arXiv subjects

Fredrik D. Johansson

Publications and source records attributed to Fredrik D. Johansson.

At least 37 records · Page 2Linked to original sources

arXiv2024

Pure Exploration in Bandits with Linear Constraints

We address the problem of identifying the optimal policy with a fixed confidence level in a multi-armed bandit setup, when \emph{the arms are subject to linear constraints}. Unlike the standard best-arm identification problem which is well studied, the optimal policy in this case may not be deterministic and could mix between several arms. This changes the geometry of the problem which we characterize via an information-theoretic lower bound. We introduce two asymptotically optimal algorithms for this setting, one based on the Track-and-Stop method and the other based on a game-theoretic approach. Both these algorithms try to track an optimal allocation based on the lower bound and computed by a weighted projection onto the boundary of a normal cone. Finally, we provide empirical results that validate our bounds and visualize how constraints change the hardness of the problem.

cs.LG↗

arXiv2023

Sharing pattern submodels for prediction with missing values

Missing values are unavoidable in many applications of machine learning and present challenges both during training and at test time. When variables are missing in recurring patterns, fitting separate pattern submodels have been proposed as a solution. However, fitting models independently does not make efficient use of all available data. Conversely, fitting a single shared model to the full data set relies on imputation which often leads to biased results when missingness depends on unobserved factors. We propose an alternative approach, called sharing pattern submodels, which i) makes predictions that are robust to missing values at test time, ii) maintains or improves the predictive power of pattern submodels, and iii) has a short description, enabling improved interpretability. Parameter sharing is enforced through sparsity-inducing regularization which we prove leads to consistent estimation. Finally, we give conditions for when a sharing model is optimal, even when both missingness and the target outcome depend on unobserved variables. Classification and regression experiments on synthetic and real-world data sets demonstrate that our models achieve a favorable tradeoff between pattern specialization and information sharing.

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arXiv2023

MINTY: Rule-based Models that Minimize the Need for Imputing Features with Missing Values

Rule models are often preferred in prediction tasks with tabular inputs as they can be easily interpreted using natural language and provide predictive performance on par with more complex models. However, most rule models' predictions are undefined or ambiguous when some inputs are missing, forcing users to rely on statistical imputation models or heuristics like zero imputation, undermining the interpretability of the models. In this work, we propose fitting concise yet precise rule models that learn to avoid relying on features with missing values and, therefore, limit their reliance on imputation at test time. We develop MINTY, a method that learns rules in the form of disjunctions between variables that act as replacements for each other when one or more is missing. This results in a sparse linear rule model, regularized to have small dependence on features with missing values, that allows a trade-off between goodness of fit, interpretability, and robustness to missing values at test time. We demonstrate the value of MINTY in experiments using synthetic and real-world data sets and find its predictive performance comparable or favorable to baselines, with smaller reliance on features with missing values.

cs.LG↗

arXiv2023

Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects

Practitioners in diverse fields such as healthcare, economics and education are eager to apply machine learning to improve decision making. The cost and impracticality of performing experiments and a recent monumental increase in electronic record keeping has brought attention to the problem of evaluating decisions based on non-experimental observational data. This is the setting of this work. In particular, we study estimation of individual-level causal effects, such as a single patient's response to alternative medication, from recorded contexts, decisions and outcomes. We give generalization bounds on the error in estimated effects based on distance measures between groups receiving different treatments, allowing for sample re-weighting. We provide conditions under which our bound is tight and show how it relates to results for unsupervised domain adaptation. Led by our theoretical results, we devise representation learning algorithms that minimize our bound, by regularizing the representation's induced treatment group distance, and encourage sharing of information between treatment groups. We extend these algorithms to simultaneously learn a weighted representation to further reduce treatment group distances. Finally, an experimental evaluation on real and synthetic data shows the value of our proposed representation architecture and regularization scheme.

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arXiv2023

Off-Policy Evaluation with Out-of-Sample Guarantees

We consider the problem of evaluating the performance of a decision policy using past observational data. The outcome of a policy is measured in terms of a loss (aka. disutility or negative reward) and the main problem is making valid inferences about its out-of-sample loss when the past data was observed under a different and possibly unknown policy. Using a sample-splitting method, we show that it is possible to draw such inferences with finite-sample coverage guarantees about the entire loss distribution, rather than just its mean. Importantly, the method takes into account model misspecifications of the past policy - including unmeasured confounding. The evaluation method can be used to certify the performance of a policy using observational data under a specified range of credible model assumptions.

stat.ML↗

arXiv2023

Practicality of generalization guarantees for unsupervised domain adaptation with neural networks

