This work proposes a new computational framework for learning a structured generative model for real-world datasets. In particular, we propose to learn a Closed-loop Transcriptionbetween a multi-class, multi-dimensional data distribution and a Linear discriminative representation (CTRL) in the feature space that consists of multiple independent multi-dimensional linear subspaces. In particular, we argue that the optimal encoding and decoding mappings sought can be formulated as a two-player minimax game between the encoder and decoderfor the learned representation. A natural utility function for this game is the so-called rate reduction, a simple information-theoretic measure for distances between mixtures of subspace-like Gaussians in the feature space. Our formulation draws inspiration from closed-loop error feedback from control systems and avoids expensive evaluating and minimizing of approximated distances between arbitrary distributions in either the data space or the feature space. To a large extent, this new formulation unifies the concepts and benefits of Auto-Encoding and GAN and naturally extends them to the settings of learning a both discriminative and generative representation for multi-class and multi-dimensional real-world data. Our extensive experiments on many benchmark imagery datasets demonstrate tremendous potential of this new closed-loop formulation: under fair comparison, visual quality of the learned decoder and classification performance of the encoder is competitive and arguably better than existing methods based on GAN, VAE, or a combination of both. Unlike existing generative models, the so-learned features of the multiple classes are structured instead of hidden: different classes are explicitly mapped onto corresponding independent principal subspaces in the feature space, and diverse visual attributes within each class are modeled by the independent principal components within each subspace.
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Equi-explanation Maps: Concise and Informative Global Summary Explanations
We propose equi-explanation maps to study the variation in model logic across the input space. These global model-agnostic structures partition the hyper-space of explanation features into regions of similar model logic. Equi-explanation maps act as a concise summary of instance explanations and can provide laymen an at-a-glance understanding of the basis on which the classifier makes its decisions. We thus propose the task of generating $\epsilon$-equi-explanation maps, a partitioning of the input space into subspaces such that the standard deviation of explanation vectors in a subspace do not exceed $\epsilon$. We adapt existing local and subspace explainability techniques like LIME and MUSE to generate equi-explanation maps on two binary classification datasets using four classification models and evaluate the quality of their partitioning. We find that these techniques produce a sub-optimal number of subspaces (making the maps harder to interpret) and have a considerable run time. We then propose E-map, a new divide-and-conquer based algorithm to produce $\epsilon$-equi-explanation maps. E-map is able to decrease the number of subspaces (and hence increase interpretability) and running time as compared to the previous systems for a fixed value of $\epsilon$. Finally, given a classifier decision boundary, we try to determine what would be an optimal value for the parameter $\epsilon$. We believe good explanation representation methods can increase the trustworthiness and understanding of machine learning models for critical real world tasks.
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- NSF-PAR ID:
- 10357768
- Date Published:
- Journal Name:
- Proceedings of the 2022 ACM FAccT* Conference
- Page Range / eLocation ID:
- 464 to 472
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3531146.3533112
