Implication of binary cross entropy loss value in Keras? - keras

During training I saw that the binary cross entropy loss is positively unbounded.
So can we interpret anything from just looking at the loss value alone, for example if the binary cross entropy loss is 0.5 does this mean that the model could only guess the correct result half of the time ?

The loss seen is a mean average of the loss. When you have one output sigmoid, with a batch size of 1, in my opinion, thats right. Having a greater batch size, makes this more complicated. One example:
batch_size=4
error_batch_1 = 0.4 #close
error_batch_2 = 0.3 #close
error_batch_3 = 0.3 #close
error_batch_4 = 1 #far away
When the average is computed, we get: 2/4 = 0.5
When you look at the error that way, you would think that half of the predictions were correct, but in real, 3 of 4 were correct (implying, that the result is rounded to 1 or 0)

Related

How to customize threshold PyTorch

I have trained ResNet50 for binary image classification.
I want to descrease FalseNegatives by reducing threshold value.
How can I do that?
To decrease the number of false negatives (FN) i.e. increase the recall (since recall = TP / (TP + FN)) you should increase the positive weight (the weight of the occurrence of that class) above 1. For example nn.BCEWithLogitsLoss allows you to provide the pos_weight option:
pos_weight > 1 increases the recall, pos_weight < 1 increases the precision.
For example, if a dataset contains 100 positive and 300 negative examples of a single class, then pos_weight for the class should be equal to 300/100 = 3. The loss would act as if the dataset contains 3*100 = 300 positive examples.
As a side note, the explicit expression for the binary cross entropy with logits (where "with logits" should rather be understood as "from logits") is:
>>> z = torch.sigmoid(q)
>>> loss = -(w_p*p*torch.log(z) + (1-p)*torch.log(1-z))
Above q are the raw logit values while w_p is the weight of the positive instance.

Change the precision of torch.sigmoid?

I want my sigmoid to never print a solid 1 or 0, but to actually print the exact value
i tried using
torch.set_printoptions(precision=20)
but it didn't work. here's a sample output of the sigmoid function :
before sigmoid : tensor([[21.2955703735]])
after sigmoid : tensor([[1.]])
but i don't want it to print 1, i want it to print the exact number, how can i force this?
The difference between 1 and the exact value of sigmoid(21.2955703735) is on the order of 5e-10, which is significantly less than machine epsilon for float32 (which is about 1.19e-7). Therefore 1.0 is the best approximation that can be achieved with the default precision. You can cast your tensor to a float64 (AKA double precision) tensor to get a more precise estimate.
torch.set_printoptions(precision=20)
x = torch.tensor([21.2955703735])
result = torch.sigmoid(x.to(dtype=torch.float64))
print(result)
which results in
tensor([0.99999999943577644324], dtype=torch.float64)
Keep in mind that even with 64-bit floating point computation this is only accurate to about 6 digits past the last 9 (and will be even less precise for larger sigmoid inputs). A better way to represent numbers very close to one is to directly compute the difference between 1 and the value. In this case 1 - sigmoid(x) which is equivalent to 1 / (1 + exp(x)) or sigmoid(-x). For example,
x = torch.tensor([21.2955703735])
delta = torch.sigmoid(-x.to(dtype=torch.float64))
print(f'sigmoid({x.item()}) = 1 - {delta.item()}')
results in
sigmoid(21.295570373535156) = 1 - 5.642236648842976e-10
and is a more accurate representation of your desired result (though still not exact).

spark ml 2.0 - Naive Bayes - how to determine threshold values for each class

I am using NB for document classification and trying to understand threshold parameter to see how it can help to optimize algorithm.
Spark ML 2.0 thresholds doc says:
Param for Thresholds in multi-class classification to adjust the probability of predicting each class. Array must have length equal to the number of classes, with values >= 0. The class with largest value p/t is predicted, where p is the original probability of that class and t is the class' threshold.
0) Can someone explain this better? What goal it can achieve? My general idea is if you have threshold 0.7 then at least one class prediction probability should be more then 0.7 if not then prediction should return empty. Means classify it as 'uncertain' or just leave empty for prediction column. How can p/t function going to achieve that when you still pick the category with max probability?
1) What probability it adjust? default column 'probability' is actually conditional probability and 'rawPrediction' is
confidence according to document. I believe threshold will adjust 'rawPrediction' not 'probability' column. Am I right?
2) Here's how some of my probability and rawPrediction vector look like. How do I set threshold values based on this so I can remove certain uncertain classification? probability is between 0 and 1 but rawPrediction seems to be on log scale here.
Probability:
[2.233368649314982E-15,1.6429456680945863E-9,1.4377313514127723E-15,7.858651849363202E-15]
rawPrediction:
[-496.9606736723107,-483.452183395287,-497.40111830218746]
Basically I want classifier to leave Prediction column empty if it doesn't have any probability that is more then 0.7 percent.
Also, how to classify something as uncertain when more then one category has very close scores e.g. 0.812, 0.800, 0.799 . Picking max is something I may not want here but instead classify as "uncertain" or leave empty and I can do further analysis and treatment for those documents or train another model for those docs.
I haven't played with it, but the intent is to supply different threshold values for each class. I've extracted this example from the docstring:
model = nb.fit(df)
>>> result.prediction
1.0
>>> result.probability
DenseVector([0.42..., 0.57...])
>>> result.rawPrediction
DenseVector([-1.60..., -1.32...])
>>> nb = nb.setThresholds([0.01, 10.00])
>>> model3 = nb.fit(df)
>>> result = model3.transform(test0).head()
>>> result.prediction
0.0
If I understand correctly, the effect was to transform [0.42, 0.58] into [.42/.01, .58/10] = [42, 5.8], switching the prediction ("largest p/t") from column 1 (third row above) to column 0 (last row above). However, I couldn't find the logic in the source. Anyone?
Stepping back: I do not see a built-in way to do what you want: be agnostic if no class dominates. You will have to add that with something like:
def weak(probs, threshold=.7, epsilon=.01):
return np.all(probs < threshold) or np.max(np.diff(probs)) < epsilon
>>> cases = [[.5,.5],[.5,.7],[.7,.705],[.6,.1]]
>>> for case in cases:
... print '{:15s} - {}'.format(case, weak(case))
[0.5, 0.5] - True
[0.5, 0.7] - False
[0.7, 0.705] - True
[0.6, 0.1] - True
(Notice I haven't checked whether probs is a legal probability distribution.)
Alternatively, if you are not actually making a hard decision, use the predicted probabilities and a metric like Brier score, log loss, or info gain that accounts for the calibration as well as the accuracy.

