Add to Chrome
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A Geometric Explanation of the Likelihood OOD Detection Paradox
Mar 27, 2024
Likelihood-based deep generative models (DGMs) commonly exhibit a puzzling behaviour: when trained on a relatively complex dataset, they assign higher likelihood values to out-of-distribution (OOD) data from simpler sources. Adding to the mystery, OOD samples are never generated by these DGMs despite having higher likelihoods. This two-pronged paradox has yet to be conclusively explained, making likelihood-based OOD detection unreliable. Our primary observation is that high-likelihood regions will not be generated if they contain minimal probability mass. We demonstrate how this seeming contradiction of large densities yet low probability mass can occur around data confined to low-dimensional manifolds. We also show that this scenario can be identified through local intrinsic dimension (LID) estimation, and propose a method for OOD detection which pairs the likelihoods and LID estimates obtained from a pre-trained DGM. Our method can be applied to normalizing flows and score-based diffusion models, and obtains results which match or surpass state-of-the-art OOD detection benchmarks using the same DGM backbones. Our code is available at https://github.com/layer6ai-labs/dgm_ood_detection.
OCDaf: Ordered Causal Discovery with Autoregressive Flows
Aug 14, 2023We propose OCDaf, a novel order-based method for learning causal graphs from observational data. We establish the identifiability of causal graphs within multivariate heteroscedastic noise models, a generalization of additive noise models that allow for non-constant noise variances. Drawing upon the structural similarities between these models and affine autoregressive normalizing flows, we introduce a continuous search algorithm to find causal structures. Our experiments demonstrate state-of-the-art performance across the Sachs and SynTReN benchmarks in Structural Hamming Distance (SHD) and Structural Intervention Distance (SID). Furthermore, we validate our identifiability theory across various parametric and nonparametric synthetic datasets and showcase superior performance compared to existing baselines.