TIME-LAPSE: Learning to say “I don't know” through spatio-temporal uncertainty scoring

1 INTRODUCTION . Modern machine learning ( ML ) has seen tremendous success in various tasks across multiple domains ( Bojarski et al. , 2016 ; Hinton , 2018 ; Kreinovich & Kosheleva , 2020 ; van den Oord et al. , 2016 ) , surpassing human performance in many benchmarks ( Esteva et al. , 2017 ; Yala et al. , 2019 ; Krizhevsky et al. , 2012 ) . However , deep learning models have been known to fail silently and catastrophically with highly confident predictions ( Nguyen et al. , 2015 ; Goodfellow et al. , 2015 ; Guo et al. , 2017 ) . Such models assume a closed world scenario , i.e. , they assume that variability encountered when deployed in the real-world would be similar to the variability present in their training data . In practice , they encounter an open world where incoming samples can come from shifted distributions or completely new distributions ( Liu et al. , 2020 ) . This behaviour can have severe consequences in mission-critical domains such as healthcare and autonomous driving , where errors can be costly , resulting in injury or even death ( Amodei et al. , 2016 ) . Most widely cited models do not come with an uncertainty scoring mechanism to say “ I don ’ t know ” or to abstain from prediction ( Kompa et al. , 2021 ) . As deployed ML models are used to inform real-world decisions , it is important that they have the ability to understand when they ought to be “ unsure ” . A good uncertainty scoring framework must assign higher uncertainty estimates when the network is faced with distributional shifts or new semantic content , i.e. , out-of-distribution ( OOD ) data but must be certain ( low uncertainty ) and generalize well on learnt distributions yet unseen data ( in-distribution or InD data ) . The task of identifying when incoming inputs are drawn far from the training distribution is called out-of-distribution ( OOD ) detection . At its core , it is a binary classification problem , evaluated using measures such as area under the receiver operating curve ( AUROC ) , area under the precision recall curve ( AUPR ) and false positive rate at 80 % true positive rate ( FPR80 ) . Current OOD evaluation schemes hold different datasets to be OOD sources , without considering if the distinctions are semantic in nature ( Ahmed & Courville , 2020 ) leading to methods that are insensitive to semantic overlap and biased to dataset statistics . Closely related is the task of dataset shift detection ( MorenoTorres et al. , 2012 ) , crucial for deployed systems . Dataset shift can occur due to sample selection bias , non-stationary environments , missing values , new concepts evolving over time , etc . Most ML systems do not evaluate their ability to detect such shifts , presenting a huge gap between models performing well on test sets and models capable of being deployed in the wild . In this paper , we propose TIME-LAPSE , a predictive uncertainty quantification framework using latent space embeddings over time , evaluated through downstream tasks of OOD detection and dataset shift detection . A key insight in our approach is that most real-world scenarios ( such as electroencephalogram ( EEG ) seizure analysis , healthcare decision making , autonomous driving , etc . ) involve consecutive inputs to the model that are likely to be correlated over time . For example , an obstacle detector deployed in a self-driving car will see images correlated over time . A seizure detector installed in a neurology clinic will process hours of time-correlated EEG signals . Even low-risk image classification models deployed in search engines over the cloud will see correlated inputs over time when grouped by user ID or location . Thus , sequentially occurring samples share meaningful semantic correlations . In TIME-LAPSE ( Fig . 1 ) , we compute spatial uncertainty scores based on the following hypotheses : an encoder with enough inductive bias likely ( a ) maps OOD inputs “ far '' from other InD samples in the latent space under the Mahalanobis distance metric ( Lee et al. , 2018 ) and ( b ) produces dissimilarities between their representations under the cosine similarity metric ( Jones & Furnas , 1987 ) . We compute temporal uncertainty scores by exploiting correlations between lower dimensional representations of consecutive samples over time when examined as a sequence . A sequence of InD inputs will show more correlation than a sequence with both InD and OOD inputs or a sequence with just OOD inputs . Recent works limit themselves to OOD detection tasks with evaluations purely on highly curated image benchmarks , but do not extend their tests to more diverse and realistic scenarios required for practical applications ( Ren et al. , 2019 ; Ahmed & Courville , 2020 ) . Such OOD image benchmarks consider different datasets to be OOD sources , neglecting any semantic overlap between their OOD test sets and InD train sets , leading to narrow model capabilities ( Yang et al. , 2021 ) . We show that TIME-LAPSE is more driven by semantic content compared to other techniques , i.e . it is more robust to dataset statistics . Moreover , current evaluation schemes do not consider different dataset drift settings that could occur in the real-world . We put forth an additional sequential evaluation framework to evaluate methods under realistic conditions of data drifts and show that TIME-LAPSE outperforms other methods significantly . We demonstrate the efficacy of our proposed method by comparing against multiple baselines over different domains ( vision , audio and clinical EEGs ) . We achieve state-of-the-art ( SOTA ) on both audio and EEG datasets while improving performance on semantically corrected image benchmarks . To the best of our knowledge , we are the first to use temporal sequences of latent space embeddings for uncertainty quantification . We are also the first to use deep-learning based uncertainty scoring techniques for EEG analyses . To summarize , our key contributions are : • We propose TIME-LAPSE , an uncertainty scoring framework that uses samples ’ similarity in the latent space and