Sliced Wasserstein Distance for Learning Gaussian Mixture Models

Soheil Kolouri; Gustavo K. Rohde; Heiko Hoffmann

Home/Archive/arXiv

arXiv · 1711.05376

Sliced Wasserstein Distance for Learning Gaussian Mixture Models

Soheil Kolouri·Gustavo K. Rohde·Heiko Hoffmann

View original source ↗Read source document ↗Export metadata ↓

Abstract

Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM guarantees only convergence to a stationary point of the log-likelihood function, which could be arbitrarily worse than the optimal solution. Inspired by the relationship between the negative log-likelihood function and the Kullback-Leibler (KL) divergence, we propose an alternative formulation for estimating the GMM parameters using the sliced Wasserstein distance, which gives rise to a new algorithm. Specifically, we propose minimizing the sliced-Wasserstein distance between the mixture model and the data distribution with respect to the GMM parameters. In contrast to the KL-divergence, the energy landscape for the sliced-Wasserstein distance is more well-behaved and therefore more suitable for a stochastic gradient descent scheme to obtain the optimal GMM parameters. We show that our formulation results in parameter estimates that are more robust to random initializations and demonstrate that it can estimate high-dimensional data distributions more faithfully than the EM algorithm.

Explore related subjects

cs.CV cs.LG stat.ML

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Soheil Kolouri, Gustavo K. Rohde, Heiko Hoffmann. 2017-11-16. Sliced Wasserstein Distance for Learning Gaussian Mixture Models. https://arxiv.org/abs/1711.05376

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

KEEP EXPLORING

Related papers

arXiv2026

SSP-GNN: Learning to Track via Bilevel Optimization

We propose a graph-based tracking formulation for multi-object tracking (MOT) where target detections contain kinematic information and re-identification features (attributes). Our method applies a successive shortest paths (SSP) algorithm to a tracking graph defined over a batch of frames. The edge costs in this tracking graph are computed via a message-passing network, a graph neural network (GNN) variant. The parameters of the GNN, and hence, the tracker, are learned end-to-end on a training set of example ground-truth tracks and detections. Specifically, learning takes the form of bilevel optimization guided by our novel loss function. We evaluate our algorithm on simulated scenarios to understand its sensitivity to scenario aspects and model hyperparameters. Across varied scenario complexities, our method compares favorably to a strong baseline.

cs.CV↗

arXiv2026

AdaptiveCDM: Source-Free Few-Shot Domain Adaptation for Cell Detection in Microscopic Images

Cross-domain cell detection for microscopic images suffers from performance degradation due to distribution shifts across imaging domains. Unsupervised Domain Adaptation (UDA) strategies, attempt to overcome domain sift without requiring annotated data from target. However, requirement of availability of annotated data from the source domain and large-size data from target domain are both challenging limitations for realistic scenarios. This is especially true in medical imaging, where privacy requirements might prevent access to annotated source data, and costly data acquisition restricts extensive sampling of the target domain. To address these challenges, we propose AdaptiveCDM, a modular framework for Source-Free Few-Shot Domain Adaptive Object Detection (SF-FSDAOD) setting, that adapts a pretrained source model using only few labeled target images without accessing source data. AdaptiveCDM combines Resolution-Aware Augmentation (RAug) and Category-Aware Representation Learning (CARL). RAug alleviates the scarcity and class imbalance by augmenting instance balanced training examples, while preserving the scale fidelity and morphological properties of cellular structures. CARL enhances discriminative representation learning by encouraging class-consistent proposals, improving both localization and classification. We also introduce two competitive baselines for proposed setting: Faster-FreeShot and MT-FreeShot. Our approach achieves 40.4/43.4 mAP0.5 on M5 and 67.1/75.5 mAP0.5 on Raabin-WBC under 2-/5-shot adaptation. Despite using only a few labeled target images and no source data, AdaptiveCDM achieves competitive or superior performance compared with SOTA methods under their respective supervision settings. Ablations and qualitative analyses further substantiate the contribution of each component and the effectiveness of AdaptiveCDM in low-data regimes. Code/models will be available.

cs.CV↗

arXiv2026

Uncertainty-Weighted Fusion of Image and Synthetic Event for Video Anomaly Detection

Most existing video anomaly detectors rely on RGB frames alone, which limit their ability to capture abrupt or transient motion cues that are critical for identifying anomalous events. We propose Uncertainty Weighted Image Event Fusion (IEF-VAD), a framework that integrates complementary RGB and synthetic motion information through a principled weighting mechanism. The method models the high variance and heavy tailed characteristics of synthetic motion cues with a Student's t likelihood, computes value level inverse variance weights using a Laplace approximation to prevent the image modality from overshadowing motion information, and performs iterative refinement to suppress residual cross modal noise. This formulation provides a more balanced and reliable fusion process compared to cross attention or gating based approaches that often suffer from modality dominance. Without requiring an event camera or frame level annotations, IEF-VAD achieves new state of the art performance on multiple real world anomaly detection benchmarks and remains stable under degradation applied to individual modalities. The results indicate that extracting and integrating complementary motion cues is an effective direction for robust video understanding across diverse environments.

cs.CV↗