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I am doing a project on multiclass semantic segmentation. I have formulated a model that outputs pretty descent segmented images by decreasing the loss value. However, I cannot evaluate the model performance in metrics, such as meanIoU or Dice coefficient.
In case of binary semantic segmentation it was easy just to set the threshold of 0.5, to classify the outputs as an object or background, but it does not work in the case of multiclass semantic segmentation. Could you please tell me how to obtain model performance on the aforementioned metrics? Any help will be highly appreciated!
By the way, I am using PyTorch framework and CamVid dataset.
If anyone is interested in this answer, please also look at this issue. The author of the issue points out that mIoU can be computed in a different way (and that method is more accepted in literature). So, consider that before using the implementation for any formal publication.
Basically, the other method suggested by the issue-poster is to separately accumulate the intersections and unions over the entire dataset and divide them at the final step. The method in the below original answer computes intersection and union for a batch of images, then divides them to get IoU for the current batch, and then takes a mean of the IoUs over the entire dataset.
However, this below given original method is problematic because the final mean IoU would vary with the batch-size. On the other hand, the mIoU would not vary with the batch size for the method mentioned in the issue as the separate accumulation would ensure that batch size is irrelevant (though higher batch size can definitely help speed up the evaluation).
Original answer:
Given below is an implementation of mean IoU (Intersection over Union) in PyTorch.
def mIOU(label, pred, num_classes=19):
pred = F.softmax(pred, dim=1)
pred = torch.argmax(pred, dim=1).squeeze(1)
iou_list = list()
present_iou_list = list()
pred = pred.view(-1)
label = label.view(-1)
# Note: Following for loop goes from 0 to (num_classes-1)
# and ignore_index is num_classes, thus ignore_index is
# not considered in computation of IoU.
for sem_class in range(num_classes):
pred_inds = (pred == sem_class)
target_inds = (label == sem_class)
if target_inds.long().sum().item() == 0:
iou_now = float('nan')
else:
intersection_now = (pred_inds[target_inds]).long().sum().item()
union_now = pred_inds.long().sum().item() + target_inds.long().sum().item() - intersection_now
iou_now = float(intersection_now) / float(union_now)
present_iou_list.append(iou_now)
iou_list.append(iou_now)
return np.mean(present_iou_list)
Prediction of your model will be in one-hot form, so first take softmax (if your model doesn't already) followed by argmax to get the index with the highest probability at each pixel. Then, we calculate IoU for each class (and take the mean over it at the end).
We can reshape both the prediction and the label as 1-D vectors (I read that it makes the computation faster). For each class, we first identify the indices of that class using pred_inds = (pred == sem_class) and target_inds = (label == sem_class). The resulting pred_inds and target_inds will have 1 at pixels labelled as that particular class while 0 for any other class.
Then, there is a possibility that the target does not contain that particular class at all. This will make that class's IoU calculation invalid as it is not present in the target. So, you assign such classes a NaN IoU (so you can identify them later) and not involve them in the calculation of the mean.
If the particular class is present in the target, then pred_inds[target_inds] will give a vector of 1s and 0s where indices with 1 are those where prediction and target are equal and zero otherwise. Taking the sum of all elements of this will give us the intersection.
If we add all the elements of pred_inds and target_inds, we'll get the union + intersection of pixels of that particular class. So, we subtract the already calculated intersection to get the union. Then, we can divide the intersection and union to get the IoU of that particular class and add it to a list of valid IoUs.
At the end, you take the mean of the entire list to get the mIoU. If you want the Dice Coefficient, you can calculate it in a similar fashion.
Suppose I need to build a network that takes two inputs:
A patient's information, represented as an array of features
Selected treatment, represented as one-hot encoded array
Now how do I build a network that outputs a 2D probability matrix A where A[i,j] represents the probability the patient will end up at state j under treatment i. Let's say there are n possible states, and under any treatment, the total probability of all n states sums up to 1.
