, col).
This is not quite what the question was.
