Handling missing values at test time is challenging for machine learning models, especially when aiming for both high accuracy and interpretability. Established approaches often add bias through imputation or excessive model complexity via missingness indicators. Moreover, either method can obscure interpretability, making it harder to understand how the model utilizes the observed variables in predictions. We propose *missingness-avoiding* (MA) machine learning, a general framework for training models to rarely require the values of missing (or imputed) features at test time. We create tailored MA learning algorithms for decision trees, tree ensembles, and sparse linear models by incorporating classifier-specific regularization terms in their learning objectives. The tree-based models leverage contextual missingness by reducing reliance on missing values based on the observed context. Experiments on real-world datasets demonstrate that **MA-DT, MA-LASSO, MA-RF**, and **MA-GBT** effectively reduce the reliance on features with missing values while maintaining predictive performance competitive with their unregularized counterparts. This shows that our framework gives practitioners a powerful tool to maintain interpretability in predictions with test-time missing values.

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.

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.

Learning an ordering of items based on pairwise comparisons is useful when items are difficult to rate consistently on an absolute scale, for example, when annotators have to make subjective assessments. When exhaustive comparison is infeasible, actively sampling item pairs can reduce the number of annotations necessary for learning an accurate ordering. However, many algorithms ignore shared structure between items, limiting their sample efficiency and precluding generalization to new items. It is also common to disregard how noise in comparisons varies between item pairs, despite it being informative of item similarity. In this work, we study active preference learning for ordering items with contextual attributes, both in- and out-of-sample. We give an upper bound on the expected ordering error of a logistic preference model as a function of which items have been compared. Next, we propose an active learning strategy that samples items to minimize this bound by accounting for aleatoric and epistemic uncertainty in comparisons. We evaluate the resulting algorithm, and a variant aimed at reducing model misspecification, in multiple realistic ordering tasks with comparisons made by human annotators. Our results demonstrate superior sample efficiency and generalization compared to non-contextual ranking approaches and active preference learning baselines.

Evaluating observational estimators of causal effects demands information that is rarely available: unconfounded interventions and outcomes from the population of interest, created either by randomization or adjustment. As a result, it is customary to fall back on simulators when creating benchmark tasks. Simulators offer great control but are often too simplistic to make challenging tasks, either because they are hand-designed and lack the nuances of real-world data, or because they are fit to observational data without structural constraints. In this work, we propose a general, repeatable strategy for turning observational data into sequential structural causal models and challenging estimation tasks by following two simple principles: 1) fitting real-world data where possible, and 2) creating complexity by composing simple, hand-designed mechanisms. We implement these ideas in a highly configurable software package and apply it to the well-known Adult income data set to construct the IncomeSCM simulator. From this, we devise multiple estimation tasks and sample data sets to compare established estimators of causal effects. The tasks present a suitable challenge, with effect estimates varying greatly in quality between methods, despite similar performance in the modeling of factual outcomes, highlighting the need for dedicated causal estimators and model selection criteria.

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 (SPSM), 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.

To combat poor health and living conditions, policymakers in Africa require temporally and geographically granular data measuring economic well-being. Machine learning (ML) offers a promising alternative to expensive and time-consuming survey measurements by training models to predict economic conditions from freely available satellite imagery. However, previous efforts have failed to utilize the temporal information available in earth observation (EO) data, which may capture developments important to standards of living. In this work, we develop an EO-ML method for inferring neighborhood-level material-asset wealth using multi-temporal imagery and recurrent convolutional neural networks. Our model outperforms state-of-the-art models in several aspects of generalization, explaining 72% of the variance in wealth across held-out countries and 75% held-out time spans. Using our geographically and temporally aware models, we created spatio-temporal material-asset data maps covering the entire continent of Africa from 1990 to 2019, making our data product the largest dataset of its kind. We showcase these results by analyzing which neighborhoods are likely to escape poverty by the year 2030, which is the deadline for when the Sustainable Development Goals (SDG) are evaluated.

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.

In domains where sample sizes are limited, efficient learning algorithms are critical. Learning using privileged information (LuPI) offers increased sample efficiency by allowing prediction models access to auxiliary information at training time which is unavailable when the models are used. In recent work, it was shown that for prediction in linear-Gaussian dynamical systems, a LuPI learner with access to intermediate time series data is never worse and often better in expectation than any unbiased classical learner. We provide new insights into this analysis and generalize it to nonlinear prediction tasks in latent dynamical systems, extending theoretical guarantees to the case where the map connecting latent variables and observations is known up to a linear transform. In addition, we propose algorithms based on random features and representation learning for the case when this map is unknown. A suite of empirical results confirm theoretical findings and show the potential of using privileged time-series information in nonlinear prediction.

Importance sampling (IS) is often used to perform off-policy evaluation but it is prone to several issues—especially when the behavior policy is unknown and must be estimated from data. Significant differences between target and behavior policies can result in uncertain value estimates due to, for example, high variance. Standard practices such as inspecting IS weights may be insufficient to diagnose such problems and determine for which type of inputs the policies differ in suggested actions and resulting values. To address this, we propose estimating the behavior policy for IS using prototype learning. The learned prototypes provide a condensed summary of the input-action space, which allows for describing differences between policies and assessing the support for evaluating a certain target policy. In addition, we can describe a value estimate in terms of prototypes to understand which parts of the target policy have the most impact on the estimate. We find that this provides new insights in the examination of a learned policy for sepsis management. Moreover, we study the bias resulting from restricting models to use prototypes, how bias propagates to IS weights and estimated values and how this varies with history length.

