Conditional variance penalties and domain shift robustness

By Christina Heinze-Deml, Nicolai Meinshausen. 2017

187 citations recorded by the source corpus.

When training a deep neural network for image classification, one can broadly distinguish between two types of latent features of images that will drive the classification. We can divide latent features into (i) ‘core’ or ‘conditionally invariant’ features C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C$$\end{document} whose distribution C|Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C\vert Y$$\end{document}, conditional on the class Y, does not change substantially across domains and (ii) ‘style’ features S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S$$\end{document} whose distribution S|Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S\vert Y$$\end{document} can change substantially across domains. Examples for style features include position, rotation, image quality or brightness but also more complex ones like hair color, image quality or posture for images of persons. Our goal is to minimize a loss that is robust under changes in the distribution of these style features. In contrast to previous work, we assume that the domain itself is not observed and hence a latent variable. We do assume that we can sometimes observe a typically discrete identifier or “ID\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {ID}$$\end{document} variable”. In some applications we know, for example, that two images show the same person, and ID\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {ID}$$\end{document} then refers to the identity of the person. The proposed method requires only a small fraction of images to have ID\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {ID}$$\end{document} information. We group observations if they share the same class and identifier (Y,ID)=(y,id)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Y,\mathrm {ID})=(y,\mathrm {id})$$\end{document} and penalize the conditional variance of the prediction or the loss if we condition on (Y,ID)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Y,\mathrm {ID})$$\end{document}. Using a causal framework, this conditional variance regularization (CoRe) is shown to protect asymptotically against shifts in the distribution of the style variables in a partially linear structural equation model. Empirically, we show that the CoRe penalty improves predictive accuracy substantially in settings where domain changes occur in terms of image quality, brightness and color while we also look at more complex changes such as changes in movement and posture.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Safety, Robustness & Interpretability

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Citations in the corpus

Shortcut learning in deep neural networks (2020, background): “class-predictive pixels or image quality) and record the accuracy drop on clean test data as a way of finding out how prone a given architecture and loss function are to picking up on shortcuts [39, 40, 100, 41].”
Toward Causal Representation Learning (2021, background): “…[153], [156], [167], [195], [204], [243], [263], [267], [277], [278], [281], complementing the studies of Bareinboim and Pearl [14], [185], and it inspired a thread of work in the statistics community exploiting invariance for causal discovery and other tasks [105], [106], [114], [187], [191].”
Towards Causal Representation Learning (2021, background): “263, 243, 195, 152, 156, 153, 167, 204, 115], complementing the studies of Bareinboim and Pearl [12, 185], and it inspired a thread of work in the statistics community exploiting invariance for causal discovery and other tasks [189, 192, 105, 104, 115].”
Learning explanations that are hard to vary (2020, background): “Other works connecting causality and learning through invariances are (Subbaswamy et al., 2019; Heinze-Deml and Meinshausen, 2017), and perhaps – most related to our work – (Arjovsky et al.”
A theory of independent mechanisms for extrapolation in generative models (2020, methodology): “…akin to the use of a causal framework to enforce domain adaptation (Zhang et al. 2013; Zhang, Gong, and Sch¨olkopf 2015) and domain shift robustness of leaning algorithms, which has been done by exploiting additional information in the context of classiﬁcation (Heinze-Deml and Meinshausen 2017).”
Causality for Machine Learning (2019, background): “…community exploiting invariance for causal discovery and other tasks (Peters et al., 2016; Pfister et al., 2018a; Heinze-Deml et al., 2017; Heinze-Deml and Meinshausen, 2017).16 On the SSL side, subsequent developments include further theoretical analyses (Janzing and Schölkopf, 2015;…”
Invariant Risk Minimization (2019, background): “Some works in machine learning [45, 18, 21, 26, 36, 43, 34, 7] pursue similar questions.”
Causal Regularization (2019, background): “It is believed (and can be proven subject to appropriate model assumptions) that finding statistical models that generalize well across different background conditions is closely linked to finding causal models [7, 8, 9, 10].”
Generalizing to Unseen Domains via Adversarial Data Augmentation (2018, background): “The literature on adversarial training [10, 34, 20, 12] is closely related to our work, since the main goal is to devise training procedures that learn models robust to fluctuations in the input.”
Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization (2019, background): “…prediction models, mostly from the causal inference literature, similarly aim to achieve high performance on a range of test distributions (Peters et al., 2016; B¨uhlmann & Meinshausen, 2016; Heinze-Deml & Meinshausen, 2017; Rothenh¨ausler et al., 2018; Yang et al., 2019; Arjovsky et al., 2019).”
Learning What Makes a Difference from Counterfactual Examples and Gradient Supervision (2020, background): “Recent works have discussed generalization from a causal perspective [6,29,50,54].”
Calibrated ensembles can mitigate accuracy tradeoffs under distribution shift (2022, background): “There has been a lot of research interest in tackling this robustness problem under various settings such as robustness to spurious correlations [Heinze-Deml and Meinshausen, 2017, Sagawa et al., 2020a], domain generalization [Arjovsky et al., 2019, Sun and Saenko, 2016], demographic shifts…”
Invariance-inducing regularization using worst-case transformations suffices to boost accuracy and spatial robustness (2019, methodology): “These approaches are based on augmenting the training data either statically [17, 30, 7, 45], ie.”
An Online Learning Approach to Interpolation and Extrapolation in Domain Generalization (2021, background): “…structure of the data: a set of interventions is assumed to result in separate fixed environments (Peters et al., 2016; Heinze-Deml et al., 2018; Heinze-Deml & Meinshausen, 2020; Christiansen et al., 2020) or distribution shift over time (Tian & Pearl, 2001; Didelez et al., 2006), and the test…”
Logit Pairing Methods Can Fool Gradient-Based Attacks (2018, methodology): “Note that we use targeted PGD attacks for crafting adversarial examples and report adversarial accuracy instead of success rate in order to be consistent with Kannan et al. [2018]. We again find that both CLP and LSQ models do not provide actual robustness.”