After training any classifier, the classifier tells the probability of data point belonging to a class.
y_pred = clf.predict_proba(test_point)
Does the classifier predicts the class with the max probability or does it considers the probabilities as a distribution draws according to distribution?
In other words, suppose the output probability is -
C1 - 0.1 C2 - 0.2 C3 - 0.7
Will the output be C3 always or only 70% of the times?
When clf predict it won’t calculate the probably of each class . It will use the full connect get a array like [itemsnum ,classisnum] then you can use max output[1] get the items class
by the way when clf training it use softmax to get the probably of each class which is more smooth to optimize you can find some doc about softmax if you are interested about train process
How to go from class probability scores to a class is often called the 'decision function', and is often considered separate from the classifier itself. In scikit-learn, many estimators have a default decision function accessible via predict() for multi-class problems this generally just returns the largest value (argmax function).
However this may be extended in various ways, depending on needs. For instance if the effects of one prediction one of the classes is very costly, then one might weight those probabilities down (class weighting). Or one can have a decision function that only gives a class as output if the confidence is high, else returns an error or a fallback class.
One can also have multi-label classification, there the output is not a single class but a list of classes. [ 0.6, 0.1, 0.7, 0.2 ] -> (class0, class2) These can then use a common threshold, or a per-class threshold. This is common in tagging problems.
But in almost all cases the decision function is a deterministic function, not a probabilistic one.
Related
I'm working on a binary classification problem. I had this situation that I used the logistic regression and support vector machine model imported from sklearn. These two models were fit with the same , imbalanced training data and class weights were adjusted. And they have achieved comparable performances. When I used these two pre-trained models to predict a new dataset. The LR model and the SVM models predicted similar number of instances as positives. And the predicted instances share a big overlap.
However, when I looked at the probability scores of being classified as positives, the distribution by LR is from 0.5 to 1 while the SVM starts from around 0.1. I called the function model.predict(prediction_data) to find out the instances predicted as each class and the function
model.predict_proba(prediction_data) to give the probability scores of being classified as 0(neg) and 1(pos), and assume they all have a default threshold 0.5.
There is no error in my code and I have no idea why the SVM predicted instances with probability scores < 0.5 as positives as well. Any thoughts on how to interpret this situation?
That's a known fact in sklearn when it comes to binary classification problems with SVC(), which is reported, for instance, in these github issues
(here and here). Moreover, it is also
reported in the User guide where it is said that:
In addition, the probability estimates may be inconsistent with the scores:
the “argmax” of the scores may not be the argmax of the probabilities; in binary classification, a sample may be labeled by predict as belonging to the positive class even if the output of predict_proba is less than 0.5; and similarly, it could be labeled as negative even if the output of predict_proba is more than 0.5.
or directly within libsvm faq, where it is said that
Let's just consider two-class classification here. After probability information is obtained in training, we do not have prob > = 0.5 if and only if decision value >= 0.
All in all, the point is that:
on one side, predictions are based on decision_function values: if the decision value computed on a new instance is positive, the predicted class is the positive class and viceversa.
on the other side, as stated within one of the github issues, np.argmax(self.predict_proba(X), axis=1) != self.predict(X) which is where the inconsistency comes from. In other terms, in order to always have consistency on binary classification problems you would need a classifier whose predictions are based on the output of predict_proba() (which is btw what you'll get when considering calibrators), like so:
def predict(self, X):
y_proba = self.predict_proba(X)
return np.argmax(y_proba, axis=1)
I'd also suggest this post on the topic.
Suppose I want to use a multilayer perceptron to classify 3 classes. When it comes to number of output neurons, anybody would instantly say - use 3 output neurons with softmax activation. But what if I use 2 output neurons with sigmoid activations to output [0,0] for class 1, [0,1] for class 2 and [1,0] for class 3? Basically getting a binary encoded output with each bit being output by each output neuron. Wouldn't this technique decrease output neurons(and hence number of parameters) by a lot? A 100 class word classification for simple NLP application would require 100 output neurons for softmax where as you can cover it with 7 output neurons with the above technique. One disadvantage is that you won't get the probability scores for all the classes. My question is, is this approach correct? If so, would you consider it to be more efficient than softmaxing for datasets with large number of classes?
You could do this, but then you would have to rethink your loss function. The cross-entropy loss used in training a model for classification is the likelihood of a categorical distribution, which assumes you have a probability associated with every class. The loss function requires 3 output probabilities and you only have 2 output values.
However, there are ways to do it anyway: you could use a binary cross-entropy loss on each element of your output, but this would be a different probabilistic assumption about your model. You'd be assuming that your classes have some shared characteristics [0,0] and [0,1] share a value. The decreased degrees of freedom are probably going to give you marginally worse performance (but other parts of the MLP may pick up the slack).
