# training data SEQUENCE vs. training data SET?

My question is related to classification in Data-mining. But I believe anyone who has good background in Math/statistics can answer it.

As you remember a discrete-value training data of one dimension(e.g. sampling and quantizing a time signal) can be the

sequence [2,3,2,2] but a set should have unique values so the training set should be of the form
{2,3}.

I have the following table as my data set (the famous play golf example). this table stems from several realizations of a stochastic process:

 outlook         Temp.   Humidity      Windy   Play Golf


Rainy           Hot         High        False    No
Rainy           Hot         Low         True     No
Overcast        Hot         High        False    yes
Sunny          cold         High        False    Yes
?                ?          ?             ?      ?


As we see each feature(attribute) is a discrete variable. outlook can have 3 values. Temp.,Humidity and Windy can just have 2 values. As i said this table comes from several realizations. so i know that by doing many other experiments (realizations) all missing rows of this table can be completed (all combinations: 3*2*2*2=24).

This table is a representation of a Model(function or mapping) from these 4 features to ONE classes (Play Golf class).

Guys, Are you with me up to this point?

Here comes the question:

The (truth) above table is a way of representing a function(model) but it doesn't indicate how many times a realization can happen(its frequency).

for instance if i repeat the experiment 2 other times (2 realizations) and in both two cases i get for

outlook=Rainy, Temp=Hot, Humidity=High, Windy=False Play Golf=No ,

then I've obtained the same result as first row of my table. but I can't add it to this table, because this table shows the SETS not the repeated values.

In my real database creation, I have training data values (from different realizations) that are repetitive, so they won't complete my table because in a set we don't have a repeated value.So how can these repeated values help me in finding a Function(Model) for play golf?

• I am afraid you did lose me. Suppose the process has a nonzero (albeit small) chance of producing any five-tuple, so that after a sufficiently large number of observations, every five-tuple will occur in your dataset. What would you do then? This shows that thinking of your problem as fitting a function to a set of tuples is neither accurate nor likely to be fruitful. As far as you question goes: if you cannot add another result to your table, that can only be because you have given invalid constraints to your software: tell it to allow duplicates!
– whuber
Dec 26 '12 at 17:33
• I'm glad to see you here whuber.seems noone is interested in replying to my elementary questions! Dec 28 '12 at 12:51
• of course after a sufficiently large number of observations,all combinations will occur. but the sufficient can mean INFINITE tests.As i understand from Machine learning algorithms, the goal is to fit a function(model) to my training table SET(the aboved table with incompleted rows).So the frequency of any five-tuple would not appear in this table. so I can add another different result to my table, but can't add the same result to the table. Dec 28 '12 at 13:03
• BTW, i will use this table SET to create a decision tree model (e.g. C4.5). I think if i use a statistical model such as GMM (markov), i should take into account the frequency of their occurence. Dec 28 '12 at 13:12
• in your opinion, to find a function equation (e.g. y=3x by knowing that x can have only these values {1,3,4}) does thes frequency of occurence of experiments(observations) with x value=1 play a role? for me obviously not, therefore how approaches like GMM use the freq. of occurance of x to find the function? Dec 28 '12 at 13:29