I have a binary logistic regression model (0/1), built over binary features. The feature coefficients are usually in the range (-1, 1). After training, can I use the feature coefficients as a proxy for the 'importance' of a feature? If the coefficient is < 0, does that mean the presence of the feature is a negative for the class (i.e., reduces the probability of the output being 1)?
Right; a negative coefficient means that the feature contra-indicates that class. The magnitude is, indeed, the relative importance. -1 and +1 are imperatives: all members of the class do not / do have that feature.
You absolutely can. In fact, this idea of important or 'blame' is the main concept behind machine learning algorithms. The coefficients change many times during the training process through gradient descent. How much the weights update by is actually determined by each weight's contribution towards the cost.
That is, the more a weight is to be blamed for a high cost the more extreme the update will be. Therefore, more extreme values (high positives or low negatives) are an indication of how impactful the respective feature is when the model is making its decision.
Related
I am a beginner in machine learning. So any help or suggestion would be of great help.
I have read that putting weights on features and Predicting is a very bad idea. But what if few features needs to be weighted.
In a classification problem let's say it's a common norm that age is most dependent, how do I give weights to this feature. I was thinking to normalize it but with a variance of 1.5 or 2 (other features with variance 1), I believe that this feature will have more weight. Is this fundamentally wrong ? If wrong any other method.
Does it effect differently for classification and regression problems ?
If we are talking specifically about random forests (as you tagged) then you can use the Weighted Subspace Random Forest algorithm (in R wsrf package). The algorithm determines a weight for each variable and then uses these during the model building.
The informativeness of a variable with respect to the class is
measured by an information gain ratio. The measure is used as the
probability of that variable being selected for inclusion in the
variable subspace when splitting a specific node during the tree
building process. Therefore, variables with higher values by the
measure are more likely to be chosen as candidates during variable
selection and a stronger tree can be built.
Generally if a feature has more Importance compared to other features and the model is Dense enough, with enough training sample, your model will automatically give it more Importance by optimizing weight matrices to account for that because we have partial derivatives in back propagation which calculate change by each connection, so it learns to give more importance to that feature on itself. If you don't normalize it, but scale it to a higher scale, you might have overstated it's important.
In practice a neural network works best if the inputs are centered and white. That means that their covariance is diagonal and the mean is the zero vector. This improves optimization of the neural net, since the hidden activation functions don't saturate that fast and thus do not give you near zero gradients early on in learning.
If you do scale just one feature up by a small value, it may or may not have desired effects, but the higher probability is of saturated gradients, so we avoid it.
Using a LogisticRegression class in scikit-learn on a version of the flight delay dataset.
I use pandas to select some columns:
df = df[["MONTH", "DAY_OF_MONTH", "DAY_OF_WEEK", "ORIGIN", "DEST", "CRS_DEP_TIME", "ARR_DEL15"]]
I fill in NaN values with 0:
df = df.fillna({'ARR_DEL15': 0})
Make sure the categorical columns are marked with the 'category' data type:
df["ORIGIN"] = df["ORIGIN"].astype('category')
df["DEST"] = df["DEST"].astype('category')
Then call get_dummies() from pandas:
df = pd.get_dummies(df)
Now I train and test my data set:
from sklearn.linear_model import LogisticRegression
lr = LogisticRegression()
test_set, train_set = train_test_split(df, test_size=0.2, random_state=42)
train_set_x = train_set.drop('ARR_DEL15', axis=1)
train_set_y = train_set["ARR_DEL15"]
test_set_x = test_set.drop('ARR_DEL15', axis=1)
test_set_y = test_set["ARR_DEL15"]
lr.fit(train_set_x, train_set_y)
Once I call the score method I get around 0.867. However, when I call the roc_auc_score method I get a much lower number of around 0.583
probabilities = lr.predict_proba(test_set_x)
roc_auc_score(test_set_y, probabilities[:, 1])
Is there any reason why the ROC AUC is much lower than what the score method provides?
To start with, saying that an AUC of 0.583 is "lower" than a score* of 0.867 is exactly like comparing apples with oranges.
[* I assume your score is mean accuracy, but this is not critical for this discussion - it could be anything else in principle]
According to my experience at least, most ML practitioners think that the AUC score measures something different from what it actually does: the common (and unfortunate) use is just like any other the-higher-the-better metric, like accuracy, which may naturally lead to puzzles like the one you express yourself.
The truth is that, roughly speaking, the AUC measures the performance of a binary classifier averaged across all possible decision thresholds.
The (decision) threshold in binary classification is the value above which we decide to label a sample as 1 (recall that probabilistic classifiers actually return a value p in [0, 1], usually interpreted as a probability - in scikit-learn it is what predict_proba returns).
Now, this threshold, in methods like scikit-learn predict which return labels (1/0), is set to 0.5 by default, but this is not the only possibility, and it may not even be desirable in come cases (imbalanced data, for example).
