arXiv subjects

Bernhard Schölkopf

Publications and source records attributed to Bernhard Schölkopf.

At least 361 records · Page 20Linked to original sources

arXiv2020

Fair Decisions Despite Imperfect Predictions

Consequential decisions are increasingly informed by sophisticated data-driven predictive models. However, to consistently learn accurate predictive models, one needs access to ground truth labels. Unfortunately, in practice, labels may only exist conditional on certain decisions---if a loan is denied, there is not even an option for the individual to pay back the loan. Hence, the observed data distribution depends on how decisions are being made. In this paper, we show that in this selective labels setting, learning a predictor directly only from available labeled data is suboptimal in terms of both fairness and utility. To avoid this undesirable behavior, we propose to directly learn decision policies that maximize utility under fairness constraints and thereby take into account how decisions affect which data is observed in the future. Our results suggest the need for a paradigm shift in the context of fair machine learning from the currently prevalent idea of simply building predictive models from a single static dataset via risk minimization, to a more interactive notion of "learning to decide". In particular, such policies should not entirely neglect part of the input space, drawing connections to explore/exploit tradeoffs in reinforcement learning, data missingness, and potential outcomes in causal inference. Experiments on synthetic and real-world data illustrate the favorable properties of learning to decide in terms of utility and fairness.

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arXiv2020

Algorithmic Recourse: from Counterfactual Explanations to Interventions

As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a favorable decision. Counterfactual explanations -- "how the world would have (had) to be different for a desirable outcome to occur" -- aim to satisfy these criteria. Existing works have primarily focused on designing algorithms to obtain counterfactual explanations for a wide range of settings. However, one of the main objectives of "explanations as a means to help a data-subject act rather than merely understand" has been overlooked. In layman's terms, counterfactual explanations inform an individual where they need to get to, but not how to get there. In this work, we rely on causal reasoning to caution against the use of counterfactual explanations as a recommendable set of actions for recourse. Instead, we propose a shift of paradigm from recourse via nearest counterfactual explanations to recourse through minimal interventions, moving the focus from explanations to recommendations. Finally, we provide the reader with an extensive discussion on how to realistically achieve recourse beyond structural interventions.

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arXiv2020

Optimal Decision Making Under Strategic Behavior

We are witnessing an increasing use of data-driven predictive models to inform decisions. As decisions have implications for individuals and society, there is increasing pressure on decision makers to be transparent about their decision policies. At the same time, individuals may use knowledge, gained by transparency, to invest effort strategically in order to maximize their chances of receiving a beneficial decision. Our goal is to find decision policies that are optimal in terms of utility in such a strategic setting. To this end, we first characterize how strategic investment of effort by individuals leads to a change in the feature distribution. Using this characterization, we first show that, in general, we cannot expect to find optimal decision policies in polynomial time and there are cases in which deterministic policies are suboptimal. Then, we demonstrate that, if the cost individuals pay to change their features satisfies a natural monotonicity assumption, we can narrow down the search for the optimal policy to a particular family of decision policies with a set of desirable properties, which allow for a highly effective polynomial time heuristic search algorithm using dynamic programming. Finally, under no assumptions on the cost individuals pay to change their features, we develop an iterative search algorithm that is guaranteed to find locally optimal decision policies also in polynomial time. Experiments on synthetic and real credit card data illustrate our theoretical findings and show that the decision policies found by our algorithms achieve higher utility than those that do not account for strategic behavior.

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arXiv2020

Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem

In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kernel mean embedding. Specifically, we formulate the generalized moment problem whose ambiguity set (i.e., the moment constraint) is described by constraints in the associated reproducing kernel Hilbert space in a nonparametric manner. We then present the tractable approximation and its theoretical justification. As a concrete application, we numerically test the proposed method in characterizing the worst-case constraint violation probability in the context of a constrained stochastic control system.

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arXiv2020

Real-time Prediction of COVID-19 related Mortality using Electronic Health Records

Coronavirus Disease 2019 (COVID-19) is an emerging respiratory disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) with rapid human-to-human transmission and a high case fatality rate particularly in older patients. Due to the exponential growth of infections, many healthcare systems across the world are under pressure to care for increasing amounts of at-risk patients. Given the high number of infected patients, identifying patients with the highest mortality risk early is critical to enable effective intervention and optimal prioritisation of care. Here, we present the COVID-19 Early Warning System (CovEWS), a clinical risk scoring system for assessing COVID-19 related mortality risk. CovEWS provides continuous real-time risk scores for individual patients with clinically meaningful predictive performance up to 192 hours (8 days) in advance, and is automatically derived from patients' electronic health records (EHRs) using machine learning. We trained and evaluated CovEWS using de-identified data from a cohort of 66430 COVID-19 positive patients seen at over 69 healthcare institutions in the United States (US), Australia, Malaysia and India amounting to an aggregated total of over 2863 years of patient observation time. On an external test cohort of 5005 patients, CovEWS predicts COVID-19 related mortality from $78.8\%$ ($95\%$ confidence interval [CI]: $76.0$, $84.7\%$) to $69.4\%$ ($95\%$ CI: $57.6, 75.2\%$) specificity at a sensitivity greater than $95\%$ between respectively 1 and 192 hours prior to observed mortality events - significantly outperforming existing generic and COVID-19 specific clinical risk scores. CovEWS could enable clinicians to intervene at an earlier stage, and may therefore help in preventing or mitigating COVID-19 related mortality.