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 potential outcomes and 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 outcomes based on distributional distance measures between re-weighted samples of groups receiving different treatments. We provide conditions under which our bounds are tight and show how they relate to results for unsupervised domain adaptation. Led by our theoretical results, we devise algorithms which learn representations and weighting functions that minimize our bounds by regularizing the representation's induced treatment group distance, and encourage sharing of information between treatment groups. Finally, an experimental evaluation on real and synthetic data shows the value of our proposed representation architecture and regularization scheme.

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.

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.

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.

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.

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.

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.

Standard clustering methods such as K-means, Gaussian mixture models, and hierarchical clustering are beset by local minima, which are sometimes drastically suboptimal. Moreover the number of clusters K must be known in advance. The recently introduced the sum-of-norms (SON) or Clusterpath convex relaxation of k-means and hierarchical clustering shrinks cluster centroids toward one another and ensure a unique global minimizer. We give a scalable stochastic incremental algorithm based on proximal iterations to solve the SON problem with convergence guarantees. We also show that the algorithm recovers clusters under quite general conditions which have a similar form to the unifying proximity condition introduced in the approximation algorithms community (that covers paradigm cases such as Gaussian mixtures and planted partition models). We give experimental results to confirm that our algorithm scales much better than previous methods while producing clusters of comparable quality.

There is intense interest in applying machine learning to problems of causal inference in fields such as healthcare, economics and education. In particular, individual-level causal inference has important applications such as precision medicine. We give a new theoretical analysis and family of algorithms for predicting individual treatment effect (ITE) from observational data, under the assumption known as strong ignorability. The algorithms learn a “balanced” representation such that the induced treated and control distributions look similar, and we give a novel and intuitive generalization-error bound showing the expected ITE estimation error of a representation is bounded by a sum of the standard generalization-error of that representation and the distance between the treated and control distributions induced by the representation. We use Integral Probability Metrics to measure distances between distributions, deriving explicit bounds for the Wasserstein and Maximum Mean Discrepancy (MMD) distances. Experiments on real and simulated data show the new algorithms match or outperform the state-of-the-art.

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.

We develop and apply the Balcan-Blum-Srebro (BBS) theory of classification via similarity functions (which are not necessarily kernels) to the problem of graph classification. First we place the BBS theory into the unifying framework of optimal transport theory. This also opens the way to exploit coupling methods for establishing properties required of a good similarity function as per their definition. Next, we use the approach to the problem of graph classification via geometric embeddings such as the Laplacian, pseudo-inverse Laplacian and the Lovász orthogonal labellings. We consider the similarity function given by optimal and near--optimal matchings with respect to Euclidean distance of the corresponding embeddings of the graphs in high dimensions. We use optimal couplings to rigorously establish that this yields a "good" similarity measure in the BBS sense for two well known families of graphs. Further, we show that the similarity yields better classification accuracy in practice, on these families, than matchings of other well-known graph embeddings. Finally we perform an extensive empirical evaluation on benchmark data sets where we show that classifying graphs using matchings of geometric embeddings outperforms the previous state-of-the-art methods.

We introduce a unifying generalization of the Lovász theta function, and the associated geometric embedding, for graphs with weights on both nodes and edges. We show how it can be computed exactly by semidefinite programming, and how to approximate it using SVM computations. We show how the theta function can be interpreted as a measure of diversity in graphs and use this idea, and the graph embedding in algorithms for Max-Cut, correlation clustering and document summarization, all of which are well represented as problems on weighted graphs.

Applications of machine learning methods increasingly deal with graph structured data through kernels. Most existing graph kernels compare graphs in terms of features defined on small subgraphs such as walks, paths or graphlets, adopting an inherently local perspective. However, several interesting properties such as girth or chromatic number are global properties of the graph, and are not captured in local substructures. This paper presents two graph kernels defined on unlabeled graphs which capture global properties of graphs using the celebrated Lovász number and its associated orthonormal representation. We make progress towards theoretical results aiding kernel choice, proving a result about the separation margin of our kernel for classes of graphs. We give empirical results on classification of synthesized graphs with important global properties as well as established benchmark graph datasets, showing that the accuracy of our kernels is better than or competitive to existing graph kernels.

This paper presents a novel method for entity disambiguation in anonymized graphs using local neighborhood structure. Most existing approaches leverage node information, which might not be available in several contexts due to privacy concerns, or information about the sources of the data. We consider this problem in the supervised setting where we are provided only with a base graph and a set of nodes labelled as ambiguous or unambiguous. We characterize the similarity between two nodes based on their local neighborhood structure using graph kernels; and solve the resulting classification task using SVMs. We give empirical evidence on two real-world datasets, comparing our approach to a state-of-the-art method, highlighting the advantages of our approach. We show that using less information, our method is significantly better in terms of either speed or accuracy or both. We also present extensions of two existing graphs kernels, namely, the direct product kernel and the shortest-path kernel, with significant improvements in accuracy. For the direct product kernel, our extension also provides significant computational benefits. Moreover, we design and implement the algorithms of our method to work in a distributed fashion using the GraphLab framework, ensuring high scalability.