Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the fundamental questions like its statistical optimality and computational limit are largely under-explored. In this paper, we propose a low-rank Gaussian mixture model (LrMM) assuming each matrix-valued observation has a planted low-rank structure. Minimax lower bounds for estimating the underlying low-rank matrix are established allowing a whole range of sample sizes and signal strength. Under a minimal condition on signal strength, referred to as the information-theoretical limit or statistical limit, we prove the minimax optimality of a maximum likelihood estimator which, in general, is computationally infeasible. If the signal is stronger than a certain threshold, called the computational limit, we design a computationally fast estimator based on spectral aggregation and demonstrate its minimax optimality. Moreover, when the signal strength is smaller than the computational limit, we provide evidences based on the low-degree likelihood ratio framework to claim that no polynomial-time algorithm can consistently recover the underlying low-rank matrix. Our results reveal multiple phase transitions in the minimax error rates and the statistical-to-computational gap. Numerical experiments confirm our theoretical findings. We further showcase the merit of our spectral aggregation method on the worldwide food trading dataset.

In metric learning, the goal is to learn an embedding so that data points with the same class are close to each other and data points with different classes are far apart. We propose a distance-ratio-based (DR) formulation for metric learning. Like softmax-based formulation for metric learning, it models $p(y=c|x')$, which is a probability that a query point $x'$ belongs to a class $c$. The DR formulation has two useful properties. First, the corresponding loss is not affected by scale changes of an embedding. Second, it outputs the optimal (maximum or minimum) classification confidence scores on representing points for classes. To demonstrate the effectiveness of our formulation, we conduct few-shot classification experiments using softmax-based and DR formulations on CUB and mini-ImageNet datasets. The results show that DR formulation generally enables faster and more stable metric learning than the softmax-based formulation. As a result, using DR formulation achieves improved or comparable generalization performances.

Across research disciplines, cluster randomized trials (CRTs) are commonly implemented to evaluate interventions delivered to groups of participants, such as communities and clinics. Despite advances in the design and analysis of CRTs, several challenges remain. First, there are many possible ways to specify the intervention effect (e.g., at the individual-level or at the cluster-level). Second, the theoretical and practical performance of common methods for CRT analysis remain poorly understood. Here, we use causal models to formally define an array of causal effects as summary measures of counterfactual outcomes. Next, we provide a comprehensive overview of well-known CRT estimators, including the t-test and generalized estimating equations (GEE), as well as less known methods, including augmented-GEE and targeted maximum likelihood estimation (TMLE). In finite sample simulations, we illustrate the performance of these estimators and the importance of effect specification, especially when cluster size varies. Finally, our application to data from the Preterm Birth Initiative (PTBi) study demonstrates the real-world importance of selecting an analytic approach corresponding to the research question. Given its flexibility to estimate a variety of effects and ability to adaptively adjust for covariates for precision gains while maintaining Type-I error control, we conclude TMLE is a promising tool for CRT analysis.

Prescribing optimal operation based on the condition of the system and, thereby, potentially prolonging the remaining useful lifetime has a large potential for actively managing the availability, maintenance and costs of complex systems. Reinforcement learning (RL) algorithms are particularly suitable for this type of problems given their learning capabilities. A special case of a prescriptive operation is the power allocation task, which can be considered as a sequential allocation problem, where the action space is bounded by a simplex constraint. A general continuous action-space solution of such sequential allocation problems has still remained an open research question for RL algorithms. In continuous action-space, the standard Gaussian policy applied in reinforcement learning does not support simplex constraints, while the Gaussian-softmax policy introduces a bias during training. In this work, we propose the Dirichlet policy for continuous allocation tasks and analyze the bias and variance of its policy gradients. We demonstrate that the Dirichlet policy is bias-free and provides significantly faster convergence, better performance and better hyperparameters robustness over the Gaussian-softmax policy. Moreover, we demonstrate the applicability of the proposed algorithm on a prescriptive operation case, where we propose the Dirichlet power allocation policy and evaluate the performance on a case study of a set of multiple lithium-ion (Li-I) battery systems. The experimental results show the potential to prescribe optimal operation, improve the efficiency and sustainability of multi-power source systems.

