1. A Unified Framework for Tuning Hyperparameters in Clustering Problems
- Author
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Fan, Xinjie, Yue, Yuguang, Sarkar, Purnamrita, and Wang, Y. X. Rachel
- Subjects
FOS: Computer and information sciences ,Statistics and Probability ,Computer Science - Machine Learning ,Statistics - Machine Learning ,FOS: Mathematics ,Machine Learning (stat.ML) ,Mathematics - Statistics Theory ,Statistics Theory (math.ST) ,Statistics, Probability and Uncertainty ,Machine Learning (cs.LG) - Abstract
Selecting hyperparameters for unsupervised learning problems is challenging in general due to the lack of ground truth for validation. Despite the prevalence of this issue in statistics and machine learning, especially in clustering problems, there are not many methods for tuning these hyperparameters with theoretical guarantees. In this paper, we provide a framework with provable guarantees for selecting hyperparameters in a number of distinct models. We consider both the subgaussian mixture model and network models to serve as examples of i.i.d. and non-i.i.d. data. We demonstrate that the same framework can be used to choose the Lagrange multipliers of penalty terms in semi-definite programming (SDP) relaxations for community detection, and the bandwidth parameter for constructing kernel similarity matrices for spectral clustering. By incorporating a cross-validation procedure, we show the framework can also do consistent model selection for network models. Using a variety of simulated and real data examples, we show that our framework outperforms other widely used tuning procedures in a broad range of parameter settings.
- Published
- 2024