Adaptive Transfer Clustering: A Unified Framework

We propose a general transfer learning framework for clustering given a main dataset and an auxiliary one about the same subjects. The two datasets may reflect similar but different latent grouping structures of the subjects. We propose an adaptive transfer clustering (ATC) algorithm that automatically leverages the commonality in the presence of unknown discrepancy, by optimizing an estimated bias-variance decomposition. It applies to a broad class of statistical models including Gaussian mixture models, stochastic block models, and latent class models. A theoretical analysis proves the optimality of ATC under the Gaussian mixture model and explicitly quantifies the benefit of transfer. Extensive simulations and real data experiments confirm our method's effectiveness in various scenarios.

Learning from Similar Linear Representations: Adaptivity, Minimaxity, and Robustness

Representation multi-task learning (MTL) and transfer learning (TL) have achieved tremendous success in practice. However, the theoretical understanding of these methods is still lacking. Most existing theoretical works focus on cases where all tasks share the same representation, and claim that MTL and TL almost always improve performance. However, as the number of tasks grow, assuming all tasks share the same representation is unrealistic. Also, this does not always match empirical findings, which suggest that a shared representation may not necessarily improve single-task or target-only learning performance. In this paper, we aim to understand how to learn from tasks with \textit{similar but not exactly the same} linear representations, while dealing with outlier tasks. We propose two algorithms that are \textit{adaptive} to the similarity structure and \textit{robust} to outlier tasks under both MTL and TL settings. Our algorithms outperform single-task or target-only learning when representations across tasks are sufficiently similar and the fraction of outlier tasks is small. Furthermore, they always perform no worse than single-task learning or target-only learning, even when the representations are dissimilar. We provide information-theoretic lower bounds to show that our algorithms are nearly \textit{minimax} optimal in a large regime.

Identification and Estimation of Hierarchical Latent Attribute Models

Hierarchical Latent Attribute Models (HLAMs) are a popular family of discrete latent variable models widely used in social and biological sciences. The key ingredients of an HLAM include a binary structural matrix specifying how the observed variables depend on the latent attributes, and also certain hierarchical constraints on allowable configurations of the latent attributes. This paper studies the theoretical identifiability issue and the practical estimation problem of HLAMs. For identification, the challenging problem of identifiability under a complex hierarchy is addressed and sufficient and almost necessary identification conditions are proposed. For estimation, a scalable algorithm for estimating both the structural matrix and the attribute hierarchy is developed. The superior performance of the proposed algorithm is demonstrated in various experimental settings, including both synthetic data and a real dataset from an international educational assessment.

Learning Attribute Patterns in High-Dimensional Structured Latent Attribute Models

Structured latent attribute models (SLAMs) are a special family of discrete latent variable models widely used in social and biological sciences. This paper considers the problem of learning significant attribute patterns from a SLAM with potentially high-dimensional configurations of the latent attributes. We address the theoretical identifiability issue, propose a penalized likelihood method for the selection of the attribute patterns, and further establish the selection consistency in such an overfitted SLAM with diverging number of latent patterns. The good performance of the proposed methodology is illustrated by simulation studies and two real datasets in educational assessment.