5 min
Formulating Efficient Data Deletion
The authors reiterate in their work that deletion is not privacy. In a trade-off between efficiency and privacy, a challenge arises because algorithms that support efficient deletion need not be private, and algorithms that are private do not have to support efficient deletion. Data deletion is simple and in this work, the main focus is on k-means clustering. The authors propose two algorithms for deletion with efficient k-means clustering.
In the context of k-means, the output centroids are treated as the model from which we are interested in deleting data points. A quantized variant of Lloyd’s algorithm is also proposed as a deletion efficient solution to k-means clustering, called Q-k-means.
In this solution, the centroids are quantized at each iteration to show that the algorithm’s centroids are constant with respect to deletions with high probability.
Q-k-means tends to have higher variance around its deletion efficiency, due to the randomness in centroid stabilization having a larger impact than the randomness in the dataset partitioning.
Based on their experiment, the authors identify a few design principles. Some of which are listed below:
- Linear computation allows for simple post-processing to undo the influence of a single data point on a set of parameters. The Sherman-Morrison-Woodbury matrix identity and matrix factorization techniques can be used to derive fast and explicit formulas for updating linear computations.
- Modularity should be most effective in regimes for which the dimension of the data is small compared to the dataset size, allowing for partitions of the dataset to capture the important structure and features. Modularity is the restriction of the dependence of computation state or model parameters to specific partitions of the dataset.
- Many models come with a sense of continuity from dataset space to model space — small changes to the dataset should result in small changes to the (distribution over the) model space. This can be leveraged by quantizing the mapping from datasets to models (either explicitly or implicitly).
Key Ideas
The objectives of the authors can be summarized as follows:- Introduce deletion efficient learning, based on an intuitive and operational notion of what it means to (efficiently) delete data.
- Demonstrate why data deletion is an online problem, from which a notion of optimal deletion efficiency emerges
- Perform a case-study on deletion efficient learning using the k-means clustering problem
- Propose two deletion efficient algorithms that (in certain regimes) achieve optimal deletion efficiency.
- Synthesize an algorithmic toolbox for designing deletion efficient learning systems
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