Best classifier machine-learning model for data with few samples What machine-learning algorithm do you use if you have an attribute matrix that was rows = samples and cols = attributes and a target vector that matched the attributes to a specific classifier? 
Would I want something like a neural network?  Unfortunately, I have many more attributes than samples but only categories to classify (i.e. 0,1, and 2). Considering this, what would be the best algorithm to use for a dataset like the one below? Values will be positive floats. 
My data looks something like the DataFrames below.  I'm trying to use the attributes to predict the target. I use Python for everything so I was going to try sklearn or tensorflow. 
In the end, I would like to have a model that predict the classifier and ALSO to be able to output the important variables that were useful in the model prediction. 
import pandas as pd
DF_attributes = pd.DataFrame([
                               [0.1, 12, 0.3, 0.4, 3.4],
                               [0.3, 15, 0.2, 0.7, 6.9],
                               [0.5, 10, 0.8, 0.4, 5.3],
                               [0.6, 13, 0.5, 0.5, 6.3],
                               [0.4, 11, 0.8, 0.4, 7.3],
                               [0.3, 11, 0.4, 0.5, 6.3]
                              ],index=["s1","s2","s3","s4","s5","s6"],columns=["att_1","att_2","att_3","att_4","att_5"])

SR_target = pd.Series([0,0,1,0,2,1],index=["s1","s2","s3","s4","s5","s6"])
    att_1  att_2  att_3  att_4  att_5
s1    0.1     12    0.3    0.4    3.4
s2    0.3     15    0.2    0.7    6.9
s3    0.5     10    0.8    0.4    5.3
s4    0.6     13    0.5    0.5    6.3
s5    0.4     11    0.8    0.4    7.3
s6    0.3     11    0.4    0.5    6.3
s1    0
s2    0
s3    1
s4    0
s5    2
s6    1
dtype: int64

 A: I am guessing that your data will be much larger. If you are interested in using Python then for Neural Networks (NN) you can look into the library you mentioned tensorFlow but I also recommend looking into theano and lasange.
There are however many different algorithms that I would suggest for this type of classification based off of personal experience. There is an extension of gradient boosting machines library in both Python and R called xgboost. This particular library is very powerful and is responsible for a lot of winning algorithms on Kaggle. 
Finally, I think you will find a fairly good classification in both the RandomForestClassifier and ExtraTressClassifier found in the sklearn.ensemble modules in python. In general, these algorithms perform fairly well and are also robust to things like missing values and outliers.  
Note
Just to add a little more to this, another way to create a more powerful classifier would be to run all of the different algorithms mentioned above and take a majority vote of the classification. 
