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

Ruas e a ocupação vertical recente: labirintos murados

Resumo No Brasil, o processo de verticalização nas cidades é cada vez mais intenso e, por conseguinte, verifica-se um grande número de lançamentos imobiliários em torres altas. A partir do exame das implantações de edifícios residenciais recentes, pontua-se a relação insuficiente entre esses espaços privados com as ruas nas quais estão inseridos. Essas construções ocupam grandes lotes, possuem fechamentos extensos e não evidenciam nenhum cuidado quanto à sua colocação no espaço urbano. Este estudo pretende abordar a qualidade da rua em uma conjuntura de ocupação vertical contemporânea. O estudo de caso abrange uma rua no bairro Gleba Palhano, em Londrina, PR, que apresenta uma concentração de edifícios verticais e em processo de consolidação. A fundamentação teórica possibilitou a extração de atributos analíticos dos espaços públicos e o exame do estudo de caso. O resultado obtido aponta prejuízos desse contexto no cotidiano dos cidadãos, uma vez que o espaço público não é utilizado como lugar de interação e troca social. O artigo conclui afirmando ser indispensável a retificação dessa forma de produção, objetivando a concepção de ambientes de maior qualidade

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

Algorithms for Hidden Markov Models With Imprecisely Specified Parameters

\u3cp\u3eHidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, which can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we formalize iHMMs and develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that iHMMs produce more reliable inferences without compromising efficiency.\u3c/p\u3

Probabilistic Inference in Credal Networks: New Complexity Results

Credal networks are graph-based statistical models whose param-eters take values in a set, instead of being sharply specified as in tra-ditional statistical models (e.g., Bayesian networks). The computa-tional complexity of inferences on such models depends on the irrele-vance/independence concept adopted. In this paper, we study inferen-tial complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where in-ferences are most likely hard, and settle several open questions regard-ing their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove an analogous result for inference in Naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and Naive Bayes networks are used in real applications of imprecise probability.

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.