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arXiv2020

Learning Neural Causal Models from Unknown Interventions

Promising results have driven a recent surge of interest in continuous optimization methods for Bayesian network structure learning from observational data. However, there are theoretical limitations on the identifiability of underlying structures obtained from observational data alone. Interventional data provides much richer information about the underlying data-generating process. However, the extension and application of methods designed for observational data to include interventions is not straightforward and remains an open problem. In this paper we provide a general framework based on continuous optimization and neural networks to create models for the combination of observational and interventional data. The proposed method is even applicable in the challenging and realistic case that the identity of the intervened upon variable is unknown. We examine the proposed method in the setting of graph recovery both de novo and from a partially-known edge set. We establish strong benchmark results on several structure learning tasks, including structure recovery of both synthetic graphs as well as standard graphs from the Bayesian Network Repository.

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arXiv2020

Learning Dynamical Systems using Local Stability Priors

A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability information as a prior on the system, effectively endowing the estimate with this important structural property. In addition, the knowledge of the region of attraction plays an experiment design role by informing the selection of initial conditions from which trajectories are generated and by enabling the use of a Lyapunov function of the system as a regularization term. Numerical results show that the proposed method allows efficient sampling and provides an accurate estimate of the dynamics in an inner approximation of its region of attraction.

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arXiv2020

Causal analysis of Covid-19 spread in Germany

In this work, we study the causal relations among German regions in terms of the spread of Covid-19 since the beginning of the pandemic, taking into account the restriction policies that were applied by the different federal states. We propose and prove a new theorem for a causal feature selection method for time series data, robust to latent confounders, which we subsequently apply on Covid-19 case numbers. We present findings about the spread of the virus in Germany and the causal impact of restriction measures, discussing the role of various policies in containing the spread. Since our results are based on rather limited target time series (only the numbers of reported cases), care should be exercised in interpreting them. However, it is encouraging that already such limited data seems to contain causal signals. This suggests that as more data becomes available, our causal approach may contribute towards meaningful causal analysis of political interventions on the development of Covid-19, and thus also towards the development of rational and data-driven methodologies for choosing interventions.

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arXiv2020

Geometrically Enriched Latent Spaces

A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through the associated Riemannian metric. Shortest paths can then be defined accordingly in the latent space to both follow the learned manifold and respect the ambient geometry. Through careful design of the ambient metric we can ensure that shortest paths are well-behaved even for deterministic generators that otherwise would exhibit a misleading bias. Experimentally we show that our approach improves interpretability of learned representations both using stochastic and deterministic generators.

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arXiv2020

A Commentary on the Unsupervised Learning of Disentangled Representations

The goal of the unsupervised learning of disentangled representations is to separate the independent explanatory factors of variation in the data without access to supervision. In this paper, we summarize the results of Locatello et al., 2019, and focus on their implications for practitioners. We discuss the theoretical result showing that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases and the practical challenges it entails. Finally, we comment on our experimental findings, highlighting the limitations of state-of-the-art approaches and directions for future research.

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arXiv2020

S2RMs: Spatially Structured Recurrent Modules

Capturing the structure of a data-generating process by means of appropriate inductive biases can help in learning models that generalize well and are robust to changes in the input distribution. While methods that harness spatial and temporal structures find broad application, recent work has demonstrated the potential of models that leverage sparse and modular structure using an ensemble of sparingly interacting modules. In this work, we take a step towards dynamic models that are capable of simultaneously exploiting both modular and spatiotemporal structures. We accomplish this by abstracting the modeled dynamical system as a collection of autonomous but sparsely interacting sub-systems. The sub-systems interact according to a topology that is learned, but also informed by the spatial structure of the underlying real-world system. This results in a class of models that are well suited for modeling the dynamics of systems that only offer local views into their state, along with corresponding spatial locations of those views. On the tasks of video prediction from cropped frames and multi-agent world modeling from partial observations in the challenging Starcraft2 domain, we find our models to be more robust to the number of available views and better capable of generalization to novel tasks without additional training, even when compared against strong baselines that perform equally well or better on the training distribution.

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arXiv2020

Orthogonal Structure Search for Efficient Causal Discovery from Observational Data

The problem of inferring the direct causal parents of a response variable among a large set of explanatory variables is of high practical importance in many disciplines. Recent work exploits stability of regression coefficients or invariance properties of models across different experimental conditions for reconstructing the full causal graph. These approaches generally do not scale well with the number of the explanatory variables and are difficult to extend to nonlinear relationships. Contrary to existing work, we propose an approach which even works for observational data alone, while still offering theoretical guarantees including the case of partially nonlinear relationships. Our algorithm requires only one estimation for each variable and in our experiments we apply our causal discovery algorithm even to large graphs, demonstrating significant improvements compared to well established approaches.

