arXiv subjects

Mihaela van der Schaar

Publications and source records attributed to Mihaela van der Schaar.

At least 199 records · Page 11Linked to original sources

arXiv2021

MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms

Missing data is an important problem in machine learning practice. Starting from the premise that imputation methods should preserve the causal structure of the data, we develop a regularization scheme that encourages any baseline imputation method to be causally consistent with the underlying data generating mechanism. Our proposal is a causally-aware imputation algorithm (MIRACLE). MIRACLE iteratively refines the imputation of a baseline by simultaneously modeling the missingness generating mechanism, encouraging imputation to be consistent with the causal structure of the data. We conduct extensive experiments on synthetic and a variety of publicly available datasets to show that MIRACLE is able to consistently improve imputation over a variety of benchmark methods across all three missingness scenarios: at random, completely at random, and not at random.

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arXiv2021

Explaining Latent Representations with a Corpus of Examples

Modern machine learning models are complicated. Most of them rely on convoluted latent representations of their input to issue a prediction. To achieve greater transparency than a black-box that connects inputs to predictions, it is necessary to gain a deeper understanding of these latent representations. To that aim, we propose SimplEx: a user-centred method that provides example-based explanations with reference to a freely selected set of examples, called the corpus. SimplEx uses the corpus to improve the user's understanding of the latent space with post-hoc explanations answering two questions: (1) Which corpus examples explain the prediction issued for a given test example? (2) What features of these corpus examples are relevant for the model to relate them to the test example? SimplEx provides an answer by reconstructing the test latent representation as a mixture of corpus latent representations. Further, we propose a novel approach, the Integrated Jacobian, that allows SimplEx to make explicit the contribution of each corpus feature in the mixture. Through experiments on tasks ranging from mortality prediction to image classification, we demonstrate that these decompositions are robust and accurate. With illustrative use cases in medicine, we show that SimplEx empowers the user by highlighting relevant patterns in the corpus that explain model representations. Moreover, we demonstrate how the freedom in choosing the corpus allows the user to have personalized explanations in terms of examples that are meaningful for them.

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arXiv2021

On Inductive Biases for Heterogeneous Treatment Effect Estimation

We investigate how to exploit structural similarities of an individual's potential outcomes (POs) under different treatments to obtain better estimates of conditional average treatment effects in finite samples. Especially when it is unknown whether a treatment has an effect at all, it is natural to hypothesize that the POs are similar - yet, some existing strategies for treatment effect estimation employ regularization schemes that implicitly encourage heterogeneity even when it does not exist and fail to fully make use of shared structure. In this paper, we investigate and compare three end-to-end learning strategies to overcome this problem - based on regularization, reparametrization and a flexible multi-task architecture - each encoding inductive bias favoring shared behavior across POs. To build understanding of their relative strengths, we implement all strategies using neural networks and conduct a wide range of semi-synthetic experiments. We observe that all three approaches can lead to substantial improvements upon numerous baselines and gain insight into performance differences across various experimental settings.

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arXiv2021

Conservative Policy Construction Using Variational Autoencoders for Logged Data with Missing Values

In high-stakes applications of data-driven decision making like healthcare, it is of paramount importance to learn a policy that maximizes the reward while avoiding potentially dangerous actions when there is uncertainty. There are two main challenges usually associated with this problem. Firstly, learning through online exploration is not possible due to the critical nature of such applications. Therefore, we need to resort to observational datasets with no counterfactuals. Secondly, such datasets are usually imperfect, additionally cursed with missing values in the attributes of features. In this paper, we consider the problem of constructing personalized policies using logged data when there are missing values in the attributes of features in both training and test data. The goal is to recommend an action (treatment) when $\Xt$, a degraded version of $\Xb$ with missing values, is observed. We consider three strategies for dealing with missingness. In particular, we introduce the \textit{conservative strategy} where the policy is designed to safely handle the uncertainty due to missingness. In order to implement this strategy we need to estimate posterior distribution $p(\Xb|\Xt)$, we use variational autoencoder to achieve this. In particular, our method is based on partial variational autoencoders (PVAE) which are designed to capture the underlying structure of features with missing values.

