Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both theoretical and algorithmic perspectives. For the theoretical part, we reduce general MAP inference to its special case without evidence and hidden variables; we also show that it is NP-hard to approximate the MAP problem to 2 nε for fixed 0 ≤ ε < 1, where n is the input size. For the algorithmic part, we first present an exact MAP solver that runs reasonably fast and could handle SPNs with up to 1k variables and 150k arcs in our experiments. We then present a new approximate MAP solver with a good balance between speed and accuracy, and our comprehensive experiments on real-world datasets show that it has better overall performance than existing approximate solvers.

Modern object detection methods typically rely on bounding box proposals as input. While initially popularized in the 2D case, this idea has received increasing attention for 3D bounding boxes. Nevertheless, existing 3D box proposal techniques all assume having access to depth as input, which is unfortunately not always available in practice. In this paper, we therefore introduce an approach to generating 3D box proposals from a single monocular RGB image. To this end, we develop an integrated, fully differentiable framework that inherently predicts a depth map, extracts a 3D volumetric scene representation and generates 3D object proposals. At the core of our approach lies a novel residual, differentiable truncated signed distance function module, which, accounting for the relatively low accuracy of the predicted depth map, extracts a 3D volumetric representation of the scene. Our experiments on the standard NYUv2 dataset demonstrate that our framework lets us generate high-quality 3D box proposals and that it outperforms the two-stage technique consisting of successively performing state-of-the-art depth prediction and depth-based 3D proposal generation.

Probabilistic modeling is one of the foundations of modern Learning the structure of a probabilistic model resembles machine learning and artificial intelligence, which aims to learning the set of production rules of a grammar, while compactly represent the joint probability distribution of random learning model parameters resembles learning grammar rule variables. The most widely used approach for probabilistic probabilities. From the unsupervised grammar learning literature, modeling is probabilistic graphical models. A probabilistic one can see that learning approaches based on PCFGs graphical model represents a probability distribution with a have not been very successful, while the state-of-the-art performance directed or undirected graph. It represents random variables has mostly been achieved based on less expressive with the nodes in the graph and uses the edges in the graph to models such as dependency grammars (DGs) (Klein and encode the probabilistic relationships between random variables.

This paper studies an auction design problem for a seller to sell a commodity in a social network, where each individual (the seller or a buyer) can only communicate with her neighbors. The challenge to the seller is to design a mechanism to incentivize the buyers, who are aware of the auction, to further propagate the information to their neighbors so that more buyers will participate in the auction and hence, the seller will be able to make a higher revenue. We propose a novel auction mechanism, called information diffusion mechanism (IDM), which incentivizes the buyers to not only truthfully report their valuations on the commodity to the seller, but also further propagate the auction information to all their neighbors. In comparison, the direct extension of the well-known Vickrey-Clarke-Groves (VCG) mechanism in social networks can also incentivize the information diffusion, but it will decrease the seller's revenue or even lead to a deficit sometimes. The formalization of the problem has not yet been addressed in the literature of mechanism design and our solution is very significant in the presence of large-scale online social networks.

In this paper, we study a cold-start heterogeneous-devicelocalization problem. This problem is challenging, becauseit results in an extreme inductive transfer learning setting,where there is only source domain data but no target do-main data. This problem is also underexplored. As there is notarget domain data for calibration, we aim to learn a robustfeature representation only from the source domain. There islittle previous work on such a robust feature learning task; besides, the existing robust feature representation propos-als are both heuristic and inexpressive. As our contribution,we for the first time provide a principled and expressive robust feature representation to solve the challenging cold-startheterogeneous-device localization problem. We evaluate ourmodel on two public real-world data sets, and show that itsignificantly outperforms the best baseline by 23.1%–91.3%across four pairs of heterogeneous devices.

In this paper, we study the low-rank tensor completion problem, where a high-order tensor with missing entries is given and the goal is to complete the tensor. We propose to minimize a new convex objective function, based on log sum of exponentials of nuclear norms, that promotes the low-rankness of unfolding matrices of the completed tensor. We show for the first time that the proximal operator to this objective function is readily computable through a hybrid singular value thresholding scheme. This leads to a new solution to high-order (low-rank) tensor completion via convex relaxation. We show that this convex relaxation and the resulting solution are much more effective than existing tensor completion methods (including those also based on minimizing ranks of unfolding matrices). The hybrid singular value thresholding scheme can be applied to any problem where the goal is to minimize the maximum rank of a set of low-rank matrices.