If you're really worried about the parameter cost of the final layer, then you might be better just not training it at all. This paper shows a fixed Hadamard matrix on the final layer is as good as training it.
My Understanding is Softmax Regression is generalization of Logistic Regression to support multiple classes .
Softmax Regression model first computes a score for each class then estimates the probability of each class by applying the softmax function to the scores.
Each class has its own dedicated parameter vector
My question : Why can't we use Logistic Regression to classify to multiple classes in a much simpler way like if probability is 0 to 0.3 then Class A ; 0.3 to 0.6 then Class B : 0.6 to 0.9 then Class C etc.
Why separate coefficient vector is always needed ?
I'm new to ML . Not sure if this question is due to lack of any fundamental concept understanding .
First up, in terms of terminology, I'd say a more established terminology is multinomial logistic regression.
Softmax function is a natural choice for computing probabilities because it corresponds to MLE. Cross-entropy loss has a probabilistic interpretation as well - that's the "distance" between two distributions (output and target).
What you suggest is to discriminate classes in an artificial way - output a binary distribution and somehow compare it to a multi-class distribution. In theory, it is possible and may work, but surely has drawbacks. For example, it is harder to train.
Suppose the output is 0.2 (i.e. class A) and the ground truth is class B. You'd like to tell the network to shift towards a higher value. Next time, the output is 0.7 - the network actually learned and moved in the right direction, but you punish it again. In fact, there are unstable points (0.3 and 0.6 in your example) that the network need time to learn as critical ones. Two values - 0.2999999 and 0.3000001 are almost indistinguishable for the network, but they determine if the result is correct or not.
In general, output as a probability distribution is always better than direct discrimination, because it gives more information.
Given a balanced dataset (size of both classes are the same), fitting it into an SVM model I yield a high AUC value (~0.9) but a low accuracy (~0.5).
I have totally no idea why would this happen, can anyone explain this case for me?
The ROC curve is biased towards the positive class. The described situation with high AUC and low accuracy can occur when your classifier achieves the good performance on the positive class (high AUC), at the cost of a high false negatives rate (or a low number of true negatives).
The question of why the training process resulted in a classifier with poor predictive performance is very specific to your problem/data and the classification methods used.
The ROC analysis tells you how well the samples of the positive class can be separated from the other class, while the prediction accuracy hints on the actual performance of your classifier.
About ROC analysis
The general context for ROC analysis is binary classification, where a classifier assigns elements of a set into two groups. The two classes are usually referred to as "positive" and "negative". Here, we assume that the classifier can be reduced to the following functional behavior:
def classifier(observation, t):
if score_function(observation) <= t:
observation belongs to the "negative" class
else:
observation belongs to the "positive" class
The core of a classifier is the scoring function that converts observations into a numeric value measuring the affinity of the observation to the positive class. Here, the scoring function incorporates the set of rules, the mathematical functions, the weights and parameters, and all the ingenuity that makes a good classifier. For example, in logistic regression classification, one possible choice for the scoring function is the logistic function that estimates the probability p(x) of an observation x belonging to the positive class.
In a final step, the classifier converts the computed score into a binary class assignment by comparing the score against a decision threshold (or prediction cutoff) t.
Given the classifier and a fixed decision threshold t, we can compute actual class predictions y_p for given observations x. To assess the capability of a classifier, the class predictions y_p are compared with the true class labels y_t of a validation dataset. If y_p and y_t match, we refer to as true positives TP or true negatives TN, depending on the value of y_p and y_t; or false positives FP or false negatives FN if y_p and y_t do not match.
We can apply this to the entire validation dataset and count the total number of TPs, TNs, FPs and FNs, as well as the true positive rate (TPR) and false positive rate rate (FPR), which are defined as follows:
TPR = TP / P = TP / (TP+FN) = number of true positives / number of positives
FPR = FP / N = FP / (FP+TN) = number of false positives / number of negatives
Note that the TPR is often referred to as the sensitivity, and FPR is equivalent to 1-specifity.
In comparison, the accuracy is defined as the ratio of all correctly labeled cases and the total number of cases:
accuracy = (TP+TN)/(Total number of cases) = (TP+TN)/(TP+FP+TN+FN)
Given a classifier and a validation dataset, we can evaluate the true positive rate TPR(t) and false positive rate FPR(t) for varying decision thresholds t. And here we are: Plotting FPR(t) against TPR(t) yields the receiver-operator characteristic (ROC) curve. Below are some sample ROC curves, plotted in Python using roc-utils*.
Think of the decision threshold t as a final free parameter that can be tuned at the end of the training process. The ROC analysis offers means to find an optimal cutoff t* (e.g., Youden index, concordance, distance from optimal point).
