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I've been working for a long time with an artificial neural network algorithm (specifically, a siamese neural network) that I implemented in Torch & Lua.

I've been studying and playing with many details of this algorithm (momentum alpha, number of minibatches, learning rate, gradient update iterations, dropout, 10-fold cross validation, etc), but I'm still facing the same old error: after training and during testing, my artificial neural network predicts almost every test element as positive.

I train my model with a training set, and then test it on a test set. Both sets contain 2,000 elements. This is a typical confusion matrix result I get:

false negatives FN:       21
true positives TP:       179

false positives FP:    1,747
true negatives TN:        53

And these category values lead to the following rates:

f1_score = 0.16839          = 2*tp/(2*tp+fp+fn) [1: best] [0: worst]
accuracy = 0.116            = (tp+tn)/(tp+fn+fp+tn) [1: best] [0: worst]
recall = 0.9                = tp/(tp+fn) [1: best] [0: worst]
precision = 0.09            = tp/(fp+tp) [1: best] [0: worst]
specificity = 0.03          = tn/(fp+tn) [1: best] [0: worst]
fallout = 0.97              = fp/(fp+tn) [0: best] [1: worst]
false discovery rate = 0.91 = fp/(fp+tp) [0: best] [1: worst]
miss rate = 0.105           = fn/(fn+tp) [0: best] [1: worst]
MatthewsCC = -0.12008       = ((tp*tn)-(fp*fn))/math.sqrt((tp+fp)*(tp+fn)*(tn+fp)*(tn+fn)) [+1: perfect correlation] [0: no better than random prediction] [-1: total disagreement]

As you can notice, the FN and TP results are very good, but the FP and TN results are very bad. False positives are too many.

The artificial neural network thinks almost everything it processes is a positive element: it predicts the 96% of the elements as positives.

And the weird thing is that the training set is artificially balanced towards negative values: among the 2,000 elements, I'm choosing 90% of negatives and only 10% of positives. I also am using the same proportion for the test set (90% of negatives and only 10% of positives).

Does anyone have any idea about what is going on? Why does my neural network predict so many positives?


EDIT: Thanks to all for the help. Here are some data and the main core of my code.

Here are some toy data (you can copy them into your Torch terminal):

first_datasetTrain={};

first_datasetTrain[1]=torch.Tensor{4, 5, 8, 10, 36, 0, 11, 22, 23, 44, 49, 35, 22, 6, 12, 16, 16, 4, 8, 10, 12, 14, 3, 30, 11, 12, 1, 3, 12, 16, 3, 4, 3, 6, 8, 0, 5, 12, 5, 4, 18, 10, 6, 8, 4, 7, 12, 7, 13, 3, 66, 61, 9, 51, 28, 7, 24, 8, 43, 40, 115, 2, 5, 11, 11, 41, 8, 2, 2, 2, 11, 6, 4, 4, 5, 6, 6, 9, 25, 16, 19, 13 };

first_datasetTrain[2]=torch.Tensor{4, 5, 8, 6, 5, 0, 27, 8, 4, 8, 20, 11, 6, 7, 5, 22, 153, 3, 2, 6, 11, 28, 22, 37, 13, 5, 8, 17, 13, 8, 9, 0, 10, 14, 4, 30, 7, 17, 2, 5, 6, 9, 1, 18, 7, 3, 9, 2, 200, 7, 17, 16, 5, 5, 19, 7, 8, 8, 22, 11, 20, 0, 7, 3, 6, 7, 12, 7, 9, 9, 5, 5, 23, 2, 43, 13, 4, 10, 21, 9, 13, 15 };

