Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a widespread effect on many of the observed ones is particularly difficult because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this paper we show that beyond conditional independencies, under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph among observed variables may be recovered approximately and propose an adjusted score-based causal discovery algorithm that may be implemented with general purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions.

Trained AI systems and expert decision makers can make errors that are often difficult to identify and understand. Determining the root cause for these errors can improve future decisions. This work presents Generative Error Model (GEM), a generative model for inferring representational errors based on observations of an actor's behavior (either simulated agent, robot, or human). The model considers two sources of error: those that occur due to representational limitations -- "blind spots" -- and non-representational errors, such as those caused by noise in execution or systematic errors present in the actor's policy. Disambiguating these two error types allows for targeted refinement of the actor's policy (i.e., representational errors require perceptual augmentation, while other errors can be reduced through methods such as improved training or attention support). We present a Bayesian inference algorithm for GEM and evaluate its utility in recovering representational errors on multiple domains. Results show that our approach can recover blind spots of both reinforcement learning agents as well as human users.

Recently it was introduced a negation of a probability distribution. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example, HIGH PROFIT or HIGH PRICE can be considered. The application of this negation in Dempster-Shafer theory was considered in many works. Although several negations of probability distributions have been proposed, it was not clear how to construct other negation. In this paper, we consider negations of probability distributions as point-by-point transformations of pd using decreasing functions defined on [0,1] called negators. We propose the general method of generation of negators and corresponding negations of pd, and study their properties. We give a characterization of linear negators as a convex combination of Yager's and uniform negators. Keywords: Probability distribution, Negation, Dempster-Shafer theory 1. Introduction The concept of negation of probability distribution (pd) was recently introduced by Yager [18].

Network inference is the process of learning the properties of complex networks from data. Besides using information about known links in the network, node attributes and other forms of network metadata can help to solve network inference problems. Indeed, several approaches have been proposed to introduce metadata into probabilistic network models and to use them to make better inferences. However, we know little about the effect of such metadata in the inference process. Here, we investigate this issue. We find that, rather than affecting inference gradually, adding metadata causes abrupt transitions in the inference process and in our ability to make accurate predictions, from a situation in which metadata does not play any role to a situation in which metadata completely dominates the inference process. When network data and metadata are partly correlated, metadata optimally contributes to the inference process at the transition between data-dominated and metadata-dominated regimes.

The article provides a review of the publications on the current trends and developments in Dempster-Shafer theory and its different applications in science, engineering, and technologies. The review took account of the following provisions with a focus on some specific aspects of the theory. Firstly, the article considers the research directions whose results are known not only in scientific and academic community but understood by a wide circle of potential designers and developers of advanced engineering solutions and technologies. Secondly, the article shows the theory applications in some important areas of human activity such as manufacturing systems, diagnostics of technological processes, materials and products, building and construction, product quality control, economic and social systems. The particular attention is paid to the current state of research in the domains under consideration and, thus, the papers published, as a rule, in recent years and presenting the achievements of modern research on Dempster-Shafer theory and its application are selected and analyzed.

We study the problem of diffeomorphometric geodesic landmark matching where the objective is to find a diffeomorphism that via its group action maps between two sets of landmarks. It is well-known that the motion of the landmarks, and thereby the diffeomorphism, can be encoded by an initial momentum leading to a formulation where the landmark matching problem can be solved as an optimisation problem over such momenta. The novelty of our work lies in the application of a derivative-free Bayesian inverse method for learning the optimal momentum encoding the diffeomorphic mapping between the template and the target. The method we apply is the ensemble Kalman filter, an extension of the Kalman filter to nonlinear observation operators. We describe an efficient implementation of the algorithm and show several numerical results for various target shapes.

