A test is adaptive when its sequence and number of questions is dynamically tuned on the basis of the estimated skills of the taker. Graphical models, such as Bayesian networks, are used for adaptive tests as they allow to model the uncertainty about the questions and the skills in an explainable fashion, especially when coping with multiple skills. A better elicitation of the uncertainty in the question/skills relations can be achieved by interval probabilities. This turns the model into a credal network, thus making more challenging the inferential complexity of the queries required to select questions. This is especially the case for the information theoretic quantities used as scores to drive the adaptive mechanism. We present an alternative family of scores, based on the mode of the posterior probabilities, and hence easier to explain. This makes considerably simpler the evaluation in the credal case, without significantly affecting the quality of the adaptive process. Numerical tests on synthetic and real-world data are used to support this claim.

Machine learning has achieved an important role in the automatic classification of variable stars, and several classifiers have been proposed over the last decade. These classifiers have achieved impressive performance in several astronomical catalogues. However, some scientific articles have also shown that the training data therein contain multiple sources of bias. Hence, the performance of those classifiers on objects not belonging to the training data is uncertain, potentially resulting in the selection of incorrect models. Besides, it gives rise to the deployment of misleading classifiers. An example of the latter is the creation of open-source labelled catalogues with biased predictions. In this paper, we develop a method based on an informative marginal likelihood to evaluate variable star classifiers. We collect deterministic rules that are based on physical descriptors of RR Lyrae stars, and then, to mitigate the biases, we introduce those rules into the marginal likelihood estimation. We perform experiments with a set of Bayesian Logistic Regressions, which are trained to classify RR Lyraes, and we found that our method outperforms traditional non-informative cross-validation strategies, even when penalized models are assessed. Our methodology provides a more rigorous alternative to assess machine learning models using astronomical knowledge. From this approach, applications to other classes of variable stars and algorithmic improvements can be developed.

Explainable AI (XAI) has been investigated for decades and, together with AI itself, has witnessed unprecedented growth in recent years. Among various approaches to XAI, argumentative models have been advocated in both the AI and social science literature, as their dialectical nature appears to match some basic desirable features of the explanation activity. In this survey we overview XAI approaches built using methods from the field of computational argumentation, leveraging its wide array of reasoning abstractions and explanation delivery methods. We overview the literature focusing on different types of explanation (intrinsic and post-hoc), different models with which argumentation-based explanations are deployed, different forms of delivery, and different argumentation frameworks they use. We also lay out a roadmap for future work.

In some cases we will need an array with more than two axes. In the general case, an array of numbers arranged on a regular grid with a variable number of axes is known as a tensor. Tensors and Multidimensional arrays are different types of object, the first is a type of function, the second is a data structure suitable for representing a tensor in a coordinate system. A scalar is just a single number, in contrast to most of the other objects studied in linear algebra, which are usually arrays of multiple numbers. In terms of tensor -- A tensor that contains only one number is called a Scalar(or scalar tensor, or 0-dimensional tensor, or 0D tensor).

It's well known across the machine learning community that choosing the right prior -- an initial belief re an event expressed in terms of a probability distribution -- is crucial for Bayesian inference. Many recent Bayesian deep learning models however resort to established but uninformative or weak informative priors that may have detrimental consequences on their models' inference abilities. In the paper Priors in Bayesian Deep Learning: A Review, a research team from ETH Zürich presents an overview of different priors for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks. The team proposes that well-chosen priors can actually achieve theoretical and empirical properties such as uncertainty estimation, model selection and optimal decision support; and provides guidance on how to choose them. The main idea of Bayesian models is to infer a posterior distribution over the parameters of a model based on a prior probability for some observed data.

Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the weight matrices in neural networks have been shown to empirically correlate with test set accuracy in several works (e.g. arXiv:1901.08276), but a formal relationship between heavy-tail distributed parameters and generalization bounds was yet to be demonstrated. In this work, the compression framework of arXiv:1802.05296 is utilized to show that matrices with heavy-tail distributed matrix elements can be compressed, resulting in networks with sparse weight matrices. Since the parameter count has been reduced to a sum of the non-zero elements of sparse matrices, the compression framework allows us to bound the generalization gap of the resulting compressed network with a non-vacuous generalization bound. Further, the action of these matrices on a vector is discussed, and how they may relate to compression and resilient classification is analyzed.

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused on formally evaluating the predictive uncertainties of these models. Furthermore, existing works point out the difficulties of encoding domain knowledge in models like NLMs, making them unsuitable for applications where interpretability is required. In this work, we show that traditional training procedures for NLMs can drastically underestimate uncertainty in data-scarce regions. We identify the underlying reasons for this behavior and propose a novel training method that can both capture useful predictive uncertainties as well as allow for incorporation of domain knowledge.

Random Forest (RFs) are among the most widely used Machine Learning (ML) classifiers. Even though RFs are not interpretable, there are no dedicated non-heuristic approaches for computing explanations of RFs. Moreover, there is recent work on polynomial algorithms for explaining ML models, including naive Bayes classifiers. Hence, one question is whether finding explanations of RFs can be solved in polynomial time. This paper answers this question negatively, by proving that computing one PI-explanation of an RF is D^P-complete. Furthermore, the paper proposes a propositional encoding for computing explanations of RFs, thus enabling finding PI-explanations with a SAT solver. This contrasts with earlier work on explaining boosted trees (BTs) and neural networks (NNs), which requires encodings based on SMT/MILP. Experimental results, obtained on a wide range of publicly available datasets, demontrate that the proposed SAT-based approach scales to RFs of sizes common in practical applications. Perhaps more importantly, the experimental results demonstrate that, for the vast majority of examples considered, the SAT-based approach proposed in this paper significantly outperforms existing heuristic approaches.

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. However, the most popular inference algorithms for SBL become too expensive for high-dimensional problems due to the need to maintain a large covariance matrix. To resolve this issue, we introduce a new SBL inference algorithm that avoids explicit computation of the covariance matrix, thereby saving significant time and space. Instead of performing costly matrix inversions, our covariance-free method solves multiple linear systems to obtain provably unbiased estimates of the posterior statistics needed by SBL. These systems can be solved in parallel, enabling further acceleration of the algorithm via graphics processing units. In practice, our method can be up to thousands of times faster than existing baselines, reducing hours of computation time to seconds. We showcase how our new algorithm enables SBL to tractably tackle high-dimensional signal recovery problems, such as deconvolution of calcium imaging data and multi-contrast reconstruction of magnetic resonance images. Finally, we open-source a toolbox containing all of our implementations to drive future research in SBL.

The evolution of electronic media is a mixed blessing. Due to the easy access, low cost, and faster reach of the information, people search out and devour news from online social networks. In contrast, the increasing acceptance of social media reporting leads to the spread of fake news. This is a minacious problem that causes disputes and endangers societal stability and harmony. Fake news spread has gained attention from researchers due to its vicious nature. proliferation of misinformation in all media, from the internet to cable news, paid advertising and local news outlets, has made it essential for people to identify the misinformation and sort through the facts. Researchers are trying to analyze the credibility of information and curtail false information on such platforms. Credibility is the believability of the piece of information at hand. Analyzing the credibility of fake news is challenging due to the intent of its creation and the polychromatic nature of the news. In this work, we propose a model for detecting fake news. Our method investigates the content of the news at the early stage i.e. when the news is published but is yet to be disseminated through social media. Our work interprets the content with automatic feature extraction and the relevance of the text pieces. In summary, we introduce stance as one of the features along with the content of the article and employ the pre-trained contextualized word embeddings BERT to obtain the state-of-art results for fake news detection. The experiment conducted on the real-world dataset indicates that our model outperforms the previous work and enables fake news detection with an accuracy of 95.32%.