first_datasetTrain[3]=torch.Tensor{10, 4, 11, 16, 20, 0, 2, 10, 17, 10, 32, 30, 9, 11, 10, 11, 9, 8, 21, 21, 9, 16, 19, 13, 11, 16, 9, 12, 20, 14, 2, 9, 7, 13, 0, 17, 11, 26, 10, 11, 8, 2, 18, 16, 10, 10, 10, 7, 4, 11, 32, 20, 8, 19, 21, 3, 7, 26, 17, 19, 139, 5, 10, 11, 15, 13, 2, 3, 2, 4, 24, 11, 11, 1, 8, 11, 3, 7, 20, 29, 24, 13 };

first_datasetTrain[4]=torch.Tensor{3, 6, 6, 10, 24, 0, 22, 3, 16, 7, 25, 13, 11, 24, 20, 14, 9, 7, 9, 10, 9, 15, 7, 49, 2, 13, 12, 4, 21, 7, 22, 14, 4, 12, 14, 13, 4, 12, 8, 8, 88, 88, 105, 87, 9, 35, 12, 16, 17, 18, 26, 12, 9, 23, 200, 13, 25, 12, 29, 28, 200, 10, 4, 17, 16, 10, 18, 3, 5, 2, 26, 11, 14, 3, 30, 4, 4, 0, 27, 25, 24, 18 };

first_datasetTrain[5]=torch.Tensor{14, 18, 17, 14, 16, 0, 19, 10, 14, 6, 15, 21, 15, 5, 14, 22, 7, 14, 18, 107, 13, 18, 19, 22, 25, 11, 32, 46, 14, 26, 8, 20, 29, 64, 24, 14, 25, 20, 42, 7, 18, 12, 14, 32, 12, 20, 19, 17, 35, 14, 19, 12, 8, 18, 32, 13, 23, 35, 24, 14, 32, 9, 34, 39, 6, 10, 51, 19, 8, 23, 39, 13, 200, 6, 32, 21, 18, 3, 32, 21, 133, 38 };

first_datasetTrain[6]=torch.Tensor{8, 5, 10, 9, 15, 0, 199, 23, 21, 15, 21, 17, 13, 16, 11, 34, 89, 7, 8, 16, 7, 19, 41, 61, 22, 28, 4, 44, 18, 17, 10, 9, 31, 16, 5, 23, 10, 11, 23, 6, 7, 5, 6, 6, 11, 3, 12, 16, 200, 17, 30, 10, 95, 32, 22, 6, 11, 41, 33, 24, 19, 11, 10, 13, 12, 21, 11, 1, 6, 10, 15, 6, 22, 3, 13, 29, 14, 2, 111, 24, 27, 15 };

first_datasetTrain[7]=torch.Tensor{8, 15, 46, 200, 200, 0, 200, 200, 200, 200, 92, 200, 200, 90, 42, 38, 76, 55, 200, 75, 16, 91, 86, 148, 200, 200, 5, 19, 22, 164, 23, 57, 172, 57, 3, 31, 8, 17, 46, 78, 11, 14, 21, 21, 12, 25, 11, 17, 86, 8, 200, 200, 200, 200, 24, 14, 15, 24, 200, 173, 200, 7, 46, 57, 25, 200, 16, 7, 9, 11, 100, 22, 46, 6, 95, 200, 9, 0, 110, 27, 30, 30 };

first_datasetTrain[8]=torch.Tensor{9, 9, 10, 34, 50, 0, 6, 27, 20, 29, 23, 21, 9, 19, 10, 16, 10, 6, 14, 16, 9, 20, 17, 33, 89, 78, 9, 8, 5, 10, 5, 5, 4, 8, 16, 8, 14, 13, 5, 3, 10, 17, 12, 15, 9, 3, 9, 16, 8, 7, 13, 14, 6, 21, 19, 13, 20, 19, 22, 22, 20, 7, 4, 7, 6, 28, 21, 3, 12, 4, 22, 6, 11, 3, 15, 20, 4, 2, 12, 7, 25, 10 };

