Diffeomorphic Explanations with Normalizing Flows
Normalizing flows are diffeomorphisms which are parameterized by neural networks. As a result, they can induce coordinate transformations in the tangent space of the data manifold. In this work, we demonstrate that such transformations can be used to generate interpretable explanations for decisions of neural networks. More specifically, we perform gradient ascent in the base space of the flow to generate counterfactuals which are classified with great confidence as a specified target class. We analyze this generation process theoretically using Riemannian differential geometry and establish a rigorous theoretical connection between gradient ascent on the data manifold and in the base space of the flow.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Neural Diffeomorphic Non-uniform B-spline Flows
Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of a simple base distribution. However, there are often applications that require more than invertibili…
Jacobian Determinant of Normalizing Flows
Normalizing flows learn a diffeomorphic mapping between the target and base distribution, while the Jacobian determinant of that mapping forms another real-valued function. In this paper, we show that the Jacobian determ…
Time-changed normalizing flows for accurate SDE modeling
The generative paradigm has become increasingly important in machine learning and deep learning models. Among popular generative models are normalizing flows, which enable exact likelihood estimation by transforming a ba…
Gaussian ProcessesTime SeriesDeep Diffeomorphic Normalizing Flows
The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Norma…
Density EstimationVariational InferenceDenoising Normalizing Flow
Normalizing flows (NF) are expressive as well as tractable density estimation methods whenever the support of the density is diffeomorphic to the entire data-space. However, real-world data sets typically live on (or ver…
DenoisingDensity Estimation