{\em “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 \emph{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 \emph{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.

In order to compute a non-invertible function on a reversible circuit, one needs to "embed" the function into a larger function which has some garbage bits, corresponding to additional lines. The problem of determining the minimal number of garbage bits that are needed to embed a given function has attracted extensive research, largely motivated by quantum computing, where the number of lines equals the number of qubits. However, all approaches that are known have either no theoretical quality guarantees (bounds on approximation factors) or require exponential runtime. We present an efficient probabilistic approximation algorithm with theoretical bounds.

Given a data set 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 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 ( N log N ) for ( ϵ , δ)-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 ( N log N ) time - an exponential improvement on computational complexity! Moreover, for ( ϵ , δ)-approximation, we are able to develop an algorithm based on Locality Sensitive Hashing (LSH) with only sublinear complexity O ( N h ( ϵ , K ) log N ) when ϵ 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 algorithm 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. Some of these extensions, although also being improved exponentially, are less practical for exact computation (e.g., O ( N K ) complexity for weigthed K NN). We thus propose an Monte Carlo approximation algorithm, which is O ( N (log N ) 2 /(log K ) 2 ) times more efficient than the baseline approximation algorithm.

Developing machine learning (ML) applications is similar to developing traditional software --- it is often an iterative process in which developers navigate within a rich space of requirements, design decisions, implementations, empirical quality , and performance . In traditional software development, software engineering is the field of study which provides principled guidelines for this iterative process. However, as of today, the counterpart of "software engineering for ML" is largely missing --- developers of ML applications are left with powerful tools (e.g., TensorFlow and PyTorch) but little guidance regarding the development lifecycle itself. In this paper, we view the management of ML development life-cycles from a data management perspective. We demonstrate two closely related systems, ease.ml/ci and ease.ml/meter, that provide some "principled guidelines" for ML application development: ci is a continuous integration engine for ML models and meter is a "profiler" for controlling overfitting of ML models. Both systems focus on managing the "statistical generalization power" of datasets used for assessing the quality of ML applications, namely, the validation set and the test set . By demonstrating these two systems we hope to spawn further discussions within our community on building this new type of data management systems for statistical generalization.