first_datasetTrain[9]=torch.Tensor{5, 7, 18, 77, 29, 0, 20, 21, 35, 53, 128, 42, 28, 104, 10, 23, 13, 11, 8, 12, 19, 26, 18, 33, 21, 19, 13, 11, 28, 87, 10, 10, 200, 35, 5, 11, 7, 13, 20, 53, 15, 7, 14, 14, 7, 13, 12, 9, 18, 10, 121, 116, 83, 72, 19, 14, 12, 8, 40, 39, 200, 12, 21, 19, 20, 25, 22, 9, 4, 6, 26, 2, 102, 2, 76, 12, 51, 3, 23, 15, 18, 29 };

first_datasetTrain[10]=torch.Tensor{4, 14, 10, 10, 12, 0, 17, 7, 17, 17, 26, 21, 6, 12, 40, 22, 12, 1, 10, 20, 6, 24, 33, 38, 8, 22, 16, 9, 12, 9, 11, 3, 5, 22, 12, 24, 9, 22, 16, 5, 17, 9, 19, 22, 9, 7, 7, 14, 7, 9, 51, 17, 84, 48, 13, 2, 11, 45, 33, 55, 88, 5, 8, 15, 5, 9, 9, 10, 9, 6, 10, 6, 7, 4, 15, 7, 6, 6, 12, 26, 36, 13 };

second_datasetTrain={};

second_datasetTrain[1]=torch.Tensor{18, 16, 29, 7, 16, 0, 11, 11, 15, 11, 45, 15, 10, 9, 17, 23, 132, 43, 27, 24, 40, 22, 42, 31, 9, 9, 110, 53, 42, 90, 3, 40, 174, 23, 41, 22, 8, 30, 200, 13, 13, 11, 11, 8, 8, 19, 90, 13, 200, 9, 29, 13, 3, 30, 25, 10, 200, 17, 31, 9, 25, 14, 28, 10, 20, 9, 34, 6, 15, 30, 8, 3, 81, 44, 23, 12, 185, 3, 11, 15, 32, 19 };

second_datasetTrain[2]=torch.Tensor{2, 6, 9, 12, 70, 0, 38, 23, 52, 54, 83, 60, 50, 129, 36, 12, 15, 17, 23, 13, 5, 45, 16, 98, 97, 13, 3, 7, 11, 26, 7, 2, 7, 13, 9, 3, 4, 9, 3, 6, 6, 7, 10, 13, 6, 5, 8, 10, 7, 11, 96, 57, 65, 177, 35, 5, 11, 17, 48, 179, 100, 7, 7, 12, 9, 21, 11, 5, 10, 6, 16, 8, 12, 2, 9, 7, 4, 3, 69, 13, 11, 7 };

second_datasetTrain[3]=torch.Tensor{3, 6, 6, 10, 24, 0, 22, 3, 16, 7, 25, 13, 11, 24, 20, 14, 9, 7, 9, 10, 9, 15, 7, 49, 2, 13, 12, 4, 21, 7, 22, 14, 4, 12, 14, 13, 4, 12, 8, 8, 88, 88, 105, 87, 9, 35, 12, 16, 17, 18, 26, 12, 9, 23, 200, 13, 25, 12, 29, 28, 200, 10, 4, 17, 16, 10, 18, 3, 5, 2, 26, 11, 14, 3, 30, 4, 4, 0, 27, 25, 24, 18 };

second_datasetTrain[4]=torch.Tensor{13, 6, 34, 155, 69, 0, 34, 44, 28, 57, 41, 45, 27, 4, 28, 29, 20, 12, 52, 28, 5, 18, 27, 29, 21, 31, 4, 7, 13, 107, 14, 16, 17, 13, 7, 23, 17, 37, 13, 29, 10, 19, 14, 13, 8, 26, 3, 10, 6, 11, 77, 85, 31, 90, 23, 27, 9, 28, 46, 34, 200, 20, 11, 23, 15, 200, 0, 4, 29, 4, 42, 3, 14, 2, 7, 15, 42, 5, 49, 12, 12, 17 };