Understanding generalization is crucial to confidently engineer and deploy machine learning models, especially when deployment implies a shift in the data domain. For such domain adaptation problems, we seek generalization bounds which are tractably computable and tight. If these desiderata can be reached, the bounds can serve as guarantees for adequate performance in deployment. However, in applications where deep neural networks are the models of choice, deriving results which fulfill these remains an unresolved challenge; most existing bounds are either vacuous or has non-estimable terms, even in favorable conditions. In this work, we evaluate existing bounds from the literature with potential to satisfy our desiderata on domain adaptation image classification tasks, where deep neural networks are preferred. We find that all bounds are vacuous and that sample generalization terms account for much of the observed looseness, especially when these terms interact with measures of domain shift. To overcome this and arrive at the tightest possible results, we combine each bound with recent data-dependent PAC-Bayes analysis, greatly improving the guarantees. We find that, when domain overlap can be assumed, a simple importance weighting extension of previous work provides the tightest estimable bound. Finally, we study which terms dominate the bounds and identify possible directions for further improvement.

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arXiv2022

Thompson Sampling for Bandits with Clustered Arms

We propose algorithms based on a multi-level Thompson sampling scheme, for the stochastic multi-armed bandit and its contextual variant with linear expected rewards, in the setting where arms are clustered. We show, both theoretically and empirically, how exploiting a given cluster structure can significantly improve the regret and computational cost compared to using standard Thompson sampling. In the case of the stochastic multi-armed bandit we give upper bounds on the expected cumulative regret showing how it depends on the quality of the clustering. Finally, we perform an empirical evaluation showing that our algorithms perform well compared to previously proposed algorithms for bandits with clustered arms.

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arXiv2022

Using Time-Series Privileged Information for Provably Efficient Learning of Prediction Models

We study prediction of future outcomes with supervised models that use privileged information during learning. The privileged information comprises samples of time series observed between the baseline time of prediction and the future outcome; this information is only available at training time which differs from the traditional supervised learning. Our question is when using this privileged data leads to more sample-efficient learning of models that use only baseline data for predictions at test time. We give an algorithm for this setting and prove that when the time series are drawn from a non-stationary Gaussian-linear dynamical system of fixed horizon, learning with privileged information is more efficient than learning without it. On synthetic data, we test the limits of our algorithm and theory, both when our assumptions hold and when they are violated. On three diverse real-world datasets, we show that our approach is generally preferable to classical learning, particularly when data is scarce. Finally, we relate our estimator to a distillation approach both theoretically and empirically.

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arXiv2021

Case-based off-policy policy evaluation using prototype learning

Importance sampling (IS) is often used to perform off-policy policy evaluation but is prone to several issues, especially when the behavior policy is unknown and must be estimated from data. Significant differences between the target and behavior policies can result in uncertain value estimates due to, for example, high variance and non-evaluated actions. If the behavior policy is estimated using black-box models, it can be hard to diagnose potential problems and to determine for which inputs the policies differ in their suggested actions and resulting values. To address this, we propose estimating the behavior policy for IS using prototype learning. We apply this approach in the evaluation of policies for sepsis treatment, demonstrating how the prototypes give a condensed summary of differences between the target and behavior policies while retaining an accuracy comparable to baseline estimators. We also describe estimated values in terms of the prototypes to better understand which parts of the target policies have the most impact on the estimates. Using a simulator, we study the bias resulting from restricting models to use prototypes.

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arXiv2021

ADCB: An Alzheimer's disease benchmark for evaluating observational estimators of causal effects

Simulators make unique benchmarks for causal effect estimation since they do not rely on unverifiable assumptions or the ability to intervene on real-world systems, but are often too simple to capture important aspects of real applications. We propose a simulator of Alzheimer's disease aimed at modeling intricacies of healthcare data while enabling benchmarking of causal effect and policy estimators. We fit the system to the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and ground hand-crafted components in results from comparative treatment trials and observational treatment patterns. The simulator includes parameters which alter the nature and difficulty of the causal inference tasks, such as latent variables, effect heterogeneity, length of observed history, behavior policy and sample size. We use the simulator to compare estimators of average and conditional treatment effects.

cs.LG↗

arXiv2021

Learning to search efficiently for causally near-optimal treatments

Finding an effective medical treatment often requires a search by trial and error. Making this search more efficient by minimizing the number of unnecessary trials could lower both costs and patient suffering. We formalize this problem as learning a policy for finding a near-optimal treatment in a minimum number of trials using a causal inference framework. We give a model-based dynamic programming algorithm which learns from observational data while being robust to unmeasured confounding. To reduce time complexity, we suggest a greedy algorithm which bounds the near-optimality constraint. The methods are evaluated on synthetic and real-world healthcare data and compared to model-free reinforcement learning. We find that our methods compare favorably to the model-free baseline while offering a more transparent trade-off between search time and treatment efficacy.

