Bayesian neural networks are theoretically well-understood only in the infinite-width limit, where Gaussian priors over network weights yield Gaussian priors over network outputs. Recent work has suggested that finite Bayesian networks may outperform their infinite counterparts, but their non-Gaussian output priors have been characterized only though perturbative approaches. Here, we derive exact solutions for the output priors for individual input examples of a class of finite fully-connected feedforward Bayesian neural networks. For deep linear networks, the prior has a simple expression in terms of the Meijer $G$-function. The prior of a finite ReLU network is a mixture of the priors of linear networks of smaller widths, corresponding to different numbers of active units in each layer. Our results unify previous descriptions of finite network priors in terms of their tail decay and large-width behavior.

The emergence of Artificial Intelligence of Things (AIoT) has provided novel insights for many social computing applications such as group recommender systems. As distance among people has been greatly shortened, it has been a more general demand to provide personalized services to groups instead of individuals. In order to capture group-level preference features from individuals, existing methods were mostly established via aggregation and face two aspects of challenges: secure data management workflow is absent, and implicit preference feedbacks is ignored. To tackle current difficulties, this paper proposes secure Artificial Intelligence of Things for implicit Group Recommendations (SAIoT-GR). As for hardware module, a secure IoT structure is developed as the bottom support platform. As for software module, collaborative Bayesian network model and non-cooperative game are can be introduced as algorithms. Such a secure AIoT architecture is able to maximize the advantages of the two modules. In addition, a large number of experiments are carried out to evaluate the performance of the SAIoT-GR in terms of efficiency and robustness.

The pandemic COVID-19 disease has had a dramatic impact on almost all countries around the world so that many hospitals have been overwhelmed with Covid-19 cases. As medical resources are limited, deciding on the proper allocation of these resources is a very crucial issue. Besides, uncertainty is a major factor that can affect decisions, especially in medical fields. To cope with this issue, we use fuzzy logic (FL) as one of the most suitable methods in modeling systems with high uncertainty and complexity. We intend to make use of the advantages of FL in decisions on cases that need to treat in ICU. In this study, an interval type-2 fuzzy expert system is proposed for prediction of ICU admission in COVID-19 patients. For this prediction task, we also developed an adaptive neuro-fuzzy inference system (ANFIS). Finally, the results of these fuzzy systems are compared to some well-known classification methods such as Naive Bayes (NB), Case-Based Reasoning (CBR), Decision Tree (DT), and K Nearest Neighbor (KNN). The results show that the type-2 fuzzy expert system and ANFIS models perform competitively in terms of accuracy and F-measure compared to the other system modeling techniques.

A substantial disadvantage of traditional learning is that all students follow the same learning sequence, but not all of them have the same background of knowledge, the same preferences, the same learning goals, and the same needs. Traditional teaching resources, such as textbooks, in most cases pursue students to follow fixed sequences during the learning process, thus impairing their performance. Learning sequencing is an important research issue as part of the learning process because no fixed learning paths will be appropriate for all learners. For this reason, many research papers are focused on the development of mechanisms to offer personalization on learning paths, considering the learner needs, interests, behaviors, and abilities. In most cases, these researchers are totally focused on the student's preferences, ignoring the level of difficulty and the relation degree that exists between various concepts in a course. This research paper presents the possibility of constructing personalized learning paths using genetic algorithm-based model, encountering the level of difficulty and relation degree of the constituent concepts of a course. The experimental results shows that the genetic algorithm is suitable to generate optimal learning paths based on learning object difficulty level, duration, rating, and relation degree between each learning object as elementary parts of the sequence of the learning path. From these results compared to the quality of the traditional learning path, we observed that even the quality of the weakest learning path generated by our GA approach is in a favor compared to quality of the traditional learning path, with a difference of 3.59\%, while the highest solution generated in the end resulted 8.34\% in favor of our proposal compared to the traditional learning paths.

Fields such as phylogenetics often work with a sort of abstracted family tree, called a phylogenetic tree, frequently abbreviated here as tree. These trees have different members of a population as their tips, and their branching points describe the relations between the tips and how recently they had a common ancestor. If some of the tips are censored, the tree topology simplifies in a process we refer to as restriction. If one has multiple trees restricted from the same original, uncensored tree, one may wish to reconstruct the original supertree. Suppose instead one has multiple probability distributions of restricted trees, then one may be interested in reconstructing the supertree probability distribution.