The point to take home is that:
when you ask for score (which under the hood uses predict, i.e. labels and not probabilities), you have also implicitly set this threshold to 0.5
when you ask for AUC (which, in contrast, uses probabilities returned with predict_proba), no threshold is involved, and you get (something like) the accuracy averaged across all possible thresholds
Given these clarifications, your particular example provides a very interesting case in point:
I get a good-enough accuracy ~ 87% with my model; should I care that, according to an AUC of 0.58, my classifier does only slightly better than mere random guessing?
Provided that the class representation in your data is reasonably balanced, the answer by now should hopefully be obvious: no, you should not care; for all practical cases, what you care for is a classifier deployed with a specific threshold, and what this classifier does in a purely theoretical and abstract situation when averaged across all possible thresholds should pose very little interest for a practitioner (it does pose interest for a researcher coming up with a new algorithm, but I assume that this is not your case).
(For imbalanced data, the argument changes; accuracy here is practically useless, and you should consider precision, recall, and the confusion matrix instead).
For this reason, AUC has started receiving serious criticism in the literature (don't misread this - the analysis of the ROC curve itself is highly informative and useful); the Wikipedia entry and the references provided therein are highly recommended reading:
Thus, the practical value of the AUC measure has been called into question, raising the possibility that the AUC may actually introduce more uncertainty into machine learning classification accuracy comparisons than resolution.
[...]
One recent explanation of the problem with ROC AUC is that reducing the ROC Curve to a single number ignores the fact that it is about the tradeoffs between the different systems or performance points plotted and not the performance of an individual system
Emphasis mine - see also On the dangers of AUC...
I don't know what exactly AIR_DEL15 is, which you use as your label (it is not in the original data). My guess is that it is an imbalanced feature, i.e there are much more 0's than 1's; in such a case, accuracy as a metric is not meaningful, and you should use precision, recall, and the confusion matrix instead - see also this thread).
Just as an extreme example, if 87% of your labels are 0's, you can have a 87% accuracy "classifier" simply (and naively) by classifying all samples as 0; in such a case, you would also have a low AUC (fairly close to 0.5, as in your case).
For a more general (and much needed, in my opinion) discussion of what exactly AUC is, see my other answer.
I wonder why is our objective is to maximize AUC when maximizing accuracy yields the same?
I think that along with the primary goal to maximize accuracy, AUC will automatically be large.
I guess we use AUC because it explains how well our method is able to separate the data independently of a threshold.
For some applications, we don't want to have false positive or negative. And when we use accuracy, we already make an a priori on the best threshold to separate the data regardless of the specificity and sensitivity.
.
In binary classification, accuracy is a performance metric of a single model for a certain threshold and the AUC (Area under ROC curve) is a performance metric of a series of models for a series of thresholds.
Thanks to this question, I have learnt quite a bit on AUC and accuracy comparisons. I don't think that there's a correlation between the two and I think this is still an open problem. At the end of this answer, I've added some links like these that I think would be useful.
One scenario where accuracy fails:
Example Problem
Let's consider a binary classification problem where you evaluate the performance of your model on a data set of 100 samples (98 of class 0 and 2 of class 1).
Take out your sophisticated machine learning model and replace the whole thing with a dumb system that always outputs 0 for whatever the input it receives.
What is the accuracy now?
Accuracy = Correct predictions/Total predictions = 98/100 = 0.98
We got a stunning 98% accuracy on the "Always 0" system.
Now you convert your system to a cancer diagnosis system and start predicting (0 - No cancer, 1 - Cancer) on a set of patients. Assuming there will be a few cases that corresponds to class 1, you will still achieve a high accuracy.
Despite having a high accuracy, what is the point of the system if it fails to do well on the class 1 (Identifying patients with cancer)?
This observation suggests that accuracy is not a good evaluation metric for every type of machine learning problems. The above is known as an imbalanced class problem and there are enough practical problems of this nature.
As for the comparison of accuracy and AUC, here are some links I think would be useful,
An introduction to ROC analysis
Area under curve of ROC vs. overall accuracy
Why is AUC higher for a classifier that is less accurate than for one that is more accurate?
What does AUC stand for and what is it?
Understanding ROC curve
ROC vs. Accuracy vs. AROC
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 use logistic regression. We know that it is a supervised method and needs calculated feature values both in training and test data. There are six features. Although the functions produce these features’ values are different and their maximum value can be 1, there are four features (both in training and test data) that have very low values. e.g. they range between 0 and 0.1 and are never 1, even more than 0.1!!!. Thus these features’ values are very close to each other. Other features are distributed normally (they range between 0 and 0.9). So the difference between these two kinds of features is high, I think this causes trouble in learning process for logistic regression. Am I right?! Does it need any transforming/normalizing these features? Any help would be highly appreciated.
In short: you should normalize your features prior to training. Typically - so each is either in some range (like [0,1]) or is whitened (mean 0 and std 1).
Why is it important? In order to make "small" features important LR will need very high weights in this dimension. However, you will probably use regularized LR (typically L2 regularized) - in such case it will be very hard to assign high values to these vectors, as regularization penalty will force model to rather choose equally distributed weights instead - thus use normalization. However - if you fit LR without any regularization, then there is no point in scaling (up to numerical errors) as LR does not depend on the choice of scaling (the solution should be exactly the same)