Bayes' theorem (alternatively Bayes' law or Bayes' rule) has been called the most powerful rule of probability and statistics. It describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if a disease is related to age, then, using Bayes' theorem, a person's age can be used to more accurately assess the probability that they have the disease, compared to the assessment of the probability of disease made without knowledge of the person's age. It is a powerful law of probability that brings in the concept of'subjectivity' or'the degree of belief' into the cold, hard statistical modeling. Bayes' rule is the only mechanism that can be used to gradually update the probability of an event as the evidence or data is gathered sequentially.

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior. B-PINNs make use of both physical laws and scattered noisy measurements to provide predictions and quantify the aleatoric uncertainty arising from the noisy data in the Bayesian framework. Compared with PINNs, in addition to uncertainty quantification, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting. We conduct a systematic comparison between the two different approaches for the B-PINN posterior estimation (i.e., HMC or VI), along with dropout used for quantifying uncertainty in deep neural networks. Our experiments show that HMC is more suitable than VI for the B-PINNs posterior estimation, while dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty. Finally, we replace the BNN in the prior with a truncated Karhunen-Lo\`eve (KL) expansion combined with HMC or a deep normalizing flow (DNF) model as posterior estimators. The KL is as accurate as BNN and much faster but this framework cannot be easily extended to high-dimensional problems unlike the BNN based framework.

Training generative models that can generate high-quality text with sufficient diversity is an important open problem for Natural Language Generation (NLG) community. Recently, generative adversarial models have been applied extensively on text generation tasks, where the adversarially trained generators alleviate the exposure bias experienced by conventional maximum likelihood approaches and result in promising generation quality. However, due to the notorious defect of mode collapse for adversarial training, the adversarially trained generators face a quality-diversity trade-off, i.e., the generator models tend to sacrifice generation diversity severely for increasing generation quality. In this paper, we propose a novel approach which aims to improve the performance of adversarial text generation via efficiently decelerating mode collapse of the adversarial training. To this end, we introduce a cooperative training paradigm, where a language model is cooperatively trained with the generator and we utilize the language model to efficiently shape the data distribution of the generator against mode collapse. Moreover, instead of engaging the cooperative update for the generator in a principled way, we formulate a meta learning mechanism, where the cooperative update to the generator serves as a high level meta task, with an intuition of ensuring the parameters of the generator after the adversarial update would stay resistant against mode collapse. In the experiment, we demonstrate our proposed approach can efficiently slow down the pace of mode collapse for the adversarial text generators. Overall, our proposed method is able to outperform the baseline approaches with significant margins in terms of both generation quality and diversity in the testified domains.

Sentiment Analysis is a branch of Affective Computing usually considered a binary classification task. In this line of reasoning, Sentiment Analysis can be applied in several contexts to classify the attitude expressed in text samples, for example, movie reviews, sarcasm, among others. A common approach to represent text samples is the use of the Vector Space Model to compute numerical feature vectors consisting of the weight of terms. The most popular term weighting scheme is TF-IDF (Term Frequency - Inverse Document Frequency). It is an Unsupervised Weighting Scheme (UWS) since it does not consider the class information in the weighting of terms. Apart from that, there are Supervised Weighting Schemes (SWS), which consider the class information on term weighting calculation. Several SWS have been recently proposed, demonstrating better results than TF-IDF. In this scenario, this work presents a comparative study on different term weighting schemes and proposes a novel supervised term weighting scheme, named as TF-IDFC-RF (Term Frequency - Inverse Document Frequency in Class - Relevance Frequency). The effectiveness of TF-IDFC-RF is validated with SVM (Support Vector Machine) and NB (Naive Bayes) classifiers on four commonly used Sentiment Analysis datasets. TF-IDFC-RF outperforms all other weighting schemes and achieves F1 results of more than 99.9% on all datasets with SVM classifier.

Spatial prediction is commonly achieved under the assumption of a Gaussian random field (GRF) by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the Expectation-Maximization (EM) algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the Spatial Mixed Effects (SME) model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an Alternating Expectation Conditional Maximization (AECM) algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature data set archived by the United States National Climate Data Center, with improved results over previous methodology.