We develop a simple and elegant method for lossless compression using latent variable models, which we call 'bits back with asymmetric numeral systems' (BB-ANS). The method involves interleaving encode and decode steps, and achieves an optimal rate when compressing batches of data. We demonstrate it firstly on the MNIST test set, showing that state-of-the-art lossless compression is possible using a small variational autoencoder (VAE) model. We then make use of a novel empirical insight, that fully convolutional generative models, trained on small images, are able to generalize to images of arbitrary size, and extend BB-ANS to hierarchical latent variable models, enabling state-of-the-art lossless compression of full-size colour images from the ImageNet dataset. We describe 'Craystack', a modular software framework which we have developed for rapid prototyping of compression using deep generative models.

Why can the Expectation-Maximization (EM) algorithm for mixture models converge? Why can different initial parameters cause various convergence difficulties? The Q-L synchronization theory explains that the observed data log-likelihood L and the complete data log-likelihood Q are positively correlated; we can achieve maximum L by maximizing Q. According to this theory, the Deterministic Annealing EM (DAEM) algorithm's authors make great efforts to eliminate locally maximal Q for avoiding L's local convergence. However, this paper proves that in some cases, Q may and should decrease for L to increase; slow or local convergence exists only because of small samples and unfair competition. This paper uses marriage competition to explain different convergence difficulties and proposes the Fair Competition Principle (FCP) with an initialization map for improving initializations. It uses the rate-verisimilitude function, extended from the rate-distortion function, to explain the convergence of the EM and improved EM algorithms. This convergence proof adopts variational and iterative methods that Shannon et al. used for analyzing rate-distortion functions. The initialization map can vastly save both algorithms' running times for binary Gaussian mixtures. The FCP and the initialization map are useful for complicated mixtures but not sufficient; we need further studies for specific methods.

Existing approaches for generating human-aware agent behaviors have considered different measures of interpretability in isolation. Further, these measures have been studied under differing assumptions, thus precluding the possibility of designing a single framework that captures these measures under the same assumptions. In this paper, we present a unifying Bayesian framework that models a human observer's evolving beliefs about an agent and thereby define the problem of Generalized Human-Aware Planning. We will show that the definitions of interpretability measures like explicability, legibility and predictability from the prior literature fall out as special cases of our general framework. Through this framework, we also bring a previously ignored fact to light that the human-robot interactions are in effect open-world problems, particularly as a result of modeling the human's beliefs over the agent. Since the human may not only hold beliefs unknown to the agent but may also form new hypotheses about the agent when presented with novel or unexpected behaviors.

Reliability of machine learning (ML) systems is crucial in safety-critical applications such as healthcare, and uncertainty estimation is a widely researched method to highlight the confidence of ML systems in deployment. Sequential and parallel ensemble techniques have shown improved performance of ML systems in multi-modal settings by leveraging the feature sets together. We propose an uncertainty-aware boosting technique for multi-modal ensembling in order to focus on the data points with higher associated uncertainty estimates, rather than the ones with higher loss values. We evaluate this method on healthcare tasks related to Dementia and Parkinson's disease which involve real-world multi-modal speech and text data, wherein our method shows an improved performance. Additional analysis suggests that introducing uncertainty-awareness into the boosted ensembles decreases the overall entropy of the system, making it more robust to heteroscedasticity in the data, as well as better calibrating each of the modalities along with high quality prediction intervals. We open-source our entire codebase at https://github.com/usarawgi911/Uncertainty-aware-boosting

In educational applications, Knowledge Tracing (KT), the problem of accurately predicting students' responses to future questions by summarizing their knowledge states, has been widely studied for decades as it is considered a fundamental task towards adaptive online learning. Among all the proposed KT methods, Deep Knowledge Tracing (DKT) and its variants are by far the most effective ones due to the high flexibility of the neural network. However, DKT often ignores the inherent differences between students (e.g. memory skills, reasoning skills, ...), averaging the performances of all students, leading to the lack of personalization, and therefore was considered insufficient for adaptive learning. To alleviate this problem, in this paper, we proposed Leveled Attentive KNowledge TrAcing (LANA), which firstly uses a novel student-related features extractor (SRFE) to distill students' unique inherent properties from their respective interactive sequences. Secondly, the pivot module was utilized to dynamically reconstruct the decoder of the neural network on attention of the extracted features, successfully distinguishing the performance between students over time. Moreover, inspired by Item Response Theory (IRT), the interpretable Rasch model was used to cluster students by their ability levels, and thereby utilizing leveled learning to assign different encoders to different groups of students. With pivot module reconstructed the decoder for individual students and leveled learning specialized encoders for groups, personalized DKT was achieved. Extensive experiments conducted on two real-world large-scale datasets demonstrated that our proposed LANA improves the AUC score by at least 1.00% (i.e. EdNet 1.46% and RAIEd2020 1.00%), substantially surpassing the other State-Of-The-Art KT methods.