I wanted to do this because I was motivated by a similar network, where the inputs are the same as above, but the output is a 1d array representing the expected lifetime after treatment i is delivered. And such network is built as follows:
def default_dense(feature_shape, n_treatment):
feature_input = keras.layers.Input(feature_shape)
treatment_input = keras.layers.Input((n_treatments,))
hidden_1 = keras.layers.Dense(16, activation = 'relu')(feature_input)
hidden_2 = keras.layers.Dense(16, activation = 'relu')(hidden_1)
output = keras.layers.Dense(n_treatments)(hidden_2)
output_on_action = keras.layers.multiply([output, treatment_input])
model = keras.models.Model([feature_input, treatment_input], output_on_action)
model.compile(optimizer=tf.optimizers.Adam(0.001),loss='mse')
return model
And the training is simply
model.fit(x = [features, encoded_treatments], y = encoded_treatments * lifetime[:, np.newaxis], verbose = 0)
This is super handy because when predicting, I can use np.ones() as the encoded_treatments, and the network gives expected lifetimes under all treatments, thus choosing the best one is one-step. Certainly I can create multiple networks, each for a treatment, but it would be much less efficient.
Now the questions is, can I do the same to probability output?
I have figured it out myself. The trick is to use RepeatVector() and Permute() layers to generate a matrix mask for treatments.
The output is an element-wise Multiply() of the mask and a Softmax() of same size.
I have read an article on data leakage. In a hackathon there are two sets of data, train data on which participants train their algorithm and test set on which performance is measured.
Data leakage helps in getting a perfect score in test data, with out viewing train data by exploiting the leak.
I have read the article, but I am missing the crux how the leakage is exploited.
Steps as shown in article are following:
Let's load the test data.
Note, that we don't have any training data here, just test data. Moreover, we will not even use any features of test objects. All we need to solve this task is the file with the indices for the pairs, that we need to compare.
Let's load the data with test indices.
test = pd.read_csv('../test_pairs.csv')
test.head(10)
pairId FirstId SecondId
0 0 1427 8053
1 1 17044 7681
2 2 19237 20966
3 3 8005 20765
4 4 16837 599
5 5 3657 12504
6 6 2836 7582
7 7 6136 6111
8 8 23295 9817
9 9 6621 7672
test.shape[0]
368550
For example, we can think that there is a test dataset of images, and each image is assigned a unique Id from 0 to N−1 (N -- is the number of images). In the dataframe from above FirstId and SecondId point to these Id's and define pairs, that we should compare: e.g. do both images in the pair belong to the same class or not. So, for example for the first row: if images with Id=1427 and Id=8053 belong to the same class, we should predict 1, and 0 otherwise.
But in our case we don't really care about the images, and how exactly we compare the images (as long as comparator is binary).
print(test['FirstId'].nunique())
print(test['SecondId'].nunique())
26325
26310
So the number of pairs we are given to classify is very very small compared to the total number of pairs.
To exploit the leak we need to assume (or prove), that the total number of positive pairs is small, compared to the total number of pairs. For example: think about an image dataset with 1000 classes, N images per class. Then if the task was to tell whether a pair of images belongs to the same class or not, we would have 1000*N*(N−1)/2 positive pairs, while total number of pairs was 1000*N(1000N−1)/2.
Another example: in Quora competitition the task was to classify whether a pair of qustions are duplicates of each other or not. Of course, total number of question pairs is very huge, while number of duplicates (positive pairs) is much much smaller.
Finally, let's get a fraction of pairs of class 1. We just need to submit a constant prediction "all ones" and check the returned accuracy. Create a dataframe with columns pairId and Prediction, fill it and export it to .csv file. Then submit
test['Prediction'] = np.ones(test.shape[0])
sub=pd.DataFrame(test[['pairId','Prediction']])
sub.to_csv('sub.csv',index=False)
All ones have accuracy score is 0.500000.
So, we assumed the total number of pairs is much higher than the number of positive pairs, but it is not the case for the test set. It means that the test set is constructed not by sampling random pairs, but with a specific sampling algorithm. Pairs of class 1 are oversampled.
Now think, how we can exploit this fact? What is the leak here? If you get it now, you may try to get to the final answer yourself, othewise you can follow the instructions below.
Building a magic feature
In this section we will build a magic feature, that will solve the problem almost perfectly. The instructions will lead you to the correct solution, but please, try to explain the purpose of the steps we do to yourself -- it is very important.
Incidence matrix
First, we need to build an incidence matrix. You can think of pairs (FirstId, SecondId) as of edges in an undirected graph.
