# What (probabilistic models) can only output decisions when they are certain?

I'm basically looking for approaches, models, algorithms for the following situation (a fault diagnosis problem):

I have an input set $$\{x_i\}_{i \in \{1..m\}}$$ with $$n$$ binary features of cases (think of "faults" or "alarms" that fired) and $$k$$ classes. Each case $$x_i$$ can belong to at least one class and at most $$k$$ (so I'm dealing with multi-label classification).

Now some relations in the data set are utterly boring/uninformative (say, feature $$a$$ says "Mechanical Error occurred" and label $$b$$ means "Mechanical Error fixed"). But even more generally, whenever $$x_a = 1$$, I see all kinds of labels, i.e., $$a$$ is not predictive. Put differently, the relation is not "functional".

Other input features $$c$$ might have a much more "functional" nature, such that whenever $$x_c = 1$$, I can easily deduce $$y_d = 1$$.

For instance my training set could look something like this:

$$[0, 1,0] \mapsto \{4, 1\}$$

$$[0, 1,0] \mapsto \{2\}$$

$$[1, 0, 0] \mapsto \{1\}$$

$$[1, 0, 0] \mapsto \{1\}$$

So, knowing $$[0,1,0]$$ is not really informative whereas $$[1,0,0]$$ tells me (with high confidence) that the label 1 is active.

I'm looking for the latter pairs, a classifier that only extracts meaningful pairs and ignores uninformative inputs.

Could you point me to relevant techniques / keywords? Thanks a lot!