The general idea of this work is clearly in a direction of interest to the community and the results look strong. However, there are a few aspects to this work that I find quite unclear. If they were clearer this work would have much more potential for impact. In particular, it is not clear enough if this work uses a truly'end-to-end' approach (as stated for one of the contributions). For example on line 46 it is stated that: "We show step by step how approximations are made to use an end-to-end learning CNN for implementing such CRF model."

Two players, Black and White, take turns to place stones on the intersections of an N N grid (usually N 19 but smaller boards are in use as well). All the stones of each player are identical. Players place their stones in order to create territory by occupying or surrounding areas of the board. The player with the most territory at the end of the game is the winner. A stone is captured if it has been completely surrounded (in the horizontal and vertical directions) by stones of the opponent's colour.

Region-based free energy was originally proposed for generalized belief propagation (GBP) to improve loopy belief propagation (loopy BP). In this paper, we propose a neural network based energy model for inference in general Markov random fields (MRFs), which directly minimizes the region-based free energy defined on region graphs. We term our model Region-based Energy Neural Network (RENN). Unlike message-passing algorithms, RENN avoids iterative message propagation and is faster. Also different from recent deep neural network based models, inference by RENN does not require sampling, and RENN works on general MRFs. RENN can also be employed for MRF learning. Our experiments on marginal distribution estimation, partition function estimation, and learning of MRFs show that RENN outperforms the mean field method, loopy BP, GBP, and the state-of-the-art neural network based model.

For many structured prediction problems, complex models often require adopting approximate inference techniques such as variational methods or sampling, which generally provide no satisfactory accuracy guarantees. In this work, we propose sidestepping intractable inference altogether by learning ensembles of tractable sub-models as part of a structured prediction cascade. We focus in particular on problems with high-treewidth and large state-spaces, which occur in many computer vision tasks. Unlike other variational methods, our ensembles do not enforce agreement between sub-models, but filter the space of possible outputs by simply adding and thresholding the max-marginals of each constituent model. Our framework jointly estimates parameters for all models in the ensemble for each level of the cascade by minimizing a novel, convex loss function, yet requires only a linear increase in computation over learning or inference in a single tractable sub-model. We provide a generalization bound on the filtering loss of the ensemble as a theoretical justification of our approach, and we evaluate our method on both synthetic data and the task of estimating articulated human pose from challenging videos. We find that our approach significantly outperforms loopy belief propagation on the synthetic data and a state-of-the-art model on the pose estimation/tracking problem.

Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models.

Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether from quantization or other simplified message representations or from stochastic approximation methods. Introducing such errors into the BP message computations has the potential to adversely affect the solution obtained. We analyze this effect with respect to a particular measure of message error, and show bounds on the accumulation of errors in the system. This leads both to convergence conditions and error bounds in traditional and approximate BP message passing.

Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether from quantization or other simplified message representations or from stochastic approximation methods. Introducing such errors into the BP message computations has the potential to adversely affect the solution obtained. We analyze this effect with respect to a particular measure of message error, and show bounds on the accumulation of errors in the system. This leads both to convergence conditions and error bounds in traditional and approximate BP message passing.

Go is an ancient oriental game whose complexity has defeated attempts to automate it. We suggest using probability in a Bayesian sense to model the uncertainty arising from the vast complexity of the game tree. We present a simple conditional Markov random field model for predicting the pointwise territory outcome of a game. The topology of the model reflects the spatial structure of the Go board. We describe a version of the Swendsen-Wang process for sampling from the model during learning and apply loopy belief propagation for rapid inference and prediction. The model is trained on several hundred records of professional games. Our experimental results indicate that the model successfully learns to predict territory despite its simplicity.

Go is an ancient oriental game whose complexity has defeated attempts to automate it. We suggest using probability in a Bayesian sense to model the uncertainty arising from the vast complexity of the game tree. We present a simple conditional Markov random field model for predicting the pointwise territory outcome of a game. The topology of the model reflects the spatial structure of the Go board. We describe a version of the Swendsen-Wang process for sampling from the model during learning and apply loopy belief propagation for rapid inference and prediction. The model is trained on several hundred records of professional games. Our experimental results indicate that the model successfully learns to predict territory despite its simplicity.

The game of G0 originated in China over 4000 years ago.