The incidence matrix is a matrix of size (maxId + 1, maxId + 1), where each row (column) i corresponds i-th Id. In this matrix we put the value 1to the position [i, j], if and only if a pair (i, j) or (j, i) is present in a given set of pais (FirstId, SecondId). All the other elements in the incidence matrix are zeros.
Important! The incidence matrices are typically very very sparse (small number of non-zero values). At the same time incidence matrices are usually huge in terms of total number of elements, and it is impossible to store them in memory in dense format. But due to their sparsity incidence matrices can be easily represented as sparse matrices. If you are not familiar with sparse matrices, please see wiki and scipy.sparse reference. Please, use any of scipy.sparseconstructors to build incidence matrix.
For example, you can use this constructor: scipy.sparse.coo_matrix((data, (i, j))). We highly recommend to learn to use different scipy.sparseconstuctors, and matrices types, but if you feel you don't want to use them, you can always build this matrix with a simple for loop. You will need first to create a matrix using scipy.sparse.coo_matrix((M, N), [dtype]) with an appropriate shape (M, N) and then iterate through (FirstId, SecondId) pairs and fill corresponding elements in matrix with ones.
Note, that the matrix should be symmetric and consist only of zeros and ones. It is a way to check yourself.
import networkx as nx
import numpy as np
import pandas as pd
import scipy.sparse
import matplotlib.pyplot as plt
test = pd.read_csv('../test_pairs.csv')
x = test[['FirstId','SecondId']].rename(columns={'FirstId':'col1', 'SecondId':'col2'})
y = test[['SecondId','FirstId']].rename(columns={'SecondId':'col1', 'FirstId':'col2'})
comb = pd.concat([x,y],ignore_index=True).drop_duplicates(keep='first')
comb.head()
col1 col2
0 1427 8053
1 17044 7681
2 19237 20966
3 8005 20765
4 16837 599
data = np.ones(comb.col1.shape, dtype=int)
inc_mat = scipy.sparse.coo_matrix((data,(comb.col1,comb.col2)), shape=(comb.col1.max() + 1, comb.col1.max() + 1))
rows_FirstId = inc_mat[test.FirstId.values,:]
rows_SecondId = inc_mat[test.SecondId.values,:]
f = rows_FirstId.multiply(rows_SecondId)
f = np.asarray(f.sum(axis=1))
f.shape
(368550, 1)
f = f.sum(axis=1)
f = np.squeeze(np.asarray(f))
print (f.shape)
Now build the magic feature
Why did we build the incidence matrix? We can think of the rows in this matix as of representations for the objects. i-th row is a representation for an object with Id = i. Then, to measure similarity between two objects we can measure similarity between their representations. And we will see, that such representations are very good.
Now select the rows from the incidence matrix, that correspond to test.FirstId's, and test.SecondId's.
So do not forget to convert pd.series to np.array
These lines should normally run very quickly
rows_FirstId = inc_mat[test.FirstId.values,:]
rows_SecondId = inc_mat[test.SecondId.values,:]
Our magic feature will be the dot product between representations of a pair of objects. Dot product can be regarded as similarity measure -- for our non-negative representations the dot product is close to 0 when the representations are different, and is huge, when representations are similar.
Now compute dot product between corresponding rows in rows_FirstId and rows_SecondId matrices.
From magic feature to binary predictions
But how do we convert this feature into binary predictions? We do not have a train set to learn a model, but we have a piece of information about test set: the baseline accuracy score that you got, when submitting constant. And we also have a very strong considerations about the data generative process, so probably we will be fine even without a training set.
We may try to choose a thresold, and set the predictions to 1, if the feature value f is higer than the threshold, and 0 otherwise. What threshold would you choose?
How do we find a right threshold? Let's first examine this feature: print frequencies (or counts) of each value in the feature f.
For example use np.unique function, check for flags
Function to count frequency of each element
from scipy.stats import itemfreq
itemfreq(f)
array([[ 14, 183279],
[ 15, 852],
[ 19, 546],
[ 20, 183799],
[ 21, 6],
[ 28, 54],
[ 35, 14]])
Do you see how this feature clusters the pairs? Maybe you can guess a good threshold by looking at the values?
In fact, in other situations it can be not that obvious, but in general to pick a threshold you only need to remember the score of your baseline submission and use this information.
