Denis Deratani Mauá

Renato Lui Geh, Jonas Gonçalves, Igor Cataneo Silveira et al.

We present dPASP, a novel declarative probabilistic logic programming framework for differentiable neuro-symbolic reasoning. The framework allows for the specification of discrete probabilistic models with neural predicates, logic constraints and interval-valued probabilistic choices, thus supporting models that combine low-level perception (images, texts, etc), common-sense reasoning, and (vague) statistical knowledge. To support all such features, we discuss the several semantics for probabilistic logic programs that can express nondeterministic, contradictory, incomplete and/or statistical knowledge. We also discuss how gradient-based learning can be performed with neural predicates and probabilistic choices under selected semantics. We then describe an implemented package that supports inference and learning in the language, along with several example programs. The package requires minimal user knowledge of deep learning system's inner workings, while allowing end-to-end training of rather sophisticated models and loss functions.

Paulo Pirozelli, Ais B. R. Castro, Ana Luiza C. de Oliveira et al.

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.

Eduardo Rocha Laurentino, Fabio Gagliardi Cozman, Denis Deratani Maua et al.

Probabilities of causation provide principled ways to assess causal relationships but face computational challenges due to partial identifiability and latent confounding. This paper introduces both algorithmic simplifications, significantly reducing the computational complexity of calculating tighter bounds for these probabilities, and a novel methodological framework for Root Cause Analysis that systematically employs these causal metrics to rank entire causal paths.

Victor Hugo Nascimento Rocha, Igor Cataneo Silveira, Paulo Pirozelli et al.

The recent success of Large Language Models (LLMs) has sparked concerns about their potential to spread misinformation. As a result, there is a pressing need for tools to identify ``fake arguments'' generated by such models. To create these tools, examples of texts generated by LLMs are needed. This paper introduces a methodology to obtain good, bad and ugly arguments from argumentative essays produced by ChatGPT, OpenAI's LLM. We then describe a novel dataset containing a set of diverse arguments, ArGPT. We assess the effectiveness of our dataset and establish baselines for several argumentation-related tasks. Finally, we show that the artificially generated data relates well to human argumentation and thus is useful as a tool to train and test systems for the defined tasks.

Marcos Menon José, Marcelo Archanjo José, Denis Deratani Mauá et al.

Deep learning transformers have drastically improved systems that automatically answer questions in natural language. However, different questions demand different answering techniques; here we propose, build and validate an architecture that integrates different modules to answer two distinct kinds of queries. Our architecture takes a free-form natural language text and classifies it to send it either to a Neural Question Answering Reasoner or a Natural Language parser to SQL. We implemented a complete system for the Portuguese language, using some of the main tools available for the language and translating training and testing datasets. Experiments show that our system selects the appropriate answering method with high accuracy (over 99\%), thus validating a modular question answering strategy.

Lilith Mattei, Alessandro Antonucci, Denis Deratani Mauá et al.

Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of Boolean variables, that are also consistent with the logical constraints defined by the circuit. The probabilities in such a model are usually learned from a set of observations. This leads to overconfident and prior-dependent inferences when data are scarce, unreliable or conflicting. In this work, we develop the credal sentential decision diagrams, a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with (so-called credal) sets of mass functions. These models induce a joint credal set over the set of Boolean variables, that sharply assigns probability zero to states inconsistent with the logical constraints. Three inference algorithms are derived for these models, these allow to compute: (i) the lower and upper probabilities of an observation for an arbitrary number of variables; (ii) the lower and upper conditional probabilities for the state of a single variable given an observation; (iii) whether or not all the probabilistic sentential decision diagrams compatible with the credal specification have the same most probable explanation of a given set of variables given an observation of the other variables. These inferences are tractable, as all the three algorithms, based on bottom-up traversal with local linear programming tasks on the disjunctive gates, can be solved in polynomial time with respect to the circuit size. For a first empirical validation, we consider a simple application based on noisy seven-segment display images. The credal models are observed to properly distinguish between easy and hard-to-detect instances and outperform other generative models not able to cope with logical constraints.

Francisco H. O. V. de Faria, Arthur C. Gusmão, Fabio G. Cozman et al.

ProbLog is a state-of-art combination of logic programming and probabilities; in particular ProbLog offers parameter learning through a variant of the EM algorithm. However, the resulting learning algorithm is rather slow, even when the data are complete. In this short paper we offer some insights that lead to orders of magnitude improvements in ProbLog's parameter learning speed with complete data.

Diarmaid Conaty, Denis D. Mauá, Cassio P. de Campos

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.

Fabio Gagliardi Cozman, Denis Deratani Mauá

We examine the meaning and the complexity of probabilistic logic programs that consist of a set of rules and a set of independent probabilistic facts (that is, programs based on Sato's distribution semantics). We focus on two semantics, respectively based on stable and on well-founded models. We show that the semantics based on stable models (referred to as the "credal semantics") produces sets of probability models that dominate infinitely monotone Choquet capacities, we describe several useful consequences of this result. We then examine the complexity of inference with probabilistic logic programs. We distinguish between the complexity of inference when a probabilistic program and a query are given (the inferential complexity), and the complexity of inference when the probabilistic program is fixed and the query is given (the query complexity, akin to data complexity as used in database theory). We obtain results on the inferential and query complexity for acyclic, stratified, and cyclic propositional and relational programs, complexity reaches various levels of the counting hierarchy and even exponential levels.

Fabio Gagliardi Cozman, Denis Deratani Mauá

We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover a variety of plate models and of probabilistic relational models. We study the complexity of inferences when network, query and domain are the input (the inferential and the combined complexity), when the network is fixed and query and domain are the input (the query/data complexity), and when the network and query are fixed and the domain is the input (the domain complexity). We draw connections with probabilistic databases and liftability results, and obtain complexity classes that range from polynomial to exponential levels.

Siqi Nie, Denis Deratani Maua, Cassio Polpo de Campos et al.

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.

Denis D. Maua, Cassio Polpo de Campos, Alessio Benavoli et al.

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with ternary variables. 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 networks). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding computational complexity.

Denis D. Maua, Cassio Polpo de Campos, Marco Zaffalon

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 tree-width and the cardinality of the variables are bounded the problem admits a fully polynomial-time approximation scheme.

Denis Maua, Cassio De Campos

This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the problem are discussed. It is shown that the algorithm runs in polynomial-time if the underlying graph of the model has bounded tree-width, and that it provides guarantees to the lower and upper bounds obtained within a fixed amount of computational resources. Experiments with both real and synthetic generated models highlight its main characteristics and show that it compares favorably against Park and Darwiche's systematic search, particularly in the case of problems with many MAP variables and moderate tree-width.