Recently, deep learning has achieved remarkable successes in medical image analysis. Although deep neural networks generate clinically important predictions, they have inherent uncertainty. Such uncertainty is a major barrier to report these predictions with confidence. In this paper, we propose a novel yet simple Bayesian inference approach called SoftDropConnect (SDC) to quantify the network uncertainty in medical imaging tasks with gliomas segmentation and metastases classification as initial examples. Our key idea is that during training and testing SDC modulates network parameters continuously so as to allow affected information processing channels still in operation, instead of disabling them as Dropout or DropConnet does. When compared with three popular Bayesian inference methods including Bayes By Backprop, Dropout, and DropConnect, our SDC method (SDC-W after optimization) outperforms the three competing methods with a substantial margin. Quantitatively, our proposed method generates results withsubstantially improved prediction accuracy (by 10.0%, 5.4% and 3.7% respectively for segmentation in terms of dice score; by 11.7%, 3.9%, 8.7% on classification in terms of test accuracy) and greatly reduced uncertainty in terms of mutual information (by 64%, 33% and 70% on segmentation; 98%, 88%, and 88% on classification). Our approach promises to deliver better diagnostic performance and make medical AI imaging more explainable and trustworthy.

Psychological curiosity plays a significant role in human intelligence to enhance learning through exploration and information acquisition. In the Artificial Intelligence (AI) community, artificial curiosity provides a natural intrinsic motivation for efficient learning as inspired by human cognitive development; meanwhile, it can bridge the existing gap between AI research and practical application scenarios, such as overfitting, poor generalization, limited training samples, high computational cost, etc. As a result, curiosity-driven learning (CDL) has become increasingly popular, where agents are self-motivated to learn novel knowledge. In this paper, we first present a comprehensive review on the psychological study of curiosity and summarize a unified framework for quantifying curiosity as well as its arousal mechanism. Based on the psychological principle, we further survey the literature of existing CDL methods in the fields of Reinforcement Learning, Recommendation, and Classification, where both advantages and disadvantages as well as future work are discussed. As a result, this work provides fruitful insights for future CDL research and yield possible directions for further improvement.

The rising popularity of explainable artificial intelligence (XAI) to understand high-performing black boxes, also raised the question of how to evaluate explanations of machine learning (ML) models. While interpretability and explainability are often presented as a subjectively validated binary property, we consider it a multi-faceted concept. We identify 12 conceptual properties, such as Compactness and Correctness, that should be evaluated for comprehensively assessing the quality of an explanation. Our so-called Co-12 properties serve as categorization scheme for systematically reviewing the evaluation practice of more than 300 papers published in the last 7 years at major AI and ML conferences that introduce an XAI method. We find that 1 in 3 papers evaluate exclusively with anecdotal evidence, and 1 in 5 papers evaluate with users. We also contribute to the call for objective, quantifiable evaluation methods by presenting an extensive overview of quantitative XAI evaluation methods. This systematic collection of evaluation methods provides researchers and practitioners with concrete tools to thoroughly validate, benchmark and compare new and existing XAI methods. This also opens up opportunities to include quantitative metrics as optimization criteria during model training in order to optimize for accuracy and interpretability simultaneously.

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. To demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed, which we will make available as open-source library of all codes included in this framework.

Fake news detection research is still in the early stage as this is a relatively new phenomenon in the interest raised by society. Machine learning helps to solve complex problems and to build AI systems nowadays and especially in those cases where we have tacit knowledge or the knowledge that is not known. We used machine learning algorithms and for identification of fake news; we applied three classifiers; Passive Aggressive, Na\"ive Bayes, and Support Vector Machine. Simple classification is not completely correct in fake news detection because classification methods are not specialized for fake news. With the integration of machine learning and text-based processing, we can detect fake news and build classifiers that can classify the news data. Text classification mainly focuses on extracting various features of text and after that incorporating those features into classification. The big challenge in this area is the lack of an efficient way to differentiate between fake and non-fake due to the unavailability of corpora. We applied three different machine learning classifiers on two publicly available datasets. Experimental analysis based on the existing dataset indicates a very encouraging and improved performance.

Graphical models in probability and statistics are a core concept in the area of probabilistic reasoning and probabilistic programming-graphical models include Bayesian networks and factor graphs. In this paper we develop a new model of mixed (nondeterministic/probabilistic) automata that subsumes both nondeterministic automata and graphical probabilistic models. Mixed Automata are equipped with parallel composition, simulation relation, and support message passing algorithms inherited from graphical probabilistic models. Segala's Probabilistic Automatacan be mapped to Mixed Automata.