While Shapley Values (SV) are one of the gold standard for interpreting machine learning models, we show that they are still poorly understood, in particular in the presence of categorical variables or of variables of low importance. For instance, we show that the popular practice that consists in summing the SV of dummy variables is false as it provides wrong estimates of all the SV in the model and implies spurious interpretations. Based on the identification of null and active coalitions, and a coalitional version of the SV, we provide a correct computation and inference of important variables. Moreover, a Python library (All the experiments and simulations can be reproduced with the publicly available library Active Coalition of Variables, https://www.github.com/salimamoukou/acv00) that computes reliably conditional expectations and SV for tree-based models, is implemented and compared with state-of-the-art algorithms on toy models and real data sets.

We consider the problem of estimating a particular type of linear non-Gaussian model. Without resorting to the overcomplete Independent Component Analysis (ICA), we show that under some mild assumptions, the model is uniquely identified by a hybrid method. Our method leverages the advantages of constraint-based methods and independent noise-based methods to handle both confounded and unconfounded situations. The first step of our method uses the FCI procedure, which allows confounders and is able to produce asymptotically correct results. The results, unfortunately, usually determine very few unconfounded direct causal relations, because whenever it is possible to have a confounder, it will indicate it. The second step of our procedure finds the unconfounded causal edges between observed variables among only those adjacent pairs informed by the FCI results. By making use of the so-called Triad condition, the third step is able to find confounders and their causal relations with other variables. Afterward, we apply ICA on a notably smaller set of graphs to identify remaining causal relationships if needed. Extensive experiments on simulated data and real-world data validate the correctness and effectiveness of the proposed method.

Causal induction, i.e., identifying unobservable mechanisms that lead to the observable relations among variables, has played a pivotal role in modern scientific discovery, especially in scenarios with only sparse and limited data. Humans, even young toddlers, can induce causal relationships surprisingly well in various settings despite its notorious difficulty. However, in contrast to the commonplace trait of human cognition is the lack of a diagnostic benchmark to measure causal induction for modern Artificial Intelligence (AI) systems. Therefore, in this work, we introduce the Abstract Causal REasoning (ACRE) dataset for systematic evaluation of current vision systems in causal induction. Motivated by the stream of research on causal discovery in Blicket experiments, we query a visual reasoning system with the following four types of questions in either an independent scenario or an interventional scenario: direct, indirect, screening-off, and backward-blocking, intentionally going beyond the simple strategy of inducing causal relationships by covariation. By analyzing visual reasoning architectures on this testbed, we notice that pure neural models tend towards an associative strategy under their chance-level performance, whereas neuro-symbolic combinations struggle in backward-blocking reasoning. These deficiencies call for future research in models with a more comprehensive capability of causal induction.

Spatial-temporal reasoning is a challenging task in Artificial Intelligence (AI) due to its demanding but unique nature: a theoretic requirement on representing and reasoning based on spatial-temporal knowledge in mind, and an applied requirement on a high-level cognitive system capable of navigating and acting in space and time. Recent works have focused on an abstract reasoning task of this kind -- Raven's Progressive Matrices (RPM). Despite the encouraging progress on RPM that achieves human-level performance in terms of accuracy, modern approaches have neither a treatment of human-like reasoning on generalization, nor a potential to generate answers. To fill in this gap, we propose a neuro-symbolic Probabilistic Abduction and Execution (PrAE) learner; central to the PrAE learner is the process of probabilistic abduction and execution on a probabilistic scene representation, akin to the mental manipulation of objects. Specifically, we disentangle perception and reasoning from a monolithic model. The neural visual perception frontend predicts objects' attributes, later aggregated by a scene inference engine to produce a probabilistic scene representation. In the symbolic logical reasoning backend, the PrAE learner uses the representation to abduce the hidden rules. An answer is predicted by executing the rules on the probabilistic representation. The entire system is trained end-to-end in an analysis-by-synthesis manner without any visual attribute annotations. Extensive experiments demonstrate that the PrAE learner improves cross-configuration generalization and is capable of rendering an answer, in contrast to prior works that merely make a categorical choice from candidates.