OASIS

The OASIS method generates estimates of the weighted F-measure for a binary classifier with respect to a finite pool (test set). In terms of Type I and II errors, the weighted F-measure is defined as follows:

\[F_\alpha = \frac{\mathrm{TP}}{\alpha (\mathrm{TP} + \mathrm{FP}) + (1-\alpha)(\mathrm{TP} + \mathrm{FN})}\]

where \(\alpha \in {[0,1]}\) is the weight, TP is the number of true positives, FP is the number of false positives and FN is the number of false negatives. The weighted F-measure takes on special values for \(\alpha = 0, 0.5, 1\). \(F_0\) corresponds to recall, \(F_{0.5}\) corresponds to F1-score (balanced F-measure), and \(F_1\) corresponds to precision.

Note

This section serves as an introductory guide to the functionality of OASIS. Please consult the API reference for the oasis.OASISSampler class for more detailed information.

Required input

OASIS requires four main inputs:

  1. alpha: the F-measure weight as defined above
  2. predictions: predicted labels for the items in the pool (according to the classifier(s))
  3. scores: classifier scores for the items in the pool (e.g. estimated positive class probability, distance from decision boundary)
  4. oracle: a function which returns ground truth labels for items in the pool (i.e. an interface to a labeller)

Multiple classifiers

OASIS supports evaluating multiple classifiers on the same test set in parallel. It will optimise the sampling strategy to ensure that the performance estimates for all of the classifiers have minimal variance. To use this functionality, simply pass two-dimensional arrays for the predictions and scores inputs. The rows of these arrays should correspond to the items and the columns should correspond to the different classifiers.

Item identifiers

OASIS permits the use of custom unique identifiers for the items in the pool. Simply pass an array to the identifiers argument. If custom identifiers are provided, they will be used when making queries to the oracle function. Otherwise OASIS will refer to the items in the pool according to their index in the input predictions/scores arrays.

Other parameters

There are several optional parameters that may be used to control the behaviour of OASIS. They are explained in detail in the API reference for the oasis.OASISSampler class. Here, we focus on two important sets of optional parameters: those that control the stratification of the pool and those that control the greediness of the sampling.

Stratification parameters

The OASIS method involves partitioning the pool into non-overlapping sets called strata. The strata should be roughly homogeneous—i.e. they should contain items with roughly the same labels (or label probabilities if the labels are uncertain). By default, OASIS will attempt to stratify the pool based on the scores using the ‘cum_sqrt_F’ method. It will also attempt to choose an appropriate number of strata automatically, based on the distribution of the scores.

On occassion, the strata chosen by the automatic method are inappropriate. For example, if the score distribution is highly skewed, the automatic method may yield some strata which are too small (containing only a couple of items). For this reason, it is always advisable to check that the strata are sensible before beginning labelling.

The strata can be tweaked as follows:

  • by providing a custom oasis.stratification.Strata instance for the strata argument
  • by providing the stratification_method, stratification_n_strata and/or stratification_n_bins keyword arguments (to override the automatic values)

Greediness parameters

OASIS samples from the “optimal” instrumental distribution with probability 1 - epsilon, and from the passive (uniform) distribution with probability epsilon. The default setting for the greediness parameter is epsilon = 1e-3—i.e. it is set to be greedy for more rapid convergence. To conduct more “explorative” sampling, you should set epsilon closer to 1.

There are other parameters which indirectly control the greediness of the sampling. The decaying_prior parameter is set to True by default and iteratively decreases the reliance on the prior in favour of the sampled labels, which is effectively a greedy approach. A related parameter is prior_strength, which quantifies the initial weight of the prior. If prior_strength is small (close to zero), then the prior will be weak in comparison to the sampled labels, which is also a greedy strategy.

Labelling and estimation

Once an instance of oasis.OASISSampler is initialised, labelling can begin. To sample and label a sequence of items, simply call the sample method. In between calls of the sample method, you may want to check the estimate of the F-measure to see whether it is converging. The history of estimates (for each iteration) is stored in the estimate_ attribute.

Note

There exists an alternative method to sample called sample_distinct, which is useful when sampling with replacement. This method continues to sample from the pool until a given number of distinct items (i.e. previously unlabelled items) have been sampled. This differs from sample, which doesn’t distinguish between previously labelled/unlabelled items.