Since deep neural networks were developed, they have made huge contributions to peoples everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures that have been alleged to be alchemy. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and tool-kits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep-learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

In solving real-world problems like changing healthcare-seeking behaviors, designing interventions to improve downstream outcomes requires an understanding of the causal links within the system. Causal Bayesian Networks (BN) have been proposed as one such powerful method. In real-world applications, however, confidence in the results of BNs are often moderate at best. This is due in part to the inability to validate against some ground truth, as the DAG is not available. This is especially problematic if the learned DAG conflicts with pre-existing domain doctrine. At the policy level, one must justify insights generated by such analysis, preferably accompanying them with uncertainty estimation. Here we propose a causal extension to the datasheet concept proposed by Gebru et al (2018) to include approximate BN performance expectations for any given dataset. To generate the results for a prototype Causal Datasheet, we constructed over 30,000 synthetic datasets with properties mirroring characteristics of real data. We then recorded the results given by state-of-the-art structure learning algorithms. These results were used to populate the Causal Datasheet, and recommendations were automatically generated dependent on expected performance. As a proof of concept, we used our Causal Datasheet Generation Tool (CDG-T) to assign expected performance expectations to a maternal health survey we conducted in Uttar Pradesh, India.

While a large body of research has formally identified apolipoprotein E (APOE) as a major genetic risk marker for Alzheimer disease, accumulating evidence supports the notion that other risk markers may exist. The traditional Alzheimer-specific signature analysis methods, however, have not been able to make full use of rich protein expression data, especially the interaction between attributes. This paper develops a novel feature selection method to identify pathogenic factors of Alzheimer disease using the proteomic and clinical data. This approach has taken the weights of network nodes as the importance order of signaling protein expression values. After generating and evaluating the candidate subset, the method helps to select an optimal subset of proteins that achieved an accuracy greater than 90%, which is superior to traditional machine learning methods for clinical Alzheimer disease diagnosis. Besides identifying a proteomic risk marker and further reinforce the link between metabolic risk factors and Alzheimer disease, this paper also suggests that apidonectin-linked pathways are a possible therapeutic drug target.

In this paper we focus on the problem of assigning uncertainties to single-point predictions generated by a deterministic model that outputs a continuous variable. This problem applies to any state-of-the-art physics or engineering models that have a computational cost that does not readily allow to run ensembles and to estimate the uncertainty associated to single-point predictions. Essentially, we devise a method to easily transform a deterministic prediction into a probabilistic one. We show that for doing so, one has to compromise between the accuracy and the reliability (calibration) of such a probabilistic model. Hence, we introduce a cost function that encodes their trade-off. We use the Continuous Rank Probability Score to measure accuracy and we derive an analytic formula for the reliability, in the case of forecasts of continuous scalar variables expressed in terms of Gaussian distributions. The new Accuracy-Reliability cost function is then used to estimate the input-dependent variance, given a black-box mean function, by solving a two-objective optimization problem. The simple philosophy behind this strategy is that predictions based on the estimated variances should not only be accurate, but also reliable (i.e. statistical consistent with observations). Conversely, early works based on the minimization of classical cost functions, such as the negative log probability density, cannot simultaneously enforce both accuracy and reliability. We show several examples both with synthetic data, where the underlying hidden noise can accurately be recovered, and with large real-world datasets.

Despite the massive popularity of the Asian Handicap (AH) football betting market, it has not been adequately studied by the relevant literature. This paper combines rating systems with hybrid Bayesian networks and presents the first published model specifically developed for prediction and assessment of the AH betting market. The results are based on 13 English Premier League seasons and are compared to the traditional 1X2 market. Different betting situations have been examined including a) both average and maximum (best available) market odds, b) all possible betting decision thresholds between predicted and published odds, c) optimisations for both return-on-investment and profit, and d) simple stake adjustments to investigate how the variance of returns changes when targeting equivalent profit in both 1X2 and AH markets. While the AH market is found to share the inefficiencies of the traditional 1X2 market, the findings reveal both interesting differences as well as similarities between the two.