arXiv subjects

Bernhard Schölkopf

Publications and source records attributed to Bernhard Schölkopf.

At least 289 records · Page 16Linked to original sources

arXiv2022

The Role of Pretrained Representations for the OOD Generalization of Reinforcement Learning Agents

Building sample-efficient agents that generalize out-of-distribution (OOD) in real-world settings remains a fundamental unsolved problem on the path towards achieving higher-level cognition. One particularly promising approach is to begin with low-dimensional, pretrained representations of our world, which should facilitate efficient downstream learning and generalization. By training 240 representations and over 10,000 reinforcement learning (RL) policies on a simulated robotic setup, we evaluate to what extent different properties of pretrained VAE-based representations affect the OOD generalization of downstream agents. We observe that many agents are surprisingly robust to realistic distribution shifts, including the challenging sim-to-real case. In addition, we find that the generalization performance of a simple downstream proxy task reliably predicts the generalization performance of our RL agents under a wide range of OOD settings. Such proxy tasks can thus be used to select pretrained representations that will lead to agents that generalize.

cs.LG↗

arXiv2022

Half-sibling regression meets exoplanet imaging: PSF modeling and subtraction using a flexible, domain knowledge-driven, causal framework

High-contrast imaging of exoplanets hinges on powerful post-processing methods to denoise the data and separate the signal of a companion from its host star, which is typically orders of magnitude brighter. Existing post-processing algorithms do not use all prior domain knowledge that is available about the problem. We propose a new method that builds on our understanding of the systematic noise and the causal structure of the data-generating process. Our algorithm is based on a modified version of half-sibling regression (HSR), a flexible denoising framework that combines ideas from the fields of machine learning and causality. We adapt the method to address the specific requirements of high-contrast exoplanet imaging data obtained in pupil tracking mode. The key idea is to estimate the systematic noise in a pixel by regressing the time series of this pixel onto a set of causally independent, signal-free predictor pixels. We use regularized linear models in this work; however, other (non-linear) models are also possible. In a second step, we demonstrate how the HSR framework allows us to incorporate observing conditions such as wind speed or air temperature as additional predictors. When we apply our method to four data sets from the VLT/NACO instrument, our algorithm provides a better false-positive fraction than PCA-based PSF subtraction, a popular baseline method in the field. Additionally, we find that the HSR-based method provides direct and accurate estimates for the contrast of the exoplanets without the need to insert artificial companions for calibration in the data sets. Finally, we present first evidence that using the observing conditions as additional predictors can improve the results. Our HSR-based method provides an alternative, flexible and promising approach to the challenge of modeling and subtracting the stellar PSF and systematic noise in exoplanet imaging data.

astro-ph.IM↗

arXiv2022

The unpopular Package: a Data-driven Approach to De-trend TESS Full Frame Image Light Curves

The majority of observed pixels on the Transiting Exoplanet Survey Satellite (TESS) are delivered in the form of full frame images (FFI). However, the FFIs contain systematic effects such as pointing jitter and scattered light from the Earth and Moon that must be removed before downstream analysis. We present unpopular, an open-source Python package to de-trend TESS FFI light curves based on the causal pixel model method. Under the assumption that shared flux variations across multiple distant pixels are likely to be systematics, unpopular removes these common (i.e., popular) trends by modeling the systematics in a given pixel's light curve as a linear combination of light curves from many other distant pixels. To prevent overfitting we employ ridge regression and a train-and-test framework where the data points being de-trended are separated from those used to obtain the model coefficients. We also allow for simultaneous fitting with a polynomial model to capture any long-term astrophysical trends. We validate our method by de-trending different sources (e.g., supernova, tidal disruption event, exoplanet-hosting star, fast rotating star) and comparing our light curves to those obtained by other pipelines when appropriate. We also show that unpopular is able to preserve sector-length astrophysical signals, allowing for the extraction of multi-sector light curves from the FFI data. The unpopular source code and tutorials are freely available online.