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arXiv2021

Doing Great at Estimating CATE? On the Neglected Assumptions in Benchmark Comparisons of Treatment Effect Estimators

The machine learning toolbox for estimation of heterogeneous treatment effects from observational data is expanding rapidly, yet many of its algorithms have been evaluated only on a very limited set of semi-synthetic benchmark datasets. In this paper, we show that even in arguably the simplest setting -- estimation under ignorability assumptions -- the results of such empirical evaluations can be misleading if (i) the assumptions underlying the data-generating mechanisms in benchmark datasets and (ii) their interplay with baseline algorithms are inadequately discussed. We consider two popular machine learning benchmark datasets for evaluation of heterogeneous treatment effect estimators -- the IHDP and ACIC2016 datasets -- in detail. We identify problems with their current use and highlight that the inherent characteristics of the benchmark datasets favor some algorithms over others -- a fact that is rarely acknowledged but of immense relevance for interpretation of empirical results. We close by discussing implications and possible next steps.

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arXiv2021

Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression

Modeling a system's temporal behaviour in reaction to external stimuli is a fundamental problem in many areas. Pure Machine Learning (ML) approaches often fail in the small sample regime and cannot provide actionable insights beyond predictions. A promising modification has been to incorporate expert domain knowledge into ML models. The application we consider is predicting the progression of disease under medications, where a plethora of domain knowledge is available from pharmacology. Pharmacological models describe the dynamics of carefully-chosen medically meaningful variables in terms of systems of Ordinary Differential Equations (ODEs). However, these models only describe a limited collection of variables, and these variables are often not observable in clinical environments. To close this gap, we propose the latent hybridisation model (LHM) that integrates a system of expert-designed ODEs with machine-learned Neural ODEs to fully describe the dynamics of the system and to link the expert and latent variables to observable quantities. We evaluated LHM on synthetic data as well as real-world intensive care data of COVID-19 patients. LHM consistently outperforms previous works, especially when few training samples are available such as at the beginning of the pandemic.

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arXiv2021

Explaining Time Series Predictions with Dynamic Masks

How can we explain the predictions of a machine learning model? When the data is structured as a multivariate time series, this question induces additional difficulties such as the necessity for the explanation to embody the time dependency and the large number of inputs. To address these challenges, we propose dynamic masks (Dynamask). This method produces instance-wise importance scores for each feature at each time step by fitting a perturbation mask to the input sequence. In order to incorporate the time dependency of the data, Dynamask studies the effects of dynamic perturbation operators. In order to tackle the large number of inputs, we propose a scheme to make the feature selection parsimonious (to select no more feature than necessary) and legible (a notion that we detail by making a parallel with information theory). With synthetic and real-world data, we demonstrate that the dynamic underpinning of Dynamask, together with its parsimony, offer a neat improvement in the identification of feature importance over time. The modularity of Dynamask makes it ideal as a plug-in to increase the transparency of a wide range of machine learning models in areas such as medicine and finance, where time series are abundant.

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arXiv2021

Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding

Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a widespread effect on many of the observed ones is particularly difficult because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this paper we show that beyond conditional independencies, under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph among observed variables may be recovered approximately and propose an adjusted score-based causal discovery algorithm that may be implemented with general purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions.

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arXiv2021

Learning "What-if" Explanations for Sequential Decision-Making

Building interpretable parameterizations of real-world decision-making on the basis of demonstrated behavior -- i.e. trajectories of observations and actions made by an expert maximizing some unknown reward function -- is essential for introspecting and auditing policies in different institutions. In this paper, we propose learning explanations of expert decisions by modeling their reward function in terms of preferences with respect to "what if" outcomes: Given the current history of observations, what would happen if we took a particular action? To learn these cost-benefit tradeoffs associated with the expert's actions, we integrate counterfactual reasoning into batch inverse reinforcement learning. This offers a principled way of defining reward functions and explaining expert behavior, and also satisfies the constraints of real-world decision-making -- where active experimentation is often impossible (e.g. in healthcare). Additionally, by estimating the effects of different actions, counterfactuals readily tackle the off-policy nature of policy evaluation in the batch setting, and can naturally accommodate settings where the expert policies depend on histories of observations rather than just current states. Through illustrative experiments in both real and simulated medical environments, we highlight the effectiveness of our batch, counterfactual inverse reinforcement learning approach in recovering accurate and interpretable descriptions of behavior.

