Posterior-Calibrated Causal Circuits in Variational Autoencoders: Why Image-Domain Interpretability Fails on Tabular Data
Authors: Dip Roy, Rajiv Misra, Sanjay Kumar Singh, Anisha Roy
Organizations: Department of Computer Science and Engineering, Indian Institute of Technology, Patna, India · Department of Computer Science, Rajarshi School of Management Technology, Varanasi, India · Department of Electronics and Communication Engineering, Jaypee Institute of Information Technology, Noida
Although mechanism-based interpretability has generated an abundance of insight for discriminative network analysis, generative models are less understood -- particularly outside of image-related applications. We investigate how much of the causal circuitry found within image-related variational autoencoders (VAEs) will generalize to tabular data, as VAEs are increasingly used for imputation, anomaly detection, and synthetic data generation. In addition to extending a four-level causal intervention framework to four tabular and one image benchmark across five different VAE architectures (with 75 individual training runs per architecture and three random seed values for each run), this paper introduces three new techniques: posterior-calibration of Causal Effect Strength (CES), path-specific activation patching, and Feature-Group Disentanglement (FGD). The results from our experiments demonstrate that: (i) Tabular VAEs have circuits with modularity that is approximately 50% lower than their image counterparts. (ii) β-VAE experiences nearly complete collapse in CES scores when applied to heterogeneous tabular features (0.043 CES score for tabular data compared to 0.133 CES score for images), which can be directly attributed to reconstruction quality degradation (r = -0.886 correlation coefficient between CES and MSE). (iii) CES successfully captures nine of eleven statistically significant architecture differences using Holm--Šidák corrections. (iv) Interventions with high specificity predict the highest downstream AUC values (r = 0.460, p < .001). This study challenges the common assumption that architectural guidance from image-related studies can be transferred to tabular datasets.
Tabular-to-image encoding methods enable the application of models based on both convolutional neural networks and vision transformers to tabular data, transforming feature vectors into images. Existing methods employ linear and nonlinear dimensionality reduction techniques (e.g., Principal Component Analysis (PCA), t-SNE, and UMAP) to determine pixel positions, resulting in images whose spatial layout do not inherently reflect feature relationships. This paper introduces Visibility Graphs for Tabular-to-Image Encoding (VG-TIE), a novel method that encodes the structure of feature values using Natural Visibility Graph (NVG) and Horizontal Visibility Graph (HVG) into a two-dimensional space obtained through PCA. The resulting images are model-agnostic and intrinsically interpretable. Each pixel corresponds to an input feature, its intensity reflects the magnitude and direction of deviation from the population mean, and edges represent formally defined visibility relationships between features. VG-TIE provides two interpretability methods: (i) feature ranking from node degree distributions; and (ii) local and global feature importance from pixel intensity combined with Grad-CAM. Experiments on six public tabular datasets show that VG-TIE is competitive with other tabular-to-image methods while providing interpretability on feature importance and ranking similar to intrinsic interpretable methods. The results highlight the potential of the proposed image-based transformation to provide an effective framework that expands the use of deep learning across tabular data domains.
David Chushig-Muzo, Luis M. López-Ramos, Ángeles Rodríguez de Cara +3
School of Mathematical and Computational Sciences, Yachay Tech University, Ecuador
Deep generative models reproduce the observational distribution of their training data, inheriting any spurious associations it contains. A common source is an unobserved confounder that shapes both an attribute the user wants to control at sampling time and an attribute expected to vary in response. Existing causal generative approaches resolve the resulting ambiguity by imposing structural assumptions strong enough to single out one interventional distribution; in image domains, such assumptions are rarely warranted, and the data is generally consistent with a set of distinct causal mechanisms -- a feasible region of interventional distributions. We propose CauVaDE (Causal Variational Deep Embedding), built on a canonical augmented SCM in which the unobserved confounder collapses, without loss of generality, into a discrete latent cluster of bounded support while continuous variation is absorbed into independent noises. We prove that this canonical class is dense, in both observational and interventional Wasserstein distance, in the class of augmented SCMs compatible with a given causal diagram, and instantiate it as a mixture variational autoencoder whose cluster variable plays the role of the canonical confounder. An entropy regularizer with weight γ on the cluster posterior then traces a family of candidate causal effects that fit the observational data to comparable likelihood while spanning the feasible region. Experiments on image data benchmarks show that CauVaDE produces diverse interventional samples and improves FID against an unconfounded reference.
Jingyuan Chen, Kangrui Ruan, Junzhe Zhang
Department of EECS Syracuse University · AWS AI Lab
Evaluating and interpreting latent representations, such as variational autoencoders (VAEs), remains a significant challenge for diverse data types, especially when ground-truth generative factors are unknown. To address this, we unify several state-of-the-art disentangled VAE approaches for latent space disentanglement into one framework -- bfVAE. To assess the effectiveness of a disentangled VAE model and enhance latent space interpretability, we propose Feature Variance Heterogeneity via Latent Traversal (FVH-LT) and Dirty Block Sparse Regression in Latent Space (DBSR-LS). To ensure robust interpretability of learned latent space, we develop a greedy alignment strategy (GAS) that mitigates label switching and aligns latent dimensions across runs to set the foundation of result aggregation. We also introduce a convenient scalar latent space separation index (LSSI) based on the GAS-aligned outputs of FVH-LT and DBSR-LS to summarize the overall latent structural separation without knowledge of the ground-truth generative factors. We compare bfVAE to five VAE models and validate the effectiveness FVH-LT, DBSR-LS, and LSSI in on seven tabular and image datasets. Under our examined experimental settings, bfVAE provides a more flexible disentanglement framework achieves more favorable overall trade-off between disentanglement and reconstruction than the benchmark VAE models; FVH-LT and DBSR-LS reliably uncover semantically meaningful and domain-relevant latent structures and generally yield consistent results; and LSSI makes an effective quantitative summary of latent structural separation.
Xiaoan Lang, Md Mostafizer Rahman, Fang Liu
Department of Applied and Computational Mathematics and Statistics University of Notre Dame, Notre Dame, IN, USA · Lucy Family Institute for Data & Society University of Notre Dame, Notre Dame, IN, USA