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arXiv2020

Estimation of Bounds on Potential Outcomes For Decision Making

Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of upper and lower bounds on the potential outcomes of decision alternatives to assess risks and benefits. We show that, in such cases, we can improve sample efficiency by estimating simple functions that bound these outcomes instead of estimating their conditional expectations, which may be complex and hard to estimate. Our analysis highlights a trade-off between the complexity of the learning task and the confidence with which the learned bounds hold. Guided by these findings, we develop an algorithm for learning upper and lower bounds on potential outcomes which optimize an objective function defined by the decision maker, subject to the probability that bounds are violated being small. Using a clinical dataset and a well-known causality benchmark, we demonstrate that our algorithm outperforms baselines, providing tighter, more reliable bounds.

cs.LG↗

arXiv2020

Characterization of Overlap in Observational Studies

Overlap between treatment groups is required for non-parametric estimation of causal effects. If a subgroup of subjects always receives the same intervention, we cannot estimate the effect of intervention changes on that subgroup without further assumptions. When overlap does not hold globally, characterizing local regions of overlap can inform the relevance of causal conclusions for new subjects, and can help guide additional data collection. To have impact, these descriptions must be interpretable for downstream users who are not machine learning experts, such as policy makers. We formalize overlap estimation as a problem of finding minimum volume sets subject to coverage constraints and reduce this problem to binary classification with Boolean rule classifiers. We then generalize this method to estimate overlap in off-policy policy evaluation. In several real-world applications, we demonstrate that these rules have comparable accuracy to black-box estimators and provide intuitive and informative explanations that can inform policy making.

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arXiv2020

A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification.

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arXiv2019

Support and Invertibility in Domain-Invariant Representations

Learning domain-invariant representations has become a popular approach to unsupervised domain adaptation and is often justified by invoking a particular suite of theoretical results. We argue that there are two significant flaws in such arguments. First, the results in question hold only for a fixed representation and do not account for information lost in non-invertible transformations. Second, domain invariance is often a far too strict requirement and does not always lead to consistent estimation, even under strong and favorable assumptions. In this work, we give generalization bounds for unsupervised domain adaptation that hold for any representation function by acknowledging the cost of non-invertibility. In addition, we show that penalizing distance between densities is often wasteful and propose a bound based on measuring the extent to which the support of the source domain covers the target domain. We perform experiments on well-known benchmarks that illustrate the short-comings of current standard practice.

stat.ML↗

arXiv2018

Why Is My Classifier Discriminatory?

Recent attempts to achieve fairness in predictive models focus on the balance between fairness and accuracy. In sensitive applications such as healthcare or criminal justice, this trade-off is often undesirable as any increase in prediction error could have devastating consequences. In this work, we argue that the fairness of predictions should be evaluated in context of the data, and that unfairness induced by inadequate samples sizes or unmeasured predictive variables should be addressed through data collection, rather than by constraining the model. We decompose cost-based metrics of discrimination into bias, variance, and noise, and propose actions aimed at estimating and reducing each term. Finally, we perform case-studies on prediction of income, mortality, and review ratings, confirming the value of this analysis. We find that data collection is often a means to reduce discrimination without sacrificing accuracy.

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arXiv2018

Machine Learning Analysis of Heterogeneity in the Effect of Student Mindset Interventions

We study heterogeneity in the effect of a mindset intervention on student-level performance through an observational dataset from the National Study of Learning Mindsets (NSLM). Our analysis uses machine learning (ML) to address the following associated problems: assessing treatment group overlap and covariate balance, imputing conditional average treatment effects, and interpreting imputed effects. By comparing several different model families we illustrate the flexibility of both off-the-shelf and purpose-built estimators. We find that the mindset intervention has a positive average effect of 0.26, 95%-CI [0.22, 0.30], and that heterogeneity in the range of [0.1, 0.4] is moderated by school-level achievement level, poverty concentration, urbanicity, and student prior expectations.

stat.AP↗

arXiv2018

Learning Representations for Counterfactual Inference

Observational studies are rising in importance due to the widespread accumulation of data in fields such as healthcare, education, employment and ecology. We consider the task of answering counterfactual questions such as, "Would this patient have lower blood sugar had she received a different medication?". We propose a new algorithmic framework for counterfactual inference which brings together ideas from domain adaptation and representation learning. In addition to a theoretical justification, we perform an empirical comparison with previous approaches to causal inference from observational data. Our deep learning algorithm significantly outperforms the previous state-of-the-art.

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