Search arXivSearch

arXiv · 2308.02353

Adapting to Change: Robust Counterfactual Explanations in Dynamic Data Landscapes

Abstract

We introduce a novel semi-supervised Graph Counterfactual Explainer (GCE) methodology, Dynamic GRAph Counterfactual Explainer (DyGRACE). It leverages initial knowledge about the data distribution to search for valid counterfactuals while avoiding using information from potentially outdated decision functions in subsequent time steps. Employing two graph autoencoders (GAEs), DyGRACE learns the representation of each class in a binary classification scenario. The GAEs minimise the reconstruction error between the original graph and its learned representation during training. The method involves (i) optimising a parametric density function (implemented as a logistic regression function) to identify counterfactuals by maximising the factual autoencoder's reconstruction error, (ii) minimising the counterfactual autoencoder's error, and (iii) maximising the similarity between the factual and counterfactual graphs. This semi-supervised approach is independent of an underlying black-box oracle. A logistic regression model is trained on a set of graph pairs to learn weights that aid in finding counterfactuals. At inference, for each unseen graph, the logistic regressor identifies the best counterfactual candidate using these learned weights, while the GAEs can be iteratively updated to represent the continual adaptation of the learned graph representation over iterations. DyGRACE is quite effective and can act as a drift detector, identifying distributional drift based on differences in reconstruction errors between iterations. It avoids reliance on the oracle's predictions in successive iterations, thereby increasing the efficiency of counterfactual discovery. DyGRACE, with its capacity for contrastive learning and drift detection, will offer new avenues for semi-supervised learning and explanation generation.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Bardh Prenkaj, Mario Villaizan-Vallelado, Tobias Leemann, Gjergji Kasneci. 2023-08-04. Adapting to Change: Robust Counterfactual Explanations in Dynamic Data Landscapes. https://arxiv.org/abs/2308.02353

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG

ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy

Reinforcement learning agents depend on reward signals whose density is rarely under the designer's control, and when such signals are absent, an agent must generate its own drive to explore. State entropy maximization offers a principled objective for this, but existing methods break down at scale in two ways: the intrinsic reward vanishes once a state has been visited, discouraging revisits to the very gateways that lead onward, and estimating entropy over millions of accumulated observations becomes computationally prohibitive. We address both with Episodic and Lifelong Exploration via Maximum Entropy (ELEMENT), a multiscale intrinsically motivated framework for reward-free exploration that transfers to downstream tasks. ELEMENT couples lifelong entropy maximization with a complementary episodic term acting on a faster timescale. For the episodic term, we derive average episodic state entropy, an intrinsic reward that is the exact minimizer of a tractable upper bound on the reward-decomposition objective; for the lifelong term, we propose a $k$NN graph-based estimator that keeps entropy tractable without forgetting. ELEMENT consistently outperforms state-of-the-art intrinsic reward baselines on state coverage and unsupervised pre-training. Videos, code, and supplementary material: https://sites.google.com/view/element-rl.

cs.LG