Spark : regression model threshold and precision

I have logistic regression mode, where I explicitly set the threshold to 0.5.
model.setThreshold(0.5)
I train the model and then I want to get basic stats -- precision, recall etc.
This is what I do when I evaluate the model:
val metrics = new BinaryClassificationMetrics(predictionAndLabels)
val precision = metrics.precisionByThreshold
precision.foreach { case (t, p) =>
println(s"Threshold is: $t, Precision is: $p")
}
I get results with only 0.0 and 1.0 as values of threshold and 0.5 is completely ignored.
Here is the output of the above loop:
Threshold is: 1.0, Precision is: 0.8571428571428571
Threshold is: 0.0, Precision is: 0.3005181347150259
When I call metrics.thresholds() it also returns only two values, 0.0 and 1.0.
How do I get the precision and recall values with threshold as 0.5?
You need to clear the model threshold before you make predictions. Clearing threshold makes your predictions return a score and not the classified label. If not you will only have two thresholds, i.e. your labels 0.0 and 1.0.
model.clearThreshold()
A tuple from predictionsAndLabels should look like (0.6753421,1.0) and not (1.0,1.0)
Take a look at https://github.com/apache/spark/blob/master/examples/src/main/scala/org/apache/spark/examples/mllib/BinaryClassificationMetricsExample.scala
You probably still want to set numBins to control the number of points if the input is large.
I think what happens is that all the predictions are 0.0 or 1.0. Then the intermediate threshold values make no difference.
Consider the numBins argument of BinaryClassificationMetrics:
numBins:
if greater than 0, then the curves (ROC curve, PR curve) computed internally will be down-sampled to this many "bins". If 0, no down-sampling will occur. This is useful because the curve contains a point for each distinct score in the input, and this could be as large as the input itself -- millions of points or more, when thousands may be entirely sufficient to summarize the curve. After down-sampling, the curves will instead be made of approximately numBins points instead. Points are made from bins of equal numbers of consecutive points. The size of each bin is floor(scoreAndLabels.count() / numBins), which means the resulting number of bins may not exactly equal numBins. The last bin in each partition may be smaller as a result, meaning there may be an extra sample at partition boundaries.
So if you don't set numBins, then precision will be calculated at all the different prediction values. In your case this seems to be just 0.0 and 1.0.
First, try adding more bins like this (here numBins is 10):
val metrics = new BinaryClassificationMetrics(probabilitiesAndLabels,10);
If you still only have two thresholds of 0 and 1, then check to make sure the way you have defined your predictionAndLabels. You many be having this problem if you have accidentally provided (label, prediction) instead of (prediction, label).

Precision, Recall, Accuracy calculation for Decision Tree in SCALA Spark Environment

I am trying to calculate Precision, Recall, Accuracy for decision tree. This is in relation to a previous question about the same program although the context was different. Please find the link to see the all the codes:
saving model output from Decision tree train classifier as a text file in Spark Scala platform
The codes for calculation are:
//Precision, Recall, Confusion Matrix
val evaluationMetrics = new MulticlassMetrics(labelAndPreds.map(x => (x._1, x._2)))
evaluationMetrics.precision
evaluationMetrics.recall
evaluationMetrics.confusionMatrix
Precision=98.52% and Recall= 98.52%, which seems unlikely since,
Confusion Matrix
Predicted
Actual 0 1
0 16877 251
1 2 20
The above is the Spark calculation of the Confusion Matrix.
The arrangement,
Predicted
Actual 0 1
0 TN FN
1 FP TP
So, Precision = TP/(TP+FP)=20/(20+2) =0.9091
Recall = TP/(TP+FN) = 20/(20+251) =0.074.
Please correct me if I am wrong. If I consider (0,0) group as True Positives(TP) then also Precision and Recall will not be the same. But Spark out as per the code above is showing the same.
It would be great to have suggestions and help. Thanks in advance.
I would like to know how to calculate precision , recall and accuracy from the confusion matrix that I can convert to string.

Resources