astro-ph.IM↗

arXiv2022

From Statistical to Causal Learning

We describe basic ideas underlying research to build and understand artificially intelligent systems: from symbolic approaches via statistical learning to interventional models relying on concepts of causality. Some of the hard open problems of machine learning and AI are intrinsically related to causality, and progress may require advances in our understanding of how to model and infer causality from data.

cs.AI↗

arXiv2022

Leveling Down in Computer Vision: Pareto Inefficiencies in Fair Deep Classifiers

Algorithmic fairness is frequently motivated in terms of a trade-off in which overall performance is decreased so as to improve performance on disadvantaged groups where the algorithm would otherwise be less accurate. Contrary to this, we find that applying existing fairness approaches to computer vision improve fairness by degrading the performance of classifiers across all groups (with increased degradation on the best performing groups). Extending the bias-variance decomposition for classification to fairness, we theoretically explain why the majority of fairness classifiers designed for low capacity models should not be used in settings involving high-capacity models, a scenario common to computer vision. We corroborate this analysis with extensive experimental support that shows that many of the fairness heuristics used in computer vision also degrade performance on the most disadvantaged groups. Building on these insights, we propose an adaptive augmentation strategy that, uniquely, of all methods tested, improves performance for the disadvantaged groups.

cs.CV↗

arXiv2022

Source-Free Adaptation to Measurement Shift via Bottom-Up Feature Restoration

Source-free domain adaptation (SFDA) aims to adapt a model trained on labelled data in a source domain to unlabelled data in a target domain without access to the source-domain data during adaptation. Existing methods for SFDA leverage entropy-minimization techniques which: (i) apply only to classification; (ii) destroy model calibration; and (iii) rely on the source model achieving a good level of feature-space class-separation in the target domain. We address these issues for a particularly pervasive type of domain shift called measurement shift which can be resolved by restoring the source features rather than extracting new ones. In particular, we propose Feature Restoration (FR) wherein we: (i) store a lightweight and flexible approximation of the feature distribution under the source data; and (ii) adapt the feature-extractor such that the approximate feature distribution under the target data realigns with that saved on the source. We additionally propose a bottom-up training scheme which boosts performance, which we call Bottom-Up Feature Restoration (BUFR). On real and synthetic data, we demonstrate that BUFR outperforms existing SFDA methods in terms of accuracy, calibration, and data efficiency, while being less reliant on the performance of the source model in the target domain.

cs.LG↗

arXiv2022

Phenomenology of Double Descent in Finite-Width Neural Networks

`Double descent' delineates the generalization behaviour of models depending on the regime they belong to: under- or over-parameterized. The current theoretical understanding behind the occurrence of this phenomenon is primarily based on linear and kernel regression models -- with informal parallels to neural networks via the Neural Tangent Kernel. Therefore such analyses do not adequately capture the mechanisms behind double descent in finite-width neural networks, as well as, disregard crucial components -- such as the choice of the loss function. We address these shortcomings by leveraging influence functions in order to derive suitable expressions of the population loss and its lower bound, while imposing minimal assumptions on the form of the parametric model. Our derived bounds bear an intimate connection with the spectrum of the Hessian at the optimum, and importantly, exhibit a double descent behaviour at the interpolation threshold. Building on our analysis, we further investigate how the loss function affects double descent -- and thus uncover interesting properties of neural networks and their Hessian spectra near the interpolation threshold.

stat.ML↗

arXiv2022

Score matching enables causal discovery of nonlinear additive noise models

This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of scalable causal discovery methods. To showcase our approach, we also propose a new efficient method for approximating the score's Jacobian, enabling to recover the causal graph. Empirically, we find that the new algorithm, called SCORE, is competitive with state-of-the-art causal discovery methods while being significantly faster.