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arXiv2021

Scalable Bayesian Inverse Reinforcement Learning

Bayesian inference over the reward presents an ideal solution to the ill-posed nature of the inverse reinforcement learning problem. Unfortunately current methods generally do not scale well beyond the small tabular setting due to the need for an inner-loop MDP solver, and even non-Bayesian methods that do themselves scale often require extensive interaction with the environment to perform well, being inappropriate for high stakes or costly applications such as healthcare. In this paper we introduce our method, Approximate Variational Reward Imitation Learning (AVRIL), that addresses both of these issues by jointly learning an approximate posterior distribution over the reward that scales to arbitrarily complicated state spaces alongside an appropriate policy in a completely offline manner through a variational approach to said latent reward. Applying our method to real medical data alongside classic control simulations, we demonstrate Bayesian reward inference in environments beyond the scope of current methods, as well as task performance competitive with focused offline imitation learning algorithms.

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arXiv2021

Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms

The need to evaluate treatment effectiveness is ubiquitous in most of empirical science, and interest in flexibly investigating effect heterogeneity is growing rapidly. To do so, a multitude of model-agnostic, nonparametric meta-learners have been proposed in recent years. Such learners decompose the treatment effect estimation problem into separate sub-problems, each solvable using standard supervised learning methods. Choosing between different meta-learners in a data-driven manner is difficult, as it requires access to counterfactual information. Therefore, with the ultimate goal of building better understanding of the conditions under which some learners can be expected to perform better than others a priori, we theoretically analyze four broad meta-learning strategies which rely on plug-in estimation and pseudo-outcome regression. We highlight how this theoretical reasoning can be used to guide principled algorithm design and translate our analyses into practice by considering a variety of neural network architectures as base-learners for the discussed meta-learning strategies. In a simulation study, we showcase the relative strengths of the learners under different data-generating processes.

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arXiv2021

Model-Attentive Ensemble Learning for Sequence Modeling

Medical time-series datasets have unique characteristics that make prediction tasks challenging. Most notably, patient trajectories often contain longitudinal variations in their input-output relationships, generally referred to as temporal conditional shift. Designing sequence models capable of adapting to such time-varying distributions remains a prevailing problem. To address this we present Model-Attentive Ensemble learning for Sequence modeling (MAES). MAES is a mixture of time-series experts which leverages an attention-based gating mechanism to specialize the experts on different sequence dynamics and adaptively weight their predictions. We demonstrate that MAES significantly out-performs popular sequence models on datasets subject to temporal shift.

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arXiv2021

Selecting Treatment Effects Models for Domain Adaptation Using Causal Knowledge

Selecting causal inference models for estimating individualized treatment effects (ITE) from observational data presents a unique challenge since the counterfactual outcomes are never observed. The problem is challenged further in the unsupervised domain adaptation (UDA) setting where we only have access to labeled samples in the source domain, but desire selecting a model that achieves good performance on a target domain for which only unlabeled samples are available. Existing techniques for UDA model selection are designed for the predictive setting. These methods examine discriminative density ratios between the input covariates in the source and target domain and do not factor in the model's predictions in the target domain. Because of this, two models with identical performance on the source domain would receive the same risk score by existing methods, but in reality, have significantly different performance in the test domain. We leverage the invariance of causal structures across domains to propose a novel model selection metric specifically designed for ITE methods under the UDA setting. In particular, we propose selecting models whose predictions of interventions' effects satisfy known causal structures in the target domain. Experimentally, our method selects ITE models that are more robust to covariate shifts on several healthcare datasets, including estimating the effect of ventilation in COVID-19 patients from different geographic locations.