Choose a threshold below:
pred = f > 14 # SET THRESHOLD HERE
pred
array([ True, False, True, ..., False, False, False], dtype=bool)
submission = test.loc[:,['pairId']]
submission['Prediction'] = pred.astype(int)
submission.to_csv('submission.csv', index=False)
I want to understand the idea behind this. How we are exploiting the leak from the test data only.
There's a hint in the article. The number of positive pairs should be 1000*N*(N−1)/2, while the number of all pairs is 1000*N(1000N−1)/2. Of course, the number of all pairs is much, much larger if the test set was sampled at random.
As the author mentions, after you evaluate your constant prediction of 1s on the test set, you can tell that the sampling was not done at random. The accuracy you obtain is 50%. Had the sampling been done correctly, this value should've been much lower.
Thus, they construct the incidence matrix and calculate the dot product (the measure of similarity) between the representations of our ID features. They then reuse the information about the accuracy obtained with constant predictions (at 50%) to obtain the corresponding threshold (f > 14). It's set to be greater than 14 because that constitutes roughly half of our test set, which in turn maps back to the 50% accuracy.
The "magic" value didn't have to be greater than 14. It could have been equal to 14. You could have adjusted this value after some leader board probing (as long as you're capturing half of the test set).
It was observed that the test data was not sampled properly; same-class pairs were oversampled. Thus there is a much higher probability of each pair in the training set to have target=1 than any random pair. This led to the belief that one could construct a similarity measure based only on the pairs that are present in the test, i.e., whether a pair made it to the test is itself a strong indicator of similarity.
Using this insight one can calculate an incidence matrix and represent each id j as a binary array (the i-th element representing the presence of i-j pair in test, and thus representing the strong probability of similarity between them). This is a pretty accurate measure, allowing one to find the "similarity" between two rows just by taking their dot product.
The cutoff arrived at is purely by the knowledge of target-distribution found by leaderboard probing.
This release of PyTorch seems provide the PackedSequence for variable lengths of input for recurrent neural network. However, I found it's a bit hard to use it correctly.
Using pad_packed_sequence to recover an output of a RNN layer which were fed by pack_padded_sequence, we got a T x B x N tensor outputs where T is the max time steps, B is the batch size and N is the hidden size. I found that for short sequences in the batch, the subsequent output will be all zeros.
Here are my questions.
For a single output task where the one would need the last output of all the sequences, simple outputs[-1] will give a wrong result since this tensor contains lots of zeros for short sequences. One will need to construct indices by sequence lengths to fetch the individual last output for all the sequences. Is there more simple way to do that?
For a multiple output task (e.g. seq2seq), usually one will add a linear layer N x O and reshape the batch outputs T x B x O into TB x O and compute the cross entropy loss with the true targets TB (usually integers in language model). In this situation, do these zeros in batch output matters?
Question 1 - Last Timestep
This is the code that i use to get the output of the last timestep. I don't know if there is a simpler solution. If it is, i'd like to know it. I followed this discussion and grabbed the relative code snippet for my last_timestep method. This is my forward.
class BaselineRNN(nn.Module):
def __init__(self, **kwargs):
...
def last_timestep(self, unpacked, lengths):
# Index of the last output for each sequence.
idx = (lengths - 1).view(-1, 1).expand(unpacked.size(0),
unpacked.size(2)).unsqueeze(1)
return unpacked.gather(1, idx).squeeze()
def forward(self, x, lengths):
embs = self.embedding(x)
# pack the batch
packed = pack_padded_sequence(embs, list(lengths.data),
batch_first=True)
out_packed, (h, c) = self.rnn(packed)
out_unpacked, _ = pad_packed_sequence(out_packed, batch_first=True)
# get the outputs from the last *non-masked* timestep for each sentence
last_outputs = self.last_timestep(out_unpacked, lengths)
# project to the classes using a linear layer
logits = self.linear(last_outputs)
return logits
Question 2 - Masked Cross Entropy Loss
Yes, by default the zero padded timesteps (targets) matter. However, it is very easy to mask them. You have two options, depending on the version of PyTorch that you use.