their temporal similarity amongst sequential inputs to determine their predictive uncertainty . • We show that scores from TIME-LAPSE are driven by semantic content and are more robust to dataset statistics whereas popular baselines , benchmarked on standard image datasets , are susceptible to dataset statistics and overlook semantic overlap for OOD detection . • We benchmark TIME-LAPSE on diverse domains : audio speech classification , seizure detection using clinical EEGs and image classification . TIME-LAPSE achieves state-of-the-art ( SOTA ) in audio tasks , the EEG domain and semantically corrected image benchmarks . • We propose a sequential evaluation framework for dataset shift detection to evaluate methods under realistic conditions of data drifts and show that TIME-LAPSE outperforms other methods . We hope this evaluation scheme will be adopted for routinely characterizing ML system performance in the wild . 2 RELATED WORK . Uncertainty estimation is a rich field with a long history . Classical techniques include density estimation ( Breunig et al. , 2000 ) , one-class SVMs ( Schölkopf et al. , 1999 ) , tree-isolation forests ( Liu et al. , 2008 ) , etc for one-dimensional data such as time-series However , such techniques scale badly with input dimensionality ( Rabanser et al. , 2019 ) . Calibration is a frequentist notion of uncertainty , measured by proper scoring rules like log-loss or Brier scoring ( Guo et al. , 2017 ; DeGroot & Fienberg , 1983 ; Dawid , 1982 ) . Uncertainty estimation for deep neural networks ( NNs ) ( Lakshminarayanan et al. , 2017 ) typically use a Bayesian formalism to learn distributions over model weights ( Blundell et al. , 2015 ; Malinin & Gales , 2018 ; Chen et al. , 2019 ; Graves , 2011 ; Neal , 1996 ; Welling & Teh , 2011 ) . However , most Bayesian methods are difficult to train and computationally expensive . Gal & Ghahramani ( 2016 ) use Monte-Carlo dropout at test-time with an approximate Bayesian interpretation to derive uncertainty estimates.It is also computationally expensive , requiring k forward passes for each instance during inference . Quality of uncertainty estimates are commonly evaluated using OOD detection . Moreno-Torres et al . ( 2012 ) give a complete overview of closely related topics of distributional shift detection including covariate shift , label shift and concept drift ( Gama et al. , 2014 ) . Several works consider semi-supervised techniques for OOD such as outlier exposure methods ( Hendrycks et al. , 2019a ; Ruff et al. , 2020 ) , while many assume the supervised setting where the target OOD distribution is known and propose alternative training strategies and auxillary OOD tasks ( DeVries & Taylor , 2018 ; Hendrycks et al. , 2019b ; Mohseni et al. , 2020 ; Shalev et al. , 2018 ) in a multi-task setting . In this paper , we consider the more general setting of unsupervised OOD detection where no OOD examples are labelled as such and the encoder has access to only InD training labels . Other methods use representations from NNs to infer OOD inputs . Hendrycks & Gimpel ( 2017 ) use maximum softmax probabilites ( MSP ) to detect OOD data . Liang et al . ( 2018 ) improve this by introducing a temperature parameter to the softmax equation . Lee et al . ( 2018 ) fit class-conditional Gaussians to intermediate activations and use the Mahalanobis distance to identify OOD samples . Recently , some works use self-supervision to get better representations to improve OOD detection ( Tack et al. , 2020 ; Winkens et al. , 2020 ; Sehwag et al. , 2021 ) . Several methods directly use input likelihoods as the OOD detection score . However , studies have shown that generative techniques may be overconfident on complex inputs ( Nalisnick et al. , 2019 ) . Modified likelihood scores have been proposed since then ( Serrà et al. , 2020 ; Xiao et al. , 2020 ; Choi et al. , 2019 ) including energy-based models ( Liu et al. , 2020 ; Du & Mordatch , 2019 ; Grathwohl et al. , 2020 ) and likelihood ratios ( Ren et al. , 2019 ) . Reconstruction-based OOD methods use reconstruction loss as the uncertainty score and primarily use auto-encoders ( Zong et al. , 2018 ; Pidhorskyi et al. , 2018 ) or GANs ( Schlegl et al. , 2017 ; Deecke et al. , 2019 ; Perera et al. , 2019 ) . Our temporal uncertainty scores builds upon and shares similarity to change point detection methods in time-series data ( Aminikhanghahi & Cook , 2017 ; Kifer et al. , 2004 ) along with signal processing techniques such as Particle and Kalman filtering ( van der Merwe et al. , 2001 ; Kalman , 1960 ) . 3 TIME-LAPSE : OUR UNCERTAINTY SCORING FRAMEWORK . We propose TIME-LAPSE , an uncertainty scoring framework using latent-space embeddings over time . We consider a multi-class classification setting here , though our framework can be extended to other scenarios such as regression , segmentation , etc . 3.1 PROBLEM SETUP . Let X represent our high-dimensional input space , X ⊆ Rn . Let Y = { 0 , 1 , 2 , ... , C − 1 } denote the label space where C is the number of classes . In standard multi-class classification , we learn a classifier f : X 7→ Y using a dataset Dtrain ( assumed to be sampled from an underlying distribution p∗ ) such that f ( x ) = p ( Y = yi|x ) , where x ∈ X and yi ∈ Y ∀ i . The final prediction for an unseen input x is given by ŷ = arg maxyi p ( yi|x ) . Given a sequence of unseen inputs , xt ( where t denotes time ) to a classifier during inference , our goal is to output a score s ( xt ) and a selective function g ( xt ) with threshold th ∀ xt such that ( g , s ) ( xt ) : = { ŷ = arg maxyi p ( yi|xt ) , if s ( xt ) ≤ th ABSTAIN or FLAG AS OOD , else We call the score s ( xt ) the associated uncertainty score of input sample xt

Summary: This paper was fundamentally about out of distribution detection. The authors tried to use the changing confidence around prediction values to predict changing distributions. They did so specifically for high dimensional, unstructured data, where distributions are often difficult to understand or quantify and compared their results to a number of current methods in the area on a wide variety of high dimensional data.