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Register a new userTowards Efficient Data Valuation Based on the Shapley Value
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How much is my data worth? is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining prospective compensation when data breaches happen. In this paper, we study the problem of data valuation by utilizing the Shapley value, a popular notion of value which originated in coopoerative game theory. The Shapley value defines a unique payoff scheme that satisfies many desiderata for the notion of data value. However, the Shapley value often requires exponential time to compute. To meet this challenge, we propose a repertoire of efficient algorithms for approximating the Shapley value. We also demonstrate the value of each training instance for various benchmark datasets.
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The reliability of machine learning models can be compromised when trained on low quality data. Many large-scale medical imaging datasets contain low quality labels extracted from sources such as medical reports. Moreover, images within a dataset may have heterogeneous quality due to artifacts and biases arising from equipment or measurement errors. Therefore, algorithms that can automatically identify low quality data are highly desired. In this study, we used data Shapley, a data valuation metric, to quantify the value of training data to the performance of a pneumonia detection algorithm in a large chest X-ray dataset. We characterized the effectiveness of data Shapley in identifying low quality versus valuable data for pneumonia detection. We found that removing training data with high Shapley values decreased the pneumonia detection performance, whereas removing data with low Shapley values improved the model performance. Furthermore, there were more mislabeled examples in low Shapley value data and more true pneumonia cases in high Shapley value data. Our results suggest that low Shapley value indicates mislabeled or poor quality images, whereas high Shapley value indicates data that are valuable for pneumonia detection. Our method can serve as a framework for using data Shapley to denoise large-scale medical imaging datasets.
Given a data set $mathcal{D}$ containing millions of data points and a data consumer who is willing to pay for $$X$ to train a machine learning (ML) model over $mathcal{D}$, how should we distribute this $$X$ to each data point to reflect its value? In this paper, we define the relative value of data via the Shapley value, as it uniquely possesses properties with appealing real-world interpretations, such as fairness, rationality and decentralizability. For general, bounded utility functions, the Shapley value is known to be challenging to compute: to get Shapley values for all $N$ data points, it requires $O(2^N)$ model evaluations for exact computation and $O(Nlog N)$ for $(epsilon, delta)$-approximation. In this paper, we focus on one popular family of ML models relying on $K$-nearest neighbors ($K$NN). The most surprising result is that for unweighted $K$NN classifiers and regressors, the Shapley value of all $N$ data points can be computed, exactly, in $O(Nlog N)$ time -- an exponential improvement on computational complexity! Moreover, for $(epsilon, delta)$-approximation, we are able to develop an algorithm based on Locality Sensitive Hashing (LSH) with only sublinear complexity $O(N^{h(epsilon,K)}log N)$ when $epsilon$ is not too small and $K$ is not too large. We empirically evaluate our algorithms on up to $10$ million data points and even our exact algorithm is up to three orders of magnitude faster than the baseline approximation algorithm. The LSH-based approximation algorithm can accelerate the value calculation process even further. We then extend our algorithms to other scenarios such as (1) weighed $K$NN classifiers, (2) different data points are clustered by different data curators, and (3) there are data analysts providing computation who also requires proper valuation.
Reinforcement learning (RL) algorithms usually require a substantial amount of interaction data and perform well only for specific tasks in a fixed environment. In some scenarios such as healthcare, however, usually only few records are available for each patient, and patients may show different responses to the same treatment, impeding the application of current RL algorithms to learn optimal policies. To address the issues of mechanism heterogeneity and related data scarcity, we propose a data-efficient RL algorithm that exploits structural causal models (SCMs) to model the state dynamics, which are estimated by leveraging both commonalities and differences across subjects. The learned SCM enables us to counterfactually reason what would have happened had another treatment been taken. It helps avoid real (possibly risky) exploration and mitigates the issue that limited experiences lead to biased policies. We propose counterfactual RL algorithms to learn both population-level and individual-level policies. We show that counterfactual outcomes are identifiable under mild conditions and that Q- learning on the counterfactual-based augmented data set converges to the optimal value function. Experimental results on synthetic and real-world data demonstrate the efficacy of the proposed approach.
In value-based reinforcement learning (RL), unlike in supervised learning, the agent faces not a single, stationary, approximation problem, but a sequence of value prediction problems. Each time the policy improves, the nature of the problem changes, shifting both the distribution of states and their values. In this paper we take a novel perspective, arguing that the value prediction problems faced by an RL agent should not be addressed in isolation, but rather as a single, holistic, prediction problem. An RL algorithm generates a sequence of policies that, at least approximately, improve towards the optimal policy. We explicitly characterize the associated sequence of value functions and call it the value-improvement path. Our main idea is to approximate the value-improvement path holistically, rather than to solely track the value function of the current policy. Specifically, we discuss the impact that this holistic view of RL has on representation learning. We demonstrate that a representation that spans the past value-improvement path will also provide an accurate value approximation for future policy improvements. We use this insight to better understand existing approaches to auxiliary tasks and to propose new ones. To test our hypothesis empirically, we augmented a standard deep RL agent with an auxiliary task of learning the value-improvement path. In a study of Atari 2600 games, the augmented agent achieved approximately double the mean and median performance of the baseline agent.
In data science, there is a long history of using synthetic data for method development, feature selection and feature engineering. Our current interest in synthetic data comes from recent work in explainability. Todays datasets are typically larger and more complex - requiring less interpretable models. In the setting of textit{post hoc} explainability, there is no ground truth for explanations. Inspired by recent work in explaining image classifiers that does provide ground truth, we propose a similar solution for tabular data. Using copulas, a concise specification of the desired statistical properties of a dataset, users can build intuition around explainability using controlled data sets and experimentation. The current capabilities are demonstrated on three use cases: one dimensional logistic regression, impact of correlation from informative features, impact of correlation from redundant variables.
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