PyTorch 0.2.0: Now pytorch supports masking directly in the CrossEntropyLoss, with the ignore_index argument. For example, in language modeling or seq2seq, where i add zero padding, i mask the zero padded words (target) simply like this:
loss_function = nn.CrossEntropyLoss(ignore_index=0)
PyTorch 0.1.12 and older: In the older versions of PyTorch, masking was not supported, so you had to implement your own workaround. I solution that i used, was masked_cross_entropy.py, by jihunchoi. You may be also interested in this discussion.
A few days ago, I found this method which uses indexing to accomplish the same task with a one-liner.
I have my dataset batch first ([batch size, sequence length, features]), so for me:
unpacked_out = unpacked_out[np.arange(unpacked_out.shape[0]), lengths - 1, :]
where unpacked_out is the output of torch.nn.utils.rnn.pad_packed_sequence.
I have compared it with the method described here, which looks similar to the last_timestep() method Christos Baziotis is using above (also recommended here), and the results are the same in my case.
I've read from the relevant documentation that :
Class balancing can be done by sampling an equal number of samples from each class, or preferably by normalizing the sum of the sample weights (sample_weight) for each class to the same value.
But, it is still unclear to me how this works. If I set sample_weight with an array of only two possible values, 1's and 2's, does this mean that the samples with 2's will get sampled twice as often as the samples with 1's when doing the bagging? I cannot think of a practical example for this.
Some quick preliminaries:
Let's say we have a classification problem with K classes. In a region of feature space represented by the node of a decision tree, recall that the "impurity" of the region is measured by quantifying the inhomogeneity, using the probability of the class in that region. Normally, we estimate:
Pr(Class=k) = #(examples of class k in region) / #(total examples in region)
The impurity measure takes as input, the array of class probabilities:
[Pr(Class=1), Pr(Class=2), ..., Pr(Class=K)]
and spits out a number, which tells you how "impure" or how inhomogeneous-by-class the region of feature space is. For example, the gini measure for a two class problem is 2*p*(1-p), where p = Pr(Class=1) and 1-p=Pr(Class=2).
Now, basically the short answer to your question is:
sample_weight augments the probability estimates in the probability array ... which augments the impurity measure ... which augments how nodes are split ... which augments how the tree is built ... which augments how feature space is diced up for classification.
I believe this is best illustrated through example.
First consider the following 2-class problem where the inputs are 1 dimensional:
from sklearn.tree import DecisionTreeClassifier as DTC
X = [[0],[1],[2]] # 3 simple training examples
Y = [ 1, 2, 1 ] # class labels
dtc = DTC(max_depth=1)
So, we'll look trees with just a root node and two children. Note that the default impurity measure the gini measure.
Case 1: no sample_weight
dtc.fit(X,Y)
print dtc.tree_.threshold
# [0.5, -2, -2]
print dtc.tree_.impurity
# [0.44444444, 0, 0.5]
The first value in the threshold array tells us that the 1st training example is sent to the left child node, and the 2nd and 3rd training examples are sent to the right child node. The last two values in threshold are placeholders and are to be ignored. The impurity array tells us the computed impurity values in the parent, left, and right nodes respectively.
In the parent node, p = Pr(Class=1) = 2. / 3., so that gini = 2*(2.0/3.0)*(1.0/3.0) = 0.444..... You can confirm the child node impurities as well.
Case 2: with sample_weight
Now, let's try:
dtc.fit(X,Y,sample_weight=[1,2,3])
print dtc.tree_.threshold
# [1.5, -2, -2]
print dtc.tree_.impurity
# [0.44444444, 0.44444444, 0.]
You can see the feature threshold is different. sample_weight also affects the impurity measure in each node. Specifically, in the probability estimates, the first training example is counted the same, the second is counted double, and the third is counted triple, due to the sample weights we've provided.
The impurity in the parent node region is the same. This is just a coincidence. We can compute it directly:
p = Pr(Class=1) = (1+3) / (1+2+3) = 2.0/3.0
The gini measure of 4/9 follows.
Now, you can see from the chosen threshold that the first and second training examples are sent to the left child node, while the third is sent to the right. We see that impurity is calculated to be 4/9 also in the left child node because:
p = Pr(Class=1) = 1 / (1+2) = 1/3.
The impurity of zero in the right child is due to only one training example lying in that region.
You can extend this with non-integer sample-wights similarly. I recommend trying something like sample_weight = [1,2,2.5], and confirming the computed impurities.