second_datasetTrain[5]=torch.Tensor{2, 11, 19, 27, 23, 0, 16, 11, 18, 13, 25, 18, 10, 14, 15, 40, 1, 9, 12, 21, 17, 20, 22, 25, 28, 19, 12, 25, 8, 18, 3, 15, 11, 24, 9, 16, 17, 21, 23, 9, 12, 13, 14, 25, 19, 21, 11, 8, 11, 13, 18, 10, 21, 24, 26, 5, 20, 33, 57, 25, 16, 8, 26, 15, 5, 9, 13, 9, 7, 13, 16, 11, 9, 4, 9, 21, 5, 8, 12, 22, 33, 10 };

second_datasetTrain[6]=torch.Tensor{78, 13, 200, 200, 200, 0, 70, 200, 200, 200, 200, 200, 200, 18, 21, 27, 11, 12, 20, 58, 28, 18, 22, 119, 200, 200, 65, 54, 178, 200, 88, 95, 200, 200, 24, 47, 30, 26, 200, 109, 76, 85, 50, 65, 21, 200, 4, 36, 110, 30, 200, 200, 200, 200, 200, 101, 23, 23, 200, 200, 200, 19, 123, 36, 200, 86, 69, 6, 7, 76, 38, 21, 200, 1, 200, 44, 59, 6, 142, 30, 53, 200 };

second_datasetTrain[7]=torch.Tensor{10, 5, 7, 12, 15, 0, 35, 18, 11, 11, 17, 14, 4, 9, 47, 77, 28, 33, 94, 61, 7, 37, 35, 40, 4, 21, 7, 17, 10, 25, 11, 15, 10, 20, 6, 59, 18, 16, 9, 26, 6, 10, 25, 23, 95, 13, 1, 14, 13, 11, 22, 5, 14, 20, 23, 11, 25, 33, 22, 30, 64, 7, 7, 27, 10, 14, 4, 7, 6, 4, 18, 15, 10, 4, 23, 71, 5, 3, 81, 41, 33, 13 };

second_datasetTrain[8]=torch.Tensor{6, 10, 14, 81, 200, 0, 39, 141, 200, 200, 200, 200, 200, 10, 4, 23, 16, 11, 9, 37, 8, 22, 21, 74, 200, 195, 6, 15, 16, 30, 8, 5, 19, 19, 11, 71, 7, 12, 29, 6, 11, 14, 7, 8, 7, 17, 3, 12, 14, 7, 200, 200, 200, 200, 30, 5, 17, 24, 200, 155, 200, 4, 19, 25, 26, 39, 6, 11, 4, 7, 33, 9, 30, 1, 27, 10, 9, 16, 37, 8, 30, 19 };

second_datasetTrain[9]=torch.Tensor{15, 2, 11, 160, 11, 0, 7, 9, 11, 33, 30, 14, 14, 12, 16, 18, 33, 16, 38, 12, 8, 16, 26, 21, 4, 16, 6, 11, 15, 6, 2, 4, 4, 14, 4, 12, 6, 8, 12, 9, 16, 5, 17, 13, 13, 11, 10, 3, 8, 3, 10, 8, 4, 34, 21, 6, 17, 27, 27, 25, 58, 7, 19, 10, 12, 12, 20, 4, 4, 6, 36, 5, 14, 4, 15, 12, 4, 3, 41, 11, 18, 11 };

second_datasetTrain[10]=torch.Tensor{20, 1, 27, 187, 161, 0, 200, 95, 200, 200, 200, 200, 200, 8, 51, 34, 27, 33, 50, 41, 3, 34, 49, 200, 190, 146, 5, 15, 6, 108, 30, 67, 72, 13, 10, 11, 20, 20, 14, 11, 55, 44, 56, 43, 88, 52, 7, 15, 3, 9, 97, 145, 138, 200, 200, 5, 14, 54, 110, 190, 200, 6, 24, 18, 9, 132, 8, 3, 12, 4, 50, 9, 17, 2, 16, 6, 5, 5, 43, 55, 31, 22 };

targetDatasetTrain={};

targetDatasetTrain[1]={0};

targetDatasetTrain[2]={1};

targetDatasetTrain[3]={0};

targetDatasetTrain[4]={1};

targetDatasetTrain[5]={0};

targetDatasetTrain[6]={1};

targetDatasetTrain[7]={0};

targetDatasetTrain[8]={1};

targetDatasetTrain[9]={0};

targetDatasetTrain[10]={1};

