Score-Based Variational Inference for Inverse Problems

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple samples from the posterior which is time-consuming. In this work, by analyzing the probability density evolution of the conditional reverse diffusion process, we prove that the posterior mean can be achieved by tracking the mean of each reverse diffusion step. Based on that, we establish a framework termed reverse mean propagation (RMP) that targets the posterior mean directly. We show that RMP can be implemented by solving a variational inference problem, which can be further decomposed as minimizing a reverse KL divergence at each reverse step. We further develop an algorithm that optimizes the reverse KL divergence with natural gradient descent using score functions and propagates the mean at each reverse step. Experiments demonstrate the validity of the theory of our framework and show that our algorithm outperforms state-of-the-art algorithms on reconstruction performance with lower computational complexity in various inverse problems.

CogNet: Bridging Linguistic Knowledge, World Knowledge and Commonsense Knowledge

In this paper, we present CogNet, a knowledge base (KB) dedicated to integrating three types of knowledge: (1) linguistic knowledge from FrameNet, which schematically describes situations, objects and events. (2) world knowledge from YAGO, Freebase, DBpedia and Wikidata, which provides explicit knowledge about specific instances. (3) commonsense knowledge from ConceptNet, which describes implicit general facts. To model these different types of knowledge consistently, we introduce a three-level unified frame-styled representation architecture. To integrate free-form commonsense knowledge with other structured knowledge, we propose a strategy that combines automated labeling and crowdsourced annotation. At present, CogNet integrates 1,000+ semantic frames from linguistic KBs, 20,000,000+ frame instances from world KBs, as well as 90,000+ commonsense assertions from commonsense KBs. All these data can be easily queried and explored on our online platform, and free to download in RDF format for utilization under a CC-BY-SA 4.0 license. The demo and data are available at http://cognet.top/.

Denoising-based Turbo Message Passing for Compressed Video Background Subtraction

In this paper, we consider the compressed video background subtraction problem that separates the background and foreground of a video from its compressed measurements. The background of a video usually lies in a low dimensional space and the foreground is usually sparse. More importantly, each video frame is a natural image that has textural patterns. By exploiting these properties, we develop a message passing algorithm termed offline denoising-based turbo message passing (DTMP). We show that these structural properties can be efficiently handled by the existing denoising techniques under the turbo message passing framework. We further extend the DTMP algorithm to the online scenario where the video data is collected in an online manner. The extension is based on the similarity/continuity between adjacent video frames. We adopt the optical flow method to refine the estimation of the foreground. We also adopt the sliding window based background estimation to reduce complexity. By exploiting the Gaussianity of messages, we develop the state evolution to characterize the per-iteration performance of offline and online DTMP. Comparing to the existing algorithms, DTMP can work at much lower compression rates, and can subtract the background successfully with a lower mean squared error and better visual quality for both offline and online compressed video background subtraction.