Getting a low ROC AUC score but a high accuracy
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 usespredict, 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.