cs.LG↗

arXiv2022

On the Fairness of Causal Algorithmic Recourse

Algorithmic fairness is typically studied from the perspective of predictions. Instead, here we investigate fairness from the perspective of recourse actions suggested to individuals to remedy an unfavourable classification. We propose two new fairness criteria at the group and individual level, which -- unlike prior work on equalising the average group-wise distance from the decision boundary -- explicitly account for causal relationships between features, thereby capturing downstream effects of recourse actions performed in the physical world. We explore how our criteria relate to others, such as counterfactual fairness, and show that fairness of recourse is complementary to fairness of prediction. We study theoretically and empirically how to enforce fair causal recourse by altering the classifier and perform a case study on the Adult dataset. Finally, we discuss whether fairness violations in the data generating process revealed by our criteria may be better addressed by societal interventions as opposed to constraints on the classifier.

cs.LG↗

arXiv2022

Learning Neural Causal Models with Active Interventions

Discovering causal structures from data is a challenging inference problem of fundamental importance in all areas of science. The appealing properties of neural networks have recently led to a surge of interest in differentiable neural network-based methods for learning causal structures from data. So far, differentiable causal discovery has focused on static datasets of observational or fixed interventional origin. In this work, we introduce an active intervention targeting (AIT) method which enables a quick identification of the underlying causal structure of the data-generating process. Our method significantly reduces the required number of interactions compared with random intervention targeting and is applicable for both discrete and continuous optimization formulations of learning the underlying directed acyclic graph (DAG) from data. We examine the proposed method across multiple frameworks in a wide range of settings and demonstrate superior performance on multiple benchmarks from simulated to real-world data.

stat.ML↗

arXiv2022

Resampling Base Distributions of Normalizing Flows

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as Boltzmann distributions. Several procedures have been proposed to solve this problem but many of them sacrifice invertibility and, thereby, tractability of the log-likelihood as well as other desirable properties. To address these limitations, we introduce a base distribution for normalizing flows based on learned rejection sampling, allowing the resulting normalizing flow to model complicated distributions without giving up bijectivity. Furthermore, we develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the Kullback-Leibler divergence, and apply them to various sample problems, i.e. approximating 2D densities, density estimation of tabular data, image generation, and modeling Boltzmann distributions. In these experiments our method is competitive with or outperforms the baselines.

stat.ML↗

arXiv2022

Adversarially Robust Kernel Smoothing

We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the Wasserstein distance and the maximum mean discrepancy. We adapt the integral operator using supremal convolution in convex analysis to form a novel function majorant used for enforcing robustness. Our method is simple in form and applies to general loss functions and machine learning models. Exploiting a connection with optimal transport, we prove theoretical guarantees for certified robustness under distribution shift. Furthermore, we report experiments with general machine learning models, such as deep neural networks, to demonstrate competitive performance with the state-of-the-art certifiable robust learning algorithms based on the Wasserstein distance.

cs.LG↗

arXiv2022

On Pitfalls of Identifiability in Unsupervised Learning. A Note on: "Desiderata for Representation Learning: A Causal Perspective"

Model identifiability is a desirable property in the context of unsupervised representation learning. In absence thereof, different models may be observationally indistinguishable while yielding representations that are nontrivially related to one another, thus making the recovery of a ground truth generative model fundamentally impossible, as often shown through suitably constructed counterexamples. In this note, we discuss one such construction, illustrating a potential failure case of an identifiability result presented in "Desiderata for Representation Learning: A Causal Perspective" by Wang & Jordan (2021). The construction is based on the theory of nonlinear independent component analysis. We comment on implications of this and other counterexamples for identifiable representation learning.

stat.ML↗

arXiv2022

Visual Representation Learning Does Not Generalize Strongly Within the Same Domain

