Part III: Learning from Imperfect Data _{/ by Babak Salimi}

Machine learning (ML) applications have been thriving recently, largely attributed to the increasing availability of data. However, inconsistency and incomplete information are ubiquitous in real-world datasets, and their impact on ML applications remains elusive. In this paper, we present a formal study of this impact by extending the notion of Certain Answers for Codd tables, which has been explored by the database research community for decades, into the field of machine learning. Specifically, we focus on classification problems and propose the notion of “Certain Predictions” (CP) - a test data example can be certainly predicted (CP’ed) if all possible classifiers trained on top of all possible worlds induced by the incompleteness of data would yield the same prediction. We study two fundamental CP queries: (Q1) checking query that determines whether a data example can be CP’ed; and (Q2) counting query that computes the number of classifiers that support a particular prediction (i.e., label). Given that general solutions to CP queries are, not surprisingly, hard without assumption over the type of classifier, we further present a case study in the context of nearest neighbor (NN) classifiers, where efficient solutions to CP queries can be developed - we show that it is possible to answer both queries in linear or polynomial time over exponentially many possible worlds. We demonstrate one example use case of CP in the important application of “data cleaning for machine learning (DC for ML).” We show that our proposed CPClean approach built based on CP can often significantly outperform existing techniques, particularly on datasets with systematic missing values. For example, on 5 datasets with systematic missingness, CPClean (with early termination) closes 100% gap on average by cleaning 36% of dirty data on average, while the best automatic cleaning approach BoostClean can only close 14% gap on average.

We introduce dataset multiplicity, a way to study how inaccuracies, uncertainty, and social bias in training datasets impact test-time predictions. The dataset multiplicity framework asks a counterfactual question of what the set of resultant models (and associated test-time predictions) would be if we could somehow access all hypothetical, unbiased versions of the dataset. We discuss how to use this framework to encapsulate various sources of uncertainty in datasets’ factualness, including systemic social bias, data collection practices, and noisy labels or features. We show how to exactly analyze the impacts of dataset multiplicity for a specific model architecture and type of uncertainty: linear models with label errors. Our empirical analysis shows that real-world datasets, under reasonable assumptions, contain many test samples whose predictions are affected by dataset multiplicity. Furthermore, the choice of domain-specific dataset multiplicity definition determines what samples are affected, and whether different demographic groups are disparately impacted. Finally, we discuss implications of dataset multiplicity for machine learning practice and research, including considerations for when model outcomes should not be trusted.

Real-world data is often incomplete and contains missing values. To train accurate models over real-world datasets, users need to spend a substantial amount of time and resources imputing and finding proper values for missing data items. In this paper, we demonstrate that it is possible to learn accurate models directly from data with missing values for certain training data and target models. We propose a unified approach for checking the necessity of data imputation to learn accurate models across various widely-used machine learning paradigms. We build efficient algorithms with theoretical guarantees to check this necessity and return accurate models in cases where imputation is unnecessary. Our extensive experiments indicate that our proposed algorithms significantly reduce the amount of time and effort needed for data imputation without imposing considerable computational overhead.

Datasets can be biased due to societal inequities, human biases, under-representation of minorities, etc. Our goal is to certify that models produced by a learning algorithm are pointwise-robust to dataset biases. This is a challenging problem: it entails learning models for a large, or even infinite, number of datasets, ensuring that they all produce the same prediction. We focus on decision-tree learning due to the interpretable nature of the models. Our approach allows programmatically specifying \emph{bias models} across a variety of dimensions (e.g., label-flipping or missing data), composing types of bias, and targeting bias towards a specific group. To certify robustness, we use a novel symbolic technique to evaluate a decision-tree learner on a large, or infinite, number of datasets, certifying that each and every dataset produces the same prediction for a specific test point. We evaluate our approach on datasets that are commonly used in the fairness literature, and demonstrate our approach’s viability on a range of bias models.

This paper proposes a novel framework for certifying the fairness of predictive models trained on biased data. It draws from query answering for incomplete and inconsistent databases to formulate the problem of consistent range approximation (CRA) of fairness queries for a predictive model on a target population. The framework employs background knowledge of the data collection process and biased data, working with or without limited statistics about the target population, to compute a range of answers for fairness queries. Using CRA, the framework builds predictive models that are certifiably fair on the target population, regardless of the availability of external data during training. The framework’s efficacy is demonstrated through evaluations on real data, showing substantial improvement over existing state-of-the-art methods.

We introduce an efficient method for learning linear models from uncertain data, where uncertainty is represented as a set of possible variations in the data, leading to predictive multiplicity. Our approach leverages abstract interpretation and zonotopes, a type of convex polytope, to compactly represent these dataset variations, enabling the symbolic execution of gradient descent on all possible worlds simultaneously. We develop techniques to ensure that this process converges to a fixed point and derive closed-form solutions for this fixed point. Our method provides sound over-approximations of all possible optimal models and viable prediction ranges. We demonstrate the effectiveness of our approach through theoretical and empirical analysis, highlighting its potential to reason about model and prediction uncertainty due to data quality issues in training data.