Finding the Homology of Decision Boundaries with Active Learning
Accurately and efficiently characterizing the decision boundary of classifiers is important for problems related to model selection and meta-learning. Inspired by topological data analysis, the characterization of decision boundaries using their homology has recently emerged as a general and powerful tool. In this paper, we propose an active learning algorithm to recover the homology of decision boundaries. Our algorithm sequentially and adaptively selects which samples it requires the labels of. We theoretically analyze the proposed framework and show that the query complexity of our active learning algorithm depends naturally on the intrinsic complexity of the underlying manifold. We demonstrate the effectiveness of our framework in selecting best-performing machine learning models for datasets just using their respective homological summaries. Experiments on several standard datasets show the sample complexity improvement in recovering the homology and demonstrate the practical utility of the framework for model selection. Source code for our algorithms and experimental results is available at https://github.com/wayne0908/Active-Learning-Homology.
Code (1)
Tasks
Active LearningMeta-LearningModel SelectionTopological Data AnalysisSimilar Papers 제목 키워드 기반
Topological Data Analysis of Decision Boundaries with Application to Model Selection
We propose the labeled \v{C}ech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tas…
General ClassificationModel SelectionTopological Data AnalysisProbing the Decision Boundaries of In-context Learning in Large Language Models
In-context learning is a key paradigm in large language models (LLMs) that enables them to generalize to new tasks and domains by simply prompting these models with a few exemplars without explicit parameter updates. Man…
Binary ClassificationIn-Context LearningInvestigating Decision Boundaries of Trained Neural Networks
Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined…
Adversarial AttackAdversarial Active Learning for Deep Networks: a Margin Based Approach
We propose a new active learning strategy designed for deep neural networks. The goal is to minimize the number of data annotation queried from an oracle during training. Previous active learning strategies scalable for …
Active LearningOn the Decision Boundaries of Neural Networks. A Tropical Geometry Perspective
This work tackles the problem of characterizing and understanding the decision boundaries of neural networks with piecewise linear non-linearity activations. We use tropical geometry, a new development in the area of alg…
Network Pruning