Dissmissing features based on correlation with target variable Is it valid to dismiss features based on their Pearson correlation values with the target variable in a classification problem?  

say for instance I have a dataset with the following format where the target variable takes 1 or 0: 

&gt;&gt;&gt; dt.head()
   ID  var3  var15  imp_ent_var16_ult1  imp_op_var39_comer_ult1  \
0   1     2     23                   0                        0   
1   3     2     34                   0                        0   
2   4     2     23                   0                        0   
3   8     2     37                   0                      195   
4  10     2     39                   0                        0   

   imp_op_var39_comer_ult3  imp_op_var40_comer_ult1  TARGET  
0                        0                        0       0  
1                        0                        0       0  
2                        0                        0       0  
3                      195                        0       0  
4                        0                        0       0 


Computing the correlation matrix gives the following values 

|ID|var3|var15|imp_ent_var16_ult1|imp_op_var39_comer_ult1|imp_op_var39_comer_ult3|imp_op_var40_comer_ult1|TARGET
ID|1.0|-0.00102533166614|-0.00213549813966|-0.00311137548461|-0.00143645708778|-0.00413114484307|-0.00727672024906|0.0031484687227
var3|-0.00102533166614|1.0|-0.00445177129541|0.0018681447614|0.00598903116859|0.00681691701467|0.00151753041397|0.00447479817554
var15|-0.00213549813966|-0.00445177129541|1.0|0.0437222608106|0.0947624170998|0.101177078747|0.0427540973727|0.101322098561
imp_ent_var16_ult1|-0.00311137548461|0.0018681447614|0.0437222608106|1.0|0.0412213212518|0.0348787079026|0.00989582043194|-1.74602537678e-05
imp_op_var39_comer_ult1|-0.00143645708778|0.00598903116859|0.0947624170998|0.0412213212518|1.0|0.886476049204|0.342709191344|0.0103531295754
imp_op_var39_comer_ult3|-0.00413114484307|0.00681691701467|0.101177078747|0.0348787079026|0.886476049204|1.0|0.316671244555|0.0035169224417
imp_op_var40_comer_ult1|-0.00727672024906|0.00151753041397|0.0427540973727|0.00989582043194|0.342709191344|0.316671244555|1.0|0.00311938694896
TARGET|0.0031484687227|0.00447479817554|0.101322098561|-1.74602537678e-05|0.0103531295754|0.0035169224417|0.00311938694896|1.0


Is it valid, to dismiss all features where the correlation with target is lower than a threshold (say for instance, 0.1)? 

What if there is a strong inter-attributes correlation as high as 1 where the correlated attributes are continuous variables, does this mean that these features hold redundant information for the learner? can I safely remove one of them without risking to lose information?
You've really got a classification problem on your hands, not a regression problem. Your target is not continuous, and Pearson correlation measures a relationship between continuous variables really. That's problematic enough to start.

Low correlation means there's no linear relationship; it doesn't mean there's no information in the feature that predicts the target.

I think you're really looking for mutual information, in this case between continuous and categorical variables. (I assume your other inputs are continuous?) This is a little involved; see https://stats.stackexchange.com/questions/29489/how-do-i-study-the-correlation-between-a-continuous-variable-and-a-categorical

If you're attempting to do feature selection then you could perform a logistic regression with L1 regularization and select features based on the absolute value of their coefficients.