Related papers: Encoding Markov Logic Networks in Possibilistic Lo…

Knowledge graph (KG) reasoning is a task that aims to predict unknown facts based on known factual samples. Reasoning methods can be divided into two categories: rule-based methods and KG-embedding based methods. The former possesses…

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…

Reasoning under uncertainty is a key challenge in AI, especially for real-world tasks, where problems with sparse data demands systematic generalisation. Existing approaches struggle to balance accuracy and simplicity when evaluating…

Real-data networks often appear to have strong modularity, or network-of-networks structure, in which subgraphs of various size and consistency occur. Finding the respective subgraph structure is of great importance, in particular for…

Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood…

The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…

The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with…

Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not…

In many spatial and spatial-temporal models, and more generally in models with complex dependencies, it may be too difficult to carry out full maximum likelihood (ML) analysis. Remedies include the use of pseudo-likelihood (PL) and…

The lack of interpretability has hindered the large-scale adoption of AI technologies. However, the fundamental idea of interpretability, as well as how to put it into practice, remains unclear. We provide notions of interpretability based…

The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…

In this paper a new proof is given for the supermodularity of information content. Using the decomposability of the information content an algorithm is given for discovering the Markov network graph structure endowed by the pairwise Markov…

In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…

A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge.…

The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…

Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…

Probabilistic logic reasoning is a central component of such cognitive architectures as OpenCog. However, as an integrative architecture, OpenCog facilitates cognitive synergy via hybridization of different inference methods. In this paper,…

In this paper, we are interested in optimal decisions in a partially observable Markov universe. Our viewpoint departs from the dynamic programming viewpoint: we are directly approximating an optimal strategic tree depending on the…

In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…

The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…