ALT-MAS: A Data-Efficient Framework for Active Testing of Machine Learning Algorithms

Machine learning models are being used extensively in many important areas , but there is no guarantee that a model will always perform well or as its developers intended . Understanding the correctness of a model is crucial to prevent potential failures that may have significant detrimental impact in critical application areas . In this paper , we propose a novel framework to efficiently test a machine learning model using only a small amount of labelled test data . The core idea is to efficiently estimate the metrics of interest for a model-under-test using Bayesian neural network . We develop a novel methodology to incorporate the information from the model-under test into the Bayesian neural network training process . We also devise an entropy-based sampling strategy to sample the data point such that the proposed framework can give accurate estimations for the metrics of interest . Finally , we conduct an extensive set of experiments to test various machine learning models for different types of metrics . Our experiments with multiple datasets show that given a testing budget , the estimation of the metrics by our method is significantly better compared to existing state-of-the-art approaches . 1 INTRODUCTION . Today , supervised machine learning models are employed across sectors to assist humans in making important decisions . Understanding the correctness of a model is thus crucial to avoid potential ( and severe ) failures . In practice , however , it is not always possible to accurately evaluate the model ’ s correctness using the held-out training data in the development process ( Sawade et al. , 2010 ) . Consider a hospital that buys an automated medical image classification system . The supplier will provide a performance assessment , but this evaluation may not hold in this new setting as the supplier and the hospital data distributions may differ . Similarly , an enterprise that develops a business prediction system might find that the performance changes significantly over time as the input distribution shifts from the original training data . In these cases , the model performance needs to be re-evaluated as the assessments provided from the supplier or from the development process can be inaccurate . To accurately evaluate the model performance , new labelled data points from the deployment area are needed . But the process of labelling is expensive as one would usually need a large number of test instances . Thus the open question is how to test the performance of a machine learning model ( model-under-test ) with parsimonious use of labelled data from the deployment area . This work focuses on addressing this challenge treating the model-under-test as a black-box as in common practice one only has access to the model outputs . One previous approach aims to estimate a risk score which is a function of the model-under-test output and the ground-truth ( akin to metric ) using limited labelled data ( Sawade et al. , 2010 ) . However , the approach has only been shown to be tractable for some specific risk functions ( e.g . accuracy ) . Another approach in ( Gopakumar et al. , 2018 ) suggested to search for the worst case model performance using limited labelled data , however , we posit that using worst case to assess the goodness of a model-under-test is an overkill because the worst case is often just an outlier . Recently , ( Schelter et al. , 2020 ) learns to validate the model without labelled data by generating a synthetic dataset representative of the deployment data . The restrictive assumption is that it requires domain experts to provide a set of data generators , a task usually infeasible in reality . We propose a scalable data-efficient framework that can assess the performance of a black-box model-under-test on any metric ( that is applicable for black-box models ) without prior knowledge from users . Furthermore , our framework can estimate multiple metrics simultaneously . The motivation for evaluating one or multiple metrics is inspired by the current practice of users who need to assess the model-under-test on one or varied aspects that are important to them . For instance , for a classification system , the user might want to solely check the overall accuracy or simultaneously check the overall accuracy , macro-precision ( recall ) and/or the accuracies of some classes of interest . To achieve sample efficiency , we formulate our testing framework as an active learning ( AL ) problem ( Cohn et al. , 1996 ) . First , a small subset of the test dataset is labelled , and a surrogate model is learned from this subset to predict the ground truth of the unlabelled data points in the test dataset . Second , an acquisition function is constructed to decide which data point in the test dataset should be chosen for labelling . The data point selected by the acquisition is sent to an external oracle for labelling , and is then added to the labelled set . The process is conducted iteratively until the labelling budget is depleted . The metrics of interest are then estimated using the learned surrogate model . With this framework , one choice is to use a standard AL method to learn a surrogate model that accurately predicts the labels of all the data points in the test dataset , however , this choice is not optimal . To efficiently estimate the metrics of interest , the surrogate model should not need to accurately predict the labels of all the data points ; it only needs to accurately predict the labels of those data points that contribute significantly to the accuracy of the metric estimations . For our active testing framework , we first propose a method to train the surrogate model that can provide high metric estimation accuracy ( using limited number of labelled data ) by incorporating information from the model-under-test . Second , we derive an entropy-based acquisition function that can select the data points for whom labels should be acquired so as to enable maximal reduction in the estimation uncertainty of the metric of interest . We then use this computed entropy to generalize our framework to be able to work with multiple metrics . Finally , we demonstrate the efficacy of our proposed testing framework using various models-under-test and a wide range of metric sets on different datasets . In summary , our main contributions are : 1 . ALT-MAS , a data-efficient testing framework that can accurately estimate the performance of a machine learning model ; 2 . A novel approach to train the BNN so as to accurately estimate the metrics of interest ; 3 . A novel sampling methodology so as to estimate the metrics of interest efficiently ; and , 4 . Demonstration of the empirical effectiveness of our proposed machine learning testing framework on various models-under-test for a wide range of metrics and different datasets . 2 PROBLEM FORMULATION AND BACKGROUND . 