There can be multiple techniques for solving such a problem but for the development of a baseline model for the specific task, I would suggest that you go for some sort of Ensemble technique by creating two different models with N1 set of features and N2 set of features respectively.

Dear Sabyasachi Chakraborty, thanks for your fast response. Unfortunately, for my task suggested approach does not work. Both first and second data sets don't take into account some important features, so results are not good. But using simultaneously both first and second data sets allow us to take into account all important features. May be, you can suggest some other approaches ? Regards, Sergey.

Hey Sergey,

So as I have no idea about the dataset that you are using therefore I would provide you with some explanation based on my assumptions over your question.

Assumptions:

You said you have 2 Cohorts, M1(N1 Features X Labels) and M2(N2 Features X Labels). So it means the number of Labels in both the cohorts are same and both the feature set are held towards the same labels.

Previous Way: Where I recommended using Ensemble Techniques [By creating two different models and stacking the probablilities followed by using a Meta Learner or perform some Voting]

-- I understand there would be some issues by using an Ensemble method because if we ensemble different models then we won't be able to have the have the common interation between the N1 Features and N2 Features (N3 Features).

So for such cases the best approach that I can think right away is a Multi Channel Artificial Neural Network. The usage of such network will help to you to merge the feature interactions between both the feature set.

Let me know if you face any issues.

Sabyasachi, Hi! Sorry, by my task isn't as you have written - " So it means the number of Labels in both the cohorts are same and both the feature set are held towards the same labels".

It isn't right. Two data sets have same type of label (e.g., the result of the diagnosis of a particular disease - Yes or No), but two different data sets correspond for two different cohorts and so each single record has individual values of features and individual value of label.

For best understanding I can describe example of such typical classification task.

One hospital has Data Set of the 1000 patients according Prostate Cancer (Label = Yes or No) with 5 features : Age, PSA, DRE, Free_PSA, Volume.

Second hospital has Data Set of the 5000 patients according Prostate Cancer (Label = Yes or No) with 6 features : Age, PSA, DRE, Race, Smoking, Family.

For new patient we have values of all 8 features (Age, PSA, DRE, Free_PSA, Volume, Race, Smoking, Family) and we should predict Label for this patient.

Aaah Gotcha,

This is getting pretty interesting.

**Note: All my previous mentioned techniques goes to vain right now :p :p.

Alright,

So see based on the type of data you have, there is particularly now way that standalone algorithms will work on it as the number of features are different and all the records (6000 Patients) are different.

Therefore, for such kind of problem I guess the best way would be to meddle around with the dataset.

Basically, the common features are { Age, PSA, DRE} and the uncommon features are {[Free_PSA, Volume ] & [ Race, Smoking, Family]}.

Now, based on the ground knowledge I think "Smoking" as a feature won't be important for prostrate cancer detection (I guess so) [Still you can do some exploratory analysis to see how smoking affects prostrate cancer with respect to DRE]. Also having "RACE" as a feature is against the Ethics of Artificial Intelligence [Not allowed : Gender/Race/Religion/Caste/Tribe (If the usecase is not specific to one of them)].

Family, I guess is a binary variable right ? If so, then I would suggestyou that you check coorelation between Family with the Output variable. Because presence of Cancer in the family would be highly coorelated to the output variable. If, it is highly coorelated that I would suggest you to remove it.

Method: Concatenate Both the Datasets Together (Row Wise) and perform strategic imputation on the Uncommon columns i.e. [Free_PSA, Volume, Family]

But the catch is that the imputation should be done in a very strategic way so that there is no bias and no information leak [There could be "n" number of ways]

Let's talk about one tiny method,

Let's say I want to create a Free_PSA Column in Cohort 1 [Hospital Data with 1000 Columns]. Now, Free_PSA is availiable in Cohort 2 [Hospital with 5000 records of data]. Now both the Cohorts have { Age, PSA, DRE} in common.

Therefore, I would create a tiny model based on Cohot 2's Data using { Age, PSA, DRE} and try to predict "Free_PSA". Now I would use the Same Model predict it one the data of Cohort 1 to create a "Free_PSA" column for Cohort_1. Similarly you can do stuff like that to do feature engineering and create columns because without merging both the datasets, I don't think so there is any whether way.

And yeah kindly let me know what you think ?

Sabyasachi, Hi and thanks for answer. First, above example is only example, so I am not able to discuss, are Race and Smoking really significant features or not. Your approach is very interesting, it is similar for "missing data" - when values of some features are absent in some records. But what to do, if correlations between features are very low, all features are ~ independent ? Unfortunately, it is typical situation in classification tasks.

Completely Agree !! Sergey.

Out here missing data is one of the biggest concern, but the term "Missing Data" is more relevant when we have few hundreds of data missing from certain records but in the present scenario we either need to recreate complete new columns or to remove them. So better approach would be to create synthetic samples.

Dear Sergey,

Several things need to highlight.

First, if you need to append two datasets, then they have to exactly share same features/columns (i.e., name, order, and type). Second, when, for instance, two variables are independent, their correlation is 0. Finally, in machine learning domain, having highly correlated features could decrease the performance an algorithm on the test set.

HTH.

Dr. Samer Sarsam

Dear Samer, thanks for reply. I fully agree with you, that if we want "automatically" merge two data sets, "they have to exactly share same features/columns" (moreover, they should have identical probability distribution). Unfortunately, my task is else - only part of features of two data sets are same. About correlated features - you are right. On my task features ate low correlated and this fact prevent to use regression to calculate values of absent features (as Sabyasachi proposed above). Regards, Sergey.

Dear Sabyasachi, Hi. I have checked approach, proposed of you (regression on the new-extended data set) more detail. Some preliminary results:

1. We can perform this regression by means of classic way (hew factor depending of old factors) simultaneously for all records on the new data set. But we also can perform it independently for records with positive label and for record with negative label - it can essentially increase classification accuracy.

2. For SVM using we can get only mean values for new factor, but for Logistic Regression using we can also get probability distribution parameters - it also can essentially increase classification accuracy.