And here's the short version of my Code that implements a siamese neural network having two parallel neural networks (upper and lower) that process first_datasetTrain and second_datasetTrain, and then compares their hidden representation through the Cosine distance (Inspiration from: https://github.com/torch/nn/blob/master/doc/table.md#nn.CosineDistance )

require "nn";

-- Gradient update for the siamese neural network
function gradientUpdate(perceptron, dataset_vector, targetValue, learningRate, i, ite);

   function dataset_vector:size() return #dataset_vector end

   local predictionValue = perceptron:forward(dataset_vector)[1];

   local plusChar = ""
   if targetValue == 1 then plusChar = "+"; end

   local meanSquareError = math.pow(targetValue - predictionValue,2);
   io.write("(ite="..ite..") (ele="..i..") pred = "..predictionValue.." targetValue = "..plusChar..""..targetValue .." => meanSquareError = "..meanSquareError);
    io.flush();

   if meanSquareError > 1 then 
       io.write(" LARGE MeanSquareError"); 
       io.flush();
       sys.sleep(0.1);
   end
   io.write("\n");



    if predictionValue*targetValue < 1 then
          gradientWrtOutput = torch.Tensor({-targetValue});
      perceptron:zeroGradParameters();
      perceptron:backward(dataset_vector, gradientWrtOutput);
      perceptron:updateParameters(learningRate);
    end

  return perceptron;
end


local dropOutFlag = true
local hiddenUnits = 4
local hiddenLayers = 4



print('<siameseNeuralNetworkApplication_justTraining start>');
io.write("#first_datasetTrain = ".. (#first_datasetTrain));
io.write(" #second_datasetTrain = "..(#second_datasetTrain));
io.write(" #targetDatasetTrain = "..(#targetDatasetTrain).."\n");
io.write(" dropOutFlag = "..tostring(dropOutFlag));
io.write(" hiddenUnits = "..hiddenUnits);
io.write(" hiddenLayers = "..hiddenLayers);


local input_number = (#(first_datasetTrain[1]))[1]; -- they are 6
local output_layer_number = input_number

local trainDataset = {}
local targetDataset = {}

print("Creatin\' the siamese neural network...");
print('hiddenUnits='..hiddenUnits..'\thiddenLayers='..hiddenLayers);

-- imagine we have one network we are interested in, it is called "perceptronUpper"
local perceptronUpper= nn.Sequential()

perceptronUpper:add(nn.Linear(input_number, hiddenUnits))
perceptronUpper:add(nn.Tanh())
--perceptronUpper:add(nn.ReLU())
if dropOutFlag==TRUE then perceptronUpper:add(nn.Dropout()) end

for w=1, hiddenLayers do
 perceptronUpper:add(nn.Linear(hiddenUnits,hiddenUnits))
 perceptronUpper:add(nn.Tanh())
 --perceptronUpper:add(nn.ReLU())
 if dropOutFlag==TRUE then perceptronUpper:add(nn.Dropout()) end
end

perceptronUpper:add(nn.Linear(hiddenUnits,output_layer_number))
perceptronUpper:add(nn.Tanh())
--perceptronUpper:add(nn.ReLU())


local perceptronLower = perceptronUpper:clone('weight', 'gradWeight') 

-- we make a parallel table that takes a pair of examples as input. they both go through the same (cloned) perceptron
-- ParallelTable is a container module that, in its forward() method, applies the i-th member module to the i-th input, and outputs a table of the set of outputs.
local parallel_table = nn.ParallelTable()
parallel_table:add(perceptronUpper)
parallel_table:add(perceptronLower)