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arXiv2021

A Variational Information Bottleneck Approach to Multi-Omics Data Integration

Integration of data from multiple omics techniques is becoming increasingly important in biomedical research. Due to non-uniformity and technical limitations in omics platforms, such integrative analyses on multiple omics, which we refer to as views, involve learning from incomplete observations with various view-missing patterns. This is challenging because i) complex interactions within and across observed views need to be properly addressed for optimal predictive power and ii) observations with various view-missing patterns need to be flexibly integrated. To address such challenges, we propose a deep variational information bottleneck (IB) approach for incomplete multi-view observations. Our method applies the IB framework on marginal and joint representations of the observed views to focus on intra-view and inter-view interactions that are relevant for the target. Most importantly, by modeling the joint representations as a product of marginal representations, we can efficiently learn from observed views with various view-missing patterns. Experiments on real-world datasets show that our method consistently achieves gain from data integration and outperforms state-of-the-art benchmarks.

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arXiv2021

Estimating Structural Target Functions using Machine Learning and Influence Functions

We aim to construct a class of learning algorithms that are of practical value to applied researchers in fields such as biostatistics, epidemiology and econometrics, where the need to learn from incompletely observed information is ubiquitous. We propose a new framework for statistical machine learning of target functions arising as identifiable functionals from statistical models, which we call `IF-learning' due to its reliance on influence functions (IFs). This framework is problem- and model-agnostic and can be used to estimate a broad variety of target parameters of interest in applied statistics: we can consider any target function for which an IF of a population-averaged version exists in analytic form. Throughout, we put particular focus on so-called coarsening at random/doubly robust problems with partially unobserved information. This includes problems such as treatment effect estimation and inference in the presence of missing outcome data. Within this framework, we propose two general learning algorithms that build on the idea of nonparametric plug-in bias removal via IFs: the 'IF-learner' which uses pseudo-outcomes motivated by uncentered IFs for regression in large samples and outputs entire target functions without confidence bands, and the 'Group-IF-learner', which outputs only approximations to a function but can give confidence estimates if sufficient information on coarsening mechanisms is available. We apply both in a simulation study on inferring treatment effects.

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arXiv2021

Kernel Hypothesis Testing with Set-valued Data

We present a general framework for hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of images of a given phenomenon. This observation pattern, however, differs from the common assumptions required for hypothesis testing: each set differs in size, may have differing levels of noise, and also may incorporate nuisance variability, irrelevant for the analysis of the phenomenon of interest; all features that bias test decisions if not accounted for. In this paper, we propose to interpret sets as independent samples from a collection of latent probability distributions, and introduce kernel two-sample and independence tests in this latent space of distributions. We prove the consistency of tests and observe them to outperform in a wide range of synthetic experiments. Finally, we showcase their use in practice with experiments of healthcare and climate data, where previously heuristics were needed for feature extraction and testing.

stat.ME↗

arXiv2021

Learning Matching Representations for Individualized Organ Transplantation Allocation

Organ transplantation is often the last resort for treating end-stage illness, but the probability of a successful transplantation depends greatly on compatibility between donors and recipients. Current medical practice relies on coarse rules for donor-recipient matching, but is short of domain knowledge regarding the complex factors underlying organ compatibility. In this paper, we formulate the problem of learning data-driven rules for organ matching using observational data for organ allocations and transplant outcomes. This problem departs from the standard supervised learning setup in that it involves matching the two feature spaces (i.e., donors and recipients), and requires estimating transplant outcomes under counterfactual matches not observed in the data. To address these problems, we propose a model based on representation learning to predict donor-recipient compatibility; our model learns representations that cluster donor features, and applies donor-invariant transformations to recipient features to predict outcomes for a given donor-recipient feature instance. Experiments on semi-synthetic and real-world datasets show that our model outperforms state-of-art allocation methods and policies executed by human experts.

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arXiv2021

Policy Analysis using Synthetic Controls in Continuous-Time

Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and synthetic controls expressed as linear combinations of observed control units. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations. This model is directly applicable to the general setting of irregularly-aligned multivariate time series and may be optimized in rich function spaces -- thereby improving on some limitations of existing approaches.

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