2.1 PROBLEM FORMULATION . Let us assume we are given a black-box model-under-test A that gives the prediction A ( x ) for an input x , with A ( x ) ∈ C = { 1 , . . . , C } . Let us also assume we have access to ( i ) an unlabelled test dataset X = { xi } Ni=1 , and , ( ii ) an oracle that can provide the label yx for each input x in X . Given a set of performance metrics { Qk } Kk=1 , Qk : RN × RN → R , the goal is to efficiently estimate the values of these metrics , { Q∗k } Kk=1 , when evaluating the model-under-test A on the test dataset X . That is , we aim to estimate , Q∗k = Qk ( AX , YX ) , k = 1 , . . . , K , ( 1 ) with AX = { A ( x ) } x∈X and YX = { yx } x∈X , using the minimal number of oracle queries . In this work , we focus on classifiers because they are common supervised learning models and also the target models of most machine learning testing papers ( Zhang et al. , 2019 ) . Besides , it is also worth noting that , as we only have access to the outputs of the black-box classifier , the metrics { Qk } must be those that can be computed using solely the classifier outputs AX and the groundtruth labels YX of the test dataset X . Examples of Qk include the accuracy , error rate , per-class precision/recall , macro precision/recall , Fβ score , etc . This is to distinguish with the metrics that require information from the classifier internal structure such as the log-loss metric . 2.2 BACKGROUND . Bayesian neural networks ( BNNs ) are special neural networks that maintain a distribution over its parameters ( MacKay , 1992 ; Neal , 1995 ) . Specifically , given the training data Dtr = { xi , yi } Ni=1 , a BNN can provide the posterior distribution p∗ ( ω|Dtr ) with ω being the neural network weights . In practice , performing exact inference to obtain p∗ ( ω|Dtr ) is generally intractable , hence we use a variational approximation technique to approximate this posterior . In particular , we employ the MC-dropout method ( Gal & Ghahramani , 2016 ) as it is known to be both scalable and theoretically guaranteed in terms of inferring the true model posterior distribution p∗ ( ω|Dtr ) . That is , the MCdropout method is equivalent to performing approximate variational inference to find a distribution in a tractable family that minimizes the Kullback-Leibler divergence to the true model posterior . 3 ACTIVE TESTING WITH METRIC-AWARE SAMPLING STRATEGY . Our active testing framework is summarized as follows . First , a small subset Xl of the test dataset X is labelled to construct a labelled set Dl = { Xl , YXl } , where YXl denotes the labels provided by the oracle for Xl ; and a BNN Bω ( with parameter ω ) is learned from Dl to predict the labels of the unlabelled data points in X . Second , an acquisition function is constructed based on the BNN Bω , the characteristics of the metric set , and the model-under-test outputsAX to decide which data point is to be labelled so as to maximally reduce the uncertainty in the metric estimations . This data point is sent for labelling , and is added to the labelled set Dl . This process is conducted iteratively until the labelling budget is depleted . The metrics of interest are estimated using the BNN Bω . In this section , we propose a method to train a BNN that can give accurate metric estimations from a limited number of labelled data ( Section 3.1 ) , a method to estimate the metrics of interest given the BNN ( Section 3.2 ) , and a method to sample the most informative data point to maximize the estimation accuracy of a specific metric ( Section 3.3 ) or a set of metrics ( Section 3.4 ) . 3.1 BAYESIAN NEURAL NETWORK TRAINING METHODOLOGY . Given the labelled set Dl and the model-under-test outputs AX , the goal is to train a BNN Bω such that the corresponding metric estimations are most accurate . Training BNN using solely the labelled setDl might not result in accurate enough metric estimations . Thus , to improve the metric estimation accuracy , we propose to incorporate the information from the model-under-test outputs AX into the BNN training process . In particular , using the labelled set Dl , we also train a binary classifier Cη that aims to predict the data points in the test dataset for which the model-under-test agrees with the ground-truth . Using the predictions by the classifier Cη , we then construct an augmented labelled set Sl = { XS , YXS } where XS are all the data points in the test dataset X that Cη identifies the model-under-test predictions are accurate , and YXS are the corresponding model-under-test outputs of XS . The BNN is then trained using both the labelled set Dl and the augmented labelled set Sl . To train the binary classifier Cη , we first split the labelled set Dl into two parts : training and validation , and then train Cη on the training part whilst tuning the softmax probability threshold using the validation part so that Cη achieves the highest precision on the validation part . This is because we want Cη to choose a data point only when it is most certain that the ground-truth and the modelunder-test output of that data point is the same . Besides , as the precision of Cη is rarely 100 % , thus , after obtaining the set of data points provided by Cη , we only take Ns data points from this set with the highest softmax probability . The number Ns is computed by multiplying the precision of Cη on the validation part with the cardinality of the original predicted set . For example , if the precision of the classifier Cη is 50 % on the validation part and the original predicted set consisting of 100 data points , the final augmented labelled set Sl only consists of 50 data points with the highest softmax probability . Finally , the binary classification problem can be imbalanced , particularly when the model-under-test is very accurate or very bad . Hence , when training Cη , we employ the oversampling technique ( for the minority class ) to ensure the training data of the binary classification problem to be balanced , i.e . the cardinalities of the majority and minority classes are equal . Remark 3.1 . With this training methodology , the more accurate the model-under-test , the more accurate the BNN Bω . In case when the model-under-test is bad , the augmented labelled set Sl does not consist of many elements , thus , the BNN accuracy does not improve much compared to when training solely using the labelled set Dl . However , in this case , the BNN does not need to have high accuracy in order to accurately estimate the metrics . Specifically , for any data point for which the model-under-test disagrees with the ground truth , the BNN does not need to accurately predict its label . That is , even when the BNN predicts other labels ( except the model-under-test output label ) , the metric estimation is still accurate ( more detailed examples in Section C.3 of the appendix ) . Remark 3.2 . For simplicity , we suggest to set the architecture of the binary classifier and BNN to be same . For example , if the BNN is a 2-layer MLP , then the binary classifier is also a 2-layer MLP .

Summary: The authors have proposed using an active learning approach to estimate evaluation metrics for a given model. The approach learns a sampling function that decides which observations need to be labeled, which are then fed to a Bayesian neural network (BNN) that aims to estimate the distribution Y|X. The authors select which observations to sample by maximizing the mutual information between the model evaluation metric and the BNN parameters.