An important component for generalization in machine learning is to uncover underlying latent factors of variation as well as the mechanism through which each factor acts in the world. In this paper, we test whether 17 unsupervised, weakly supervised, and fully supervised representation learning approaches correctly infer the generative factors of variation in simple datasets (dSprites, Shapes3D, MPI3D) from controlled environments, and on our contributed CelebGlow dataset. In contrast to prior robustness work that introduces novel factors of variation during test time, such as blur or other (un)structured noise, we here recompose, interpolate, or extrapolate only existing factors of variation from the training data set (e.g., small and medium-sized objects during training and large objects during testing). Models that learn the correct mechanism should be able to generalize to this benchmark. In total, we train and test 2000+ models and observe that all of them struggle to learn the underlying mechanism regardless of supervision signal and architectural bias. Moreover, the generalization capabilities of all tested models drop significantly as we move from artificial datasets towards more realistic real-world datasets. Despite their inability to identify the correct mechanism, the models are quite modular as their ability to infer other in-distribution factors remains fairly stable, providing only a single factor is out-of-distribution. These results point to an important yet understudied problem of learning mechanistic models of observations that can facilitate generalization.

cs.LG↗

arXiv2022

A Witness Two-Sample Test

The Maximum Mean Discrepancy (MMD) has been the state-of-the-art nonparametric test for tackling the two-sample problem. Its statistic is given by the difference in expectations of the witness function, a real-valued function defined as a weighted sum of kernel evaluations on a set of basis points. Typically the kernel is optimized on a training set, and hypothesis testing is performed on a separate test set to avoid overfitting (i.e., control type-I error). That is, the test set is used to simultaneously estimate the expectations and define the basis points, while the training set only serves to select the kernel and is discarded. In this work, we propose to use the training data to also define the weights and the basis points for better data efficiency. We show that 1) the new test is consistent and has a well-controlled type-I error; 2) the optimal witness function is given by a precision-weighted mean in the reproducing kernel Hilbert space associated with the kernel; and 3) the test power of the proposed test is comparable or exceeds that of the MMD and other modern tests, as verified empirically on challenging synthetic and real problems (e.g., Higgs data).

cs.LG↗

arXiv2022

Independent mechanism analysis, a new concept?

Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof. Unfortunately, when the mixing is nonlinear, the model is provably nonidentifiable, since statistical independence alone does not sufficiently constrain the problem. Identifiability can be recovered in settings where additional, typically observed variables are included in the generative process. We investigate an alternative path and consider instead including assumptions reflecting the principle of independent causal mechanisms exploited in the field of causality. Specifically, our approach is motivated by thinking of each source as independently influencing the mixing process. This gives rise to a framework which we term independent mechanism analysis. We provide theoretical and empirical evidence that our approach circumvents a number of nonidentifiability issues arising in nonlinear blind source separation.

stat.ML↗

arXiv2022

Compositional Multi-Object Reinforcement Learning with Linear Relation Networks

Although reinforcement learning has seen remarkable progress over the last years, solving robust dexterous object-manipulation tasks in multi-object settings remains a challenge. In this paper, we focus on models that can learn manipulation tasks in fixed multi-object settings and extrapolate this skill zero-shot without any drop in performance when the number of objects changes. We consider the generic task of bringing a specific cube out of a set to a goal position. We find that previous approaches, which primarily leverage attention and graph neural network-based architectures, do not generalize their skills when the number of input objects changes while scaling as $K^2$. We propose an alternative plug-and-play module based on relational inductive biases to overcome these limitations. Besides exceeding performances in their training environment, we show that our approach, which scales linearly in $K$, allows agents to extrapolate and generalize zero-shot to any new object number.

cs.RO↗

arXiv2022

Regret Bounds for Gaussian-Process Optimization in Large Domains

The goal of this paper is to characterize Gaussian-Process optimization in the setting where the function domain is large relative to the number of admissible function evaluations, i.e., where it is impossible to find the global optimum. We provide upper bounds on the suboptimality (Bayesian simple regret) of the solution found by optimization strategies that are closely related to the widely used expected improvement (EI) and upper confidence bound (UCB) algorithms. These regret bounds illuminate the relationship between the number of evaluations, the domain size (i.e. cardinality of finite domains / Lipschitz constant of the covariance function in continuous domains), and the optimality of the retrieved function value. In particular, we show that even when the number of evaluations is far too small to find the global optimum, we can find nontrivial function values (e.g. values that achieve a certain ratio with the optimal value).

cs.LG↗