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arXiv2020

Testing Goodness of Fit of Conditional Density Models with Kernels

We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some density $r_x$. Our tests, formulated with a Stein operator, can be applied to any differentiable conditional density model, and require no knowledge of the normalizing constant. We show that 1) our tests are consistent against any fixed alternative conditional model; 2) the statistics can be estimated easily, requiring no density estimation as an intermediate step; and 3) our second test offers an interpretable test result providing insight on where the conditional model does not fit well in the domain of the covariate. We demonstrate the interpretability of our test on a task of modeling the distribution of New York City's taxi drop-off location given a pick-up point. To our knowledge, our work is the first to propose such conditional goodness-of-fit tests that simultaneously have all these desirable properties.

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arXiv2020

Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.

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arXiv2020

Bayesian Online Prediction of Change Points

Online detection of instantaneous changes in the generative process of a data sequence generally focuses on retrospective inference of such change points without considering their future occurrences. We extend the Bayesian Online Change Point Detection algorithm to also infer the number of time steps until the next change point (i.e., the residual time). This enables to handle observation models which depend on the total segment duration, which is useful to model data sequences with temporal scaling. The resulting inference algorithm for segment detection can be deployed in an online fashion, and we illustrate applications to synthetic and to two medical real-world data sets.

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arXiv2020

Semi-Supervised Learning, Causality and the Conditional Cluster Assumption

While the success of semi-supervised learning (SSL) is still not fully understood, Schölkopf et al. (2012) have established a link to the principle of independent causal mechanisms. They conclude that SSL should be impossible when predicting a target variable from its causes, but possible when predicting it from its effects. Since both these cases are somewhat restrictive, we extend their work by considering classification using cause and effect features at the same time, such as predicting disease from both risk factors and symptoms. While standard SSL exploits information contained in the marginal distribution of all inputs (to improve the estimate of the conditional distribution of the target given inputs), we argue that in our more general setting we should use information in the conditional distribution of effect features given causal features. We explore how this insight generalises the previous understanding, and how it relates to and can be exploited algorithmically for SSL.

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arXiv2020

Learning to Play Table Tennis From Scratch using Muscular Robots

Dynamic tasks like table tennis are relatively easy to learn for humans but pose significant challenges to robots. Such tasks require accurate control of fast movements and precise timing in the presence of imprecise state estimation of the flying ball and the robot. Reinforcement Learning (RL) has shown promise in learning of complex control tasks from data. However, applying step-based RL to dynamic tasks on real systems is safety-critical as RL requires exploring and failing safely for millions of time steps in high-speed regimes. In this paper, we demonstrate that safe learning of table tennis using model-free Reinforcement Learning can be achieved by using robot arms driven by pneumatic artificial muscles (PAMs). Softness and back-drivability properties of PAMs prevent the system from leaving the safe region of its state space. In this manner, RL empowers the robot to return and smash real balls with 5 m\s and 12m\s on average to a desired landing point. Our setup allows the agent to learn this safety-critical task (i) without safety constraints in the algorithm, (ii) while maximizing the speed of returned balls directly in the reward function (iii) using a stochastic policy that acts directly on the low-level controls of the real system and (iv) trains for thousands of trials (v) from scratch without any prior knowledge. Additionally, we present HYSR, a practical hybrid sim and real training that avoids playing real balls during training by randomly replaying recorded ball trajectories in simulation and applying actions to the real robot. This work is the first to (a) fail-safe learn of a safety-critical dynamic task using anthropomorphic robot arms, (b) learn a precision-demanding problem with a PAM-driven system despite the control challenges and (c) train robots to play table tennis without real balls. Videos and datasets are available at muscularTT.embodied.ml.

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arXiv2020

From Variational to Deterministic Autoencoders

Variational Autoencoders (VAEs) provide a theoretically-backed and popular framework for deep generative models. However, learning a VAE from data poses still unanswered theoretical questions and considerable practical challenges. In this work, we propose an alternative framework for generative modeling that is simpler, easier to train, and deterministic, yet has many of the advantages of VAEs. We observe that sampling a stochastic encoder in a Gaussian VAE can be interpreted as simply injecting noise into the input of a deterministic decoder. We investigate how substituting this kind of stochasticity, with other explicit and implicit regularization schemes, can lead to an equally smooth and meaningful latent space without forcing it to conform to an arbitrarily chosen prior. To retrieve a generative mechanism to sample new data, we introduce an ex-post density estimation step that can be readily applied also to existing VAEs, improving their sample quality. We show, in a rigorous empirical study, that the proposed regularized deterministic autoencoders are able to generate samples that are comparable to, or better than, those of VAEs and more powerful alternatives when applied to images as well as to structured data such as molecules. \footnote{An implementation is available at: \url{https://github.com/ParthaEth/Regularized_autoencoders-RAE-}}

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