Geyu Liang

Geyu Liang, Gavin Zhang, Salar Fattahi et al.

This paper focuses on the noiseless complete dictionary learning problem, where the goal is to represent a set of given signals as linear combinations of a small number of atoms from a learned dictionary. There are two main challenges faced by theoretical and practical studies of dictionary learning: the lack of theoretical guarantees for practically-used heuristic algorithms and their poor scalability when dealing with huge-scale datasets. Towards addressing these issues, we propose a simple and efficient algorithm that provably recovers the ground truth when applied to the nonconvex and discrete formulation of the problem in the noiseless setting. We also extend our proposed method to mini-batch and online settings where the data is huge-scale or arrives continuously over time. At the core of our proposed method lies an efficient preconditioning technique that transforms the unknown dictionary to a near-orthonormal one, for which we prove a simple alternating minimization technique converges linearly to the ground truth under minimal conditions. Our numerical experiments on synthetic and real datasets showcase the superiority of our method compared with the existing techniques.

Geyu Liang, Senne Michielssen, Salar Fattahi

The trade-off between accuracy and interpretability has long been a challenge in machine learning (ML). This tension is particularly significant for emerging interpretable-by-design methods, which aim to redesign ML algorithms for trustworthy interpretability but often sacrifice accuracy in the process. In this paper, we address this gap by investigating the impact of deviations in concept representations-an essential component of interpretable models-on prediction performance and propose a novel framework to mitigate these effects. The framework builds on the principle of optimizing concept embeddings under constraints that preserve interpretability. Using a generative model as a test-bed, we rigorously prove that our algorithm achieves zero loss while progressively enhancing the interpretability of the resulting model. Additionally, we evaluate the practical performance of our proposed framework in generating explainable predictions for image classification tasks across various benchmarks. Compared to existing explainable methods, our approach not only improves prediction accuracy while preserving model interpretability across various large-scale benchmarks but also achieves this with significantly lower computational cost.

Geyu Liang, Naichen Shi, Raed Al Kontar et al.

We introduce a relevant yet challenging problem named Personalized Dictionary Learning (PerDL), where the goal is to learn sparse linear representations from heterogeneous datasets that share some commonality. In PerDL, we model each dataset's shared and unique features as global and local dictionaries. Challenges for PerDL not only are inherited from classical dictionary learning (DL), but also arise due to the unknown nature of the shared and unique features. In this paper, we rigorously formulate this problem and provide conditions under which the global and local dictionaries can be provably disentangled. Under these conditions, we provide a meta-algorithm called Personalized Matching and Averaging (PerMA) that can recover both global and local dictionaries from heterogeneous datasets. PerMA is highly efficient; it converges to the ground truth at a linear rate under suitable conditions. Moreover, it automatically borrows strength from strong learners to improve the prediction of weak learners. As a general framework for extracting global and local dictionaries, we show the application of PerDL in different learning tasks, such as training with imbalanced datasets and video surveillance.