Generative models provide a powerful framework for probabilistic reasoning. However, in many domains their use has been hampered by the practical difficulties of inference. This is particularly the case in computer vision, where models of the imaging process tend to be large, loopy and layered. For this reason bottom-up conditional models have traditionally dominated in such domains. We find that widely-used, general-purpose message passing inference algorithms such as Expectation Propagation (EP) and Variational Message Passing (VMP) fail on the simplest of vision models. With these models in mind, we introduce a modification to message passing that learns to exploit their layered structure by passing 'consensus' messages that guide inference towards good solutions. Experiments on a variety of problems show that the proposed technique leads to significantly more accurate inference results, not only when compared to standard EP and VMP, but also when compared to competitive bottom-up conditional models.

We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized linear models with nonconvex regularization and sparse elliptical random design regression. For these problems, it is intractable to calculate the global solution due to the nonconvex formulation. In this paper, we propose an approximate regularization path-following method for solving a variety of learning problems with nonconvex objective functions. Under a unified analytic framework, we simultaneously provide explicit statistical and computational rates of convergence for any local solution attained by the algorithm. Computationally, our algorithm attains a global geometric rate of convergence for calculating the full regularization path, which is optimal among all first-order algorithms. Unlike most existing methods that only attain geometric rates of convergence for one single regularization parameter, our algorithm calculates the full regularization path with the same iteration complexity. In particular, we provide a refined iteration complexity bound to sharply characterize the performance of each stage along the regularization path. Statistically, we provide sharp sample complexity analysis for all the approximate local solutions along the regularization path. In particular, our analysis improves upon existing results by providing a more refined sample complexity bound as well as an exact support recovery result for the final estimator. These results show that the final estimator attains an oracle statistical property due to the usage of nonconvex penalty.

Essentially, a connection graph is merely a data structure for a set of clauses indicating possible system. To use the graph, one has to introduce operations on the graph.

Specifically, it is concerned with control strategies governing the formation and refinement of partial hypotheses about the identity of an utterance that can guarantee the discovery of the best possible interpretation. We assume a system that contains the following components: a) A Lexical Retrieval component that can find the k best matching words in any region of an utterance subject to certain constraints and can be recalled to continue enumerating word matches in decreasing order of goodness (where possible constraints include anchoring the left or right end of the word to particular points in the utterance or to particular adjacent word matches).

In AI we talk about expert systems.

The strategy has been implemented in a simple QLISP program.

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This is the second of two papers about MOLGEN.

Instead they have commonly assigned structure to a domain using statistical techniques such as Bayes' Theorem

The first section discusses the importance of having systems that own M.S. thesis (Moore, 19)5), suggests that predicate calculus can understand the concept of knowledge, and how knowledge is be treated in a more natural manner than resolution and related to action. Section 2 points out some of the special problems combined with domain-dependent control information for greater that are involved in reasoning about knowledge, and section $ efficiency. Furthermore, the problems of reasoning about knowledge seem to require the full ability to handle quantifiers presents a logic of knowledge based on the idea of possible worlds. Section 4 integrates this with a logic of actions and gives an and logical connectives which only predicate calculus posseses.