It is well known that the problems of stochastic planning and probabilistic inference are closely related. This paper makes two contributions in this context. The first is to provide an analysis of the recently developed SOGBOFA heuristic planning algorithm that was shown to be effective for problems with large factored state and action spaces. It is shown that SOGBOFA can be seen as a specialized inference algorithm that computes its solutions through a combination of a symbolic variant of belief propagation and gradient ascent. The second contribution is a new solver for Marginal MAP (MMAP) inference. We introduce a new reduction from MMAP to maximum expected utility problems which are suitable for the symbolic computation in SOGBOFA. This yields a novel algebraic gradient-based solver (AGS) for MMAP. An experimental evaluation illustrates the potential of AGS in solving difficult MMAP problems.

Neural Information Processing Systems http://nips.cc/

It is well known that the problems of stochastic planning and probabilistic inference are closely related. This paper makes two contributions in this context. The first is to provide an analysis of the recently developed SOGBOFA heuristic planning algorithm that was shown to be effective for problems with large factored state and action spaces. It is shown that SOGBOFA can be seen as a specialized inference algorithm that computes its solutions through a combination of a symbolic variant of belief propagation and gradient ascent. The second contribution is a new solver for Marginal MAP (MMAP) inference. We introduce a new reduction from MMAP to maximum expected utility problems which are suitable for the symbolic computation in SOGBOFA. This yields a novel algebraic gradient-based solver (AGS) for MMAP. An experimental evaluation illustrates the potential of AGS in solving difficult MMAP problems.

Main ideas The paper develops the relation between solving an MDP and performing inference in a Bayesian network. The direction, however, is novel as far as I can tell: using MDP algorithms to solve an inference problem. The first part shows that an existing MDP algorithm (ARollout) is in fact performing a BP iteration over the DBN that represents the MDP. In the second part, a different MDP algorithm (SOGBOFA) is used to solve a particular inference problem of choosing a subset of values with the maximal marginals (MMAP). The resulting SOGBOFA-based solver often loses to the state-of-the-art, but for harder cases it can outperform the state of the art.

Arising from many applications at the intersection of decision-making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) problems unify the two main classes of inference, namely maximization (optimization) and marginal inference (counting), and are believed to have higher complexity than both of them. We propose XOR_MMAP, a novel approach to solve the Marginal MAP problem, which represents the intractable counting subproblem with queries to NP oracles, subject to additional parity constraints. XOR_MMAP provides a constant factor approximation to the Marginal MAP problem, by encoding it as a single optimization in a polynomial size of the original problem. We evaluate our approach in several machine learning and decision-making applications, and show that our approach outperforms several state-of-the-art Marginal MAP solvers.

It is well known that the problems of stochastic planning and probabilistic inference are closely related. This paper makes several contributions in this context for factored spaces where the complexity of solutions is challenging. First, we analyze the recently developed SOGBOFA heuristic, which performs stochastic planning by building an explicit computation graph capturing an approximate aggregate simulation of the dynamics. It is shown that the values computed by this algorithm are identical to the approximation provided by Belief Propagation (BP). Second, as a consequence of this observation, we show how ideas on lifted BP can be used to develop a lifted version of SOGBOFA. Unlike implementations of lifted BP, Lifted SOGBOFA has a very simple implementation as a dynamic programming version of the original graph construction. Third, we show that the idea of graph construction for aggregate simulation can be used to solve marginal MAP (MMAP) problems in Bayesian networks, where MAP variables are constrained to be at roots of the network. This yields a novel algorithm for MMAP for this subclass. An experimental evaluation illustrates the advantage of Lifted SOGBOFA for planning.

Probabilistic circuits (PCs) are a class of tractable probabilistic models that allow efficient, often linear-time, inference of queries such as marginals and most probable explanations (MPE). However, marginal MAP, which is central to many decision-making problems, remains a hard query for PCs unless they satisfy highly restrictive structural constraints. In this paper, we develop a pruning algorithm that removes parts of the PC that are irrelevant to a marginal MAP query, shrinking the PC while maintaining the correct solution. This pruning technique is so effective that we are able to build a marginal MAP solver based solely on iteratively transforming the circuit -- no search is required. We empirically demonstrate the efficacy of our approach on real-world datasets.

It is well known that the problems of stochastic planning and probabilistic inference are closely related. This paper makes two contributions in this context. The first is to provide an analysis of the recently developed SOGBOFA heuristic planning algorithm that was shown to be effective for problems with large factored state and action spaces. It is shown that SOGBOFA can be seen as a specialized inference algorithm that computes its solutions through a combination of a symbolic variant of belief propagation and gradient ascent. The second contribution is a new solver for Marginal MAP (MMAP) inference.

We present a heuristic strategy for marginal MAP (MMAP) queries in graphical models. The algorithm is based on a reduction of the task to a polynomial number of marginal inference computations. Given an input evidence, the marginals mass functions of the variables to be explained are computed. Marginal information gain is used to decide the variables to be explained first, and their most probable marginal states are consequently moved to the evidence. The sequential iteration of this procedure leads to a MMAP explanation and the minimum information gain obtained during the process can be regarded as a confidence measure for the explanation. Preliminary experiments show that the proposed confidence measure is properly detecting instances for which the algorithm is accurate and, for sufficiently high confidence levels, the algorithm gives the exact solution or an approximation whose Hamming distance from the exact one is small.

Lifted inference reduces the complexity of inference in relational probabilistic models by identifying groups of constants (or atoms) which behave symmetric to each other. A number of techniques have been proposed in the literature for lifting marginal as well MAP inference. We present the first application of lifting rules for marginal-MAP (MMAP), an important inference problem in models having latent (random) variables. Our main contribution is two fold: (1) we define a new equivalence class of (logical) variables, called Single Occurrence for MAX (SOM), and show that solution lies at extreme with respect to the SOM variables, i.e., predicate groundings differing only in the instantiation of the SOM variables take the same truth value (2) we define a sub-class {\em SOM-R} (SOM Reduce) and exploit properties of extreme assignments to show that MMAP inference can be performed by reducing the domain of SOM-R variables to a single constant.We refer to our lifting technique as the {\em SOM-R} rule for lifted MMAP. Combined with existing rules such as decomposer and binomial, this results in a powerful framework for lifted MMAP. Experiments on three benchmark domains show significant gains in both time and memory compared to ground inference as well as lifted approaches not using SOM-R.