Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks

We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability within a sublinear factor. We show that this is a tight bound, as we can find an approximation within a linear factor in networks of height two. We then show that, in trees of height three, it is NP-hard to approximate the problem within a factor $2^{f(n)}$ for any sublinear function $f$ of the size of the input $n$. Again, this bound is tight, as we prove that the usual max-product algorithm finds (in any network) approximations within factor $2^{c \cdot n}$ for some constant $c < 1$. Last, we present a simple algorithm, and show that it provably produces solutions at least as good as, and potentially much better than, the max-product algorithm. We empirically analyze the proposed algorithm against max-product using synthetic and realistic networks.Comment: 18 page

The BLue Amazon Brain (BLAB): A Modular Architecture of Services about the Brazilian Maritime Territory

We describe the first steps in the development of an artificial agent focused on the Brazilian maritime territory, a large region within the South Atlantic also known as the Blue Amazon. The "BLue Amazon Brain" (BLAB) integrates a number of services aimed at disseminating information about this region and its importance, functioning as a tool for environmental awareness. The main service provided by BLAB is a conversational facility that deals with complex questions about the Blue Amazon, called BLAB-Chat; its central component is a controller that manages several task-oriented natural language processing modules (e.g., question answering and summarizer systems). These modules have access to an internal data lake as well as to third-party databases. A news reporter (BLAB-Reporter) and a purposely-developed wiki (BLAB-Wiki) are also part of the BLAB service architecture. In this paper, we describe our current version of BLAB's architecture (interface, backend, web services, NLP modules, and resources) and comment on the challenges we have faced so far, such as the lack of training data and the scattered state of domain information. Solving these issues presents a considerable challenge in the development of artificial intelligence for technical domains

Solving Decision Problems with Limited Information

We present a new algorithm for exactly solving decision-making problems represented as an influence diagram. We do not require the usual assumptions of no forgetting and regularity, which allows us to solve problems with limited information. The algorithm, which implements a sophisticated variable elimination procedure, is empirically shown to outperform a state-of-the-art algorithm in randomly generated problems of up to 150 variables and 10 64 strategies.

A Fully Polynomial Time Approximation Scheme for Updating Credal Networks of Bounded Treewidth and Number of Variable States

Credal networks lift the precise probability assumption of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper we present a new algorithm which is an extension of the wellknown variable elimination algorithm for computing posterior inferences in extensively specified credal networks. The algorithm efficiency is empirically shown to outperform a state-of-the-art algorithm. We then provide the first fully polynomial time approximation scheme for inference in credal networks with bounded treewidth and number of states per variable

On the Complexity of Strong and Epistemic Credal Networks

Credal networks are graph-based statistical models whose parameters take values on a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The result of inferences with such models depends on the irrelevance/independence concept adopted. In this paper, we study the computational complexity of inferences under the concepts of epistemic irrelevance and strong independence. We strengthen complexity results by showing that inferences with strong independence are NP-hard even in credal trees with ternary variables, which indicates that tractable algorithms, including the existing one for epistemic trees, cannot be used for strong independence. We prove that the polynomial time of inferences in credal trees under epistemic irrelevance is not likely to extend to more general models, because the problem becomes NP-hard even in simple polytrees. These results draw a definite line between networks with efficient inferences and those where inferences are hard, and close several open questions regarding the computational complexity of such models.

The Complexity of Approximately Solving Influence Diagrams

Influence diagrams allow for intuitive and yet precise description of complex situations involving decision making under uncertainty. Unfortunately, most of the problems described by influence diagrams are hard to solve. In this paper we discuss the complexity of approximately solving influence diagrams. We do not assume no-forgetting or regularity, which makes the class of problems we address very broad. Remarkably, we show that when both the treewidth and the cardinality of the variables are bounded the problem admits a fully polynomial-time approximation scheme.

Updating Credal Networks is Approximable in Polynomial Time

Credal networks relax the precise probability requirement of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper, we present a new variable elimination algorithm for exactly computing posterior inferences in extensively specified credal networks, which is empirically shown to outperform a state-of-the-art algorithm. The algorithm is then turned into a provably good approximation scheme, that is, a procedure that for any input is guaranteed to return a solution not worse than the optimum by a given factor. Remarkably, we show that when the networks have bounded treewidth and bounded number of states per variable the approximation algorithm runs in time polynomial in the input size and in the inverse of the error factor, thus being the first known fully polynomial-time approximation scheme for inference in credal networks