-- now we define our top level network that takes this parallel table and computes the cosine distance betweem
-- the pair of outputs
local generalPerceptron= nn.Sequential()
generalPerceptron:add(parallel_table)
generalPerceptron:add(nn.CosineDistance())



MAX_ITERATIONS_CONST = 1000
LEARNING_RATE_CONST = 0.01
local max_iterations = MAX_ITERATIONS_CONST;
local learnRate = LEARNING_RATE_CONST;


for ite = 1, max_iterations do   
     for i=1, #first_datasetTrain do  


     trainDataset[i]={first_datasetTrain[i], second_datasetTrain[i]}
     collectgarbage();  

     local currentTarget = 1
     if tonumber(targetDatasetTrain[i][1]) == 0 
    then currentTarget = -1; 
     end

     generalPerceptron = gradientUpdate(generalPerceptron, trainDataset[i], currentTarget, learnRate, i, ite);    

     local predicted = generalPerceptron:forward(trainDataset[i])[1];  
     print("predicted = "..predicted);
     end

end

You just have to copy this code into a file say siamese.lua, then open a Torch terminal, copy and paste the data file into the terminal, run dofile("siamese.lua"), and everything should go.

The data have just 10 elements, but if you need more you can download this file

Any help will be very appreciated, thanks!

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  • 1
    $\begingroup$ How do your training and testing performance compare? $\endgroup$ – bogatron Mar 25 '16 at 13:13
  • $\begingroup$ @bogatron During training, I compute the ROC AUC (and an indicative confusion matrix with threshold = 0.5). During testing, I compute the confusion matrix. The ROC AUC's for some trained models get good values (>80%) but the confusion matrices always have too many false positives (FP). $\endgroup$ – DavideChicco.it Mar 25 '16 at 21:00
  • $\begingroup$ After your ROC AUC analysis, how are you picking your threshold parameter? There has to be a choice of threshold that reduces your FN rate. $\endgroup$ – Alex R. Mar 28 '16 at 19:14
  • $\begingroup$ I'm picking the threshold that minimizes the error FN+FP. Not much changes with threshold = 0.5, because all the predicted values are polarized in [0.0, 0.1] or in [0.9, 1.0], approximately. $\endgroup$ – DavideChicco.it Mar 28 '16 at 19:51
  • 1
    $\begingroup$ Maybe your cost function doesn't penalize positive outputs? How does the network behave when you use balanced dataset? $\endgroup$ – Joonatan Samuel Mar 29 '16 at 8:16
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You included an important detail in your comment that:

With balanced dataset (50% positives and 50% negatives) I have similar results.

I think the issue is in the activation function of your neural network. If you used a symmetric activation function in your neural network then the FP and FN rates should be roughly the same in the balanced dataset case. You can test whether this is the source of your issue by flipping the signs of the labels on your data (i.e. relabel positive as negative and negative as positive and see what happens). If the FP and FN rates stay the same even when you switch what the dataset labels positive and negative, then this shows that the large false positive rate is not coming from the data but rather from the probability model itself, in which case check your activation function to see if they are biased towards labelling something as positive.

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  • $\begingroup$ Thanks of the reply. I just added some data and my code to the question, could you please take a look to it when you've time? That would save me. Thanks! $\endgroup$ – DavideChicco.it Apr 1 '16 at 21:20
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Of course you have wrong loss function in function gradientUpdate. You are using MSE, which should be used for regression problems. When you are doing classification you should use loss function for classification problems - this is old post about it: https://jamesmccaffrey.wordpress.com/2013/11/05/why-you-should-use-cross-entropy-error-instead-of-classification-error-or-mean-squared-error-for-neural-network-classifier-training/

You could also look at wiki: https://en.wikipedia.org/wiki/Loss_functions_for_classification

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