Furthermore, we can examine with the ROC curve how well the classifier can discriminate between samples from the "positive" and the "negative" class:
Try to understand how the FPR and TPR change for increasing values of t. In the first extreme case (with some very small value for t), all samples are classified as "positive". Hence, there are no true negatives (TN=0), and thus FPR=TPR=1. By increasing t, both FPR and TPR gradually decrease, until we reach the second extreme case, where all samples are classified as negative, and none as positive: TP=FP=0, and thus FPR=TPR=0. In this process, we start in the top right corner of the ROC curve and gradually move to the bottom left.
In the case where the scoring function is able to separate the samples perfectly, leading to a perfect classifier, the ROC curve passes through the optimal point FPR(t)=0 and TPR(t)=1 (see the left figure below). In the other extreme case where the distributions of scores coincide for both classes, resulting in a random coin-flipping classifier, the ROC curve travels along the diagonal (see the right figure below).
Unfortunately, it is very unlikely that we can find a perfect classifier that reaches the optimal point (0,1) in the ROC curve. But we can try to get as close to it as possible.
The AUC, or the area under the ROC curve, tries to capture this characteristic. It is a measure for how well a classifier can discriminate between the two classes. It varies between 1. and 0. In the case of a perfect classifier, the AUC is 1. A classifier that assigns a random class label to input data would yield an AUC of 0.5.
* Disclaimer: I'm the author of roc-utils
I guess you are miss reading the correct class when calculating the roc curve...
That will explain the low accuracy and the high (wrongly calculated) AUC.
It is easy to see that AUC can be misleading when used to compare two
classifiers if their ROC curves cross. Classifier A may produce a
higher AUC than B, while B performs better for a majority of the
thresholds with which you may actually use the classifier. And in fact
empirical studies have shown that it is indeed very common for ROC
curves of common classifiers to cross. There are also deeper reasons
why AUC is incoherent and therefore an inappropriate measure (see
references below).
http://sandeeptata.blogspot.com/2015/04/on-dangers-of-auc.html
Another simple explanation for this behaviour is that your model is actually very good - just its final threshold to make predictions binary is bad.
I came across this problem with a convolutional neural network on a binary image classification task. Consider e.g, that you have 4 samples with labels 0,0,1,1. Lets say your model creates continuous predictions for these four samples like so: 0.7, 0.75, 0.9 and 0.95.
We would consider this to be a good model, since high values (> 0.8) predict class 1 and low values (< 0.8) predict class 0. Hence, the ROC-AUC would be 1. Note how I used a threshold of 0.8. However, if you use a fixed and badly-chosen threshold for these predictions, say 0.5, which is what we sometimes force upon our model output, then all 4 sample predictions would be class 1, which leads to an accuracy of 50%.
Note that most models optimize not for accuracy, but for some sort of loss function. In my CNN, training for just a few epochs longer solved the problem.
Make sure that you know what you are doing when you transform a continuous model output into a binary prediction. If you do not know what threshold to use for a given ROC curve, have a look at Youden's index or find the threshold value that represents the "most top-left" point in your ROC curve.
If this is happening every single time, may be your model is not correct.
Starting from kernel you need to change and try the model with the new sets.
Look the confusion matrix every time and check TN and TP areas. The model should be inadequate to detect one of them.
I'm trying to solve a text classification problem for academic purpose. I need to classify the tweets into labels like "cloud" ,"cold", "dry", "hot", "humid", "hurricane", "ice", "rain", "snow", "storms", "wind" and "other". Each tweet in training data has probabilities against all the label. Say the message "Can already tell it's going to be a tough scoring day. It's as windy right now as it was yesterday afternoon." has 21% chance for being hot and 79% chance for wind. I have worked on the classification problems which predicts whether its wind or hot or others. But in this problem, each training data has probabilities against all the labels. I have previously used mahout naive bayes classifier which take a specific label for a given text to build model. How to convert these input probabilities for various labels as input to any classifier?
In a probabilistic setting, these probabilities reflect uncertainty about the class label of your training instance. This affects parameter learning in your classifier.
There's a natural way to incorporate this: in Naive Bayes, for instance, when estimating parameters in your models, instead of each word getting a count of one for the class to which the document belongs, it gets a count of probability. Thus documents with high probability of belonging to a class contribute more to that class's parameters. The situation is exactly equivalent to when learning a mixture of multinomials model using EM, where the probabilities you have are identical to the membership/indicator variables for your instances.
Alternatively, if your classifier were a neural net with softmax output, instead of the target output being a vector with a single [1] and lots of zeros, the target output becomes the probability vector you're supplied with.
I don't, unfortunately, know of any standard implementations that would allow you to incorporate these ideas.
If you want an off the shelf solution, you could use a learner the supports multiclass classification and instance weights. Let's say you have k classes with probabilities p_1, ..., p_k. For each input instance, create k new training instances with identical features, and with label 1, ..., k, and assign weights p_1, ..., p_k respectively.
Vowpal Wabbit is one such learner that supports multiclass classification with instance weights.