In semi-supervised learning (SSL), a rule to predict labels $y$ for data $x$ is learned from labelled data $(x^l,y^l)$ and unlabelled samples $x^u$. Strong progress has been made by combining a variety of methods, some of which pertain to $p(x)$, e.g. data augmentation that generates artificial samples from true $x$; whilst others relate to model outputs $p(y|x)$, e.g. regularising predictions on unlabelled data to minimise entropy or induce mutual exclusivity. Focusing on the latter, we fill a gap in the standard text by introducing a unifying probabilistic model for discriminative semi-supervised learning, mirroring that for classical generative methods. We show that several SSL methods can be theoretically justified under our model as inducing approximate priors over predicted parameters of $p(y|x)$. For tasks where labels represent binary attributes, our model leads to a principled approach to neuro-symbolic SSL, bridging the divide between statistical learning and logical rules.

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance between the projected features. The sparse projection matrix is considered as an unknown parameter. We propose a forward stagewise approach with embedded gradient descent steps to co-optimize the parameter with other covariance parameters based on the maximization of a non-convex marginal likelihood function with a concave sparsity penalty, and some convergence properties of the algorithm are provided. The proposed model covers a broader class of stationary covariance functions than the existing automatic relevance determination approaches, and the solution approach is more computationally feasible than the existing MCMC sampling procedures for the automatic relevance parameter estimation with a sparsity prior. The approach is evaluated for a large number of simulated scenarios. The choice of tuning parameters and the accuracy of the parameter estimation are evaluated with the simulation study. In the comparison to some chosen benchmark approaches, the proposed approach has provided a better accuracy in the variable selection. It is applied to an important problem of identifying environmental factors that affect an atmospheric corrosion of metal alloys.

Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large number of parameters. Non-Bayesian methods are simple to implement but often conflate different sources of uncertainties and require huge computing resources. We propose a new method for quantifying uncertainties of DNNs from a dynamical system perspective. The core of our method is to view DNN transformations as state evolution of a stochastic dynamical system and introduce a Brownian motion term for capturing epistemic uncertainty. Based on this perspective, we propose a neural stochastic differential equation model (SDE-Net) which consists of (1) a drift net that controls the system to fit the predictive function; and (2) a diffusion net that captures epistemic uncertainty. We theoretically analyze the existence and uniqueness of the solution to SDE-Net. Our experiments demonstrate that the SDE-Net model can outperform existing uncertainty estimation methods across a series of tasks where uncertainty plays a fundamental role.

In this paper, we propose a novel information criteria-based approach to select the dimensionality of the word2vec Skip-gram (SG). From the perspective of the probability theory, SG is considered as an implicit probability distribution estimation under the assumption that there exists a true contextual distribution among words. Therefore, we apply information criteria with the aim of selecting the best dimensionality so that the corresponding model can be as close as possible to the true distribution. We examine the following information criteria for the dimensionality selection problem: the Akaike Information Criterion, Bayesian Information Criterion, and Sequential Normalized Maximum Likelihood (SNML) criterion. SNML is the total codelength required for the sequential encoding of a data sequence on the basis of the minimum description length. The proposed approach is applied to both the original SG model and the SG Negative Sampling model to clarify the idea of using information criteria. Additionally, as the original SNML suffers from computational disadvantages, we introduce novel heuristics for its efficient computation. Moreover, we empirically demonstrate that SNML outperforms both BIC and AIC. In comparison with other evaluation methods for word embedding, the dimensionality selected by SNML is significantly closer to the optimal dimensionality obtained by word analogy or word similarity tasks.

Thompson Sampling (TS) with Gaussian Process (GP) models is a powerful tool for optimizing non-convex objective functions. Despite favorable theoretical properties, the computational complexity of the standard algorithms quickly becomes prohibitive as the number of observation points (i.e. the time horizon) grows. Scalable TS methods can be implemented using sparse GP models, but at the price of an approximation error that invalidates the existing regret bounds. Here, we prove regret bounds for TS based on approximate GP posteriors, whose application to sparse GPs shows that the improvement in computational complexity can be achieved with no loss in terms of the order of regret performance. Specifically, when necessary conditions on some algorithmic parameters are satisfied, we show an $\tilde{O}(\gamma_T\sqrt{ T})$ bound on the regret performance of TS using sparse GP models where $\gamma_T$ is an upper bound on the information gain between the observations and the underlying model.

Deep networks are currently the state-of-the-art for sensory perception in autonomous driving and robotics. However, deep models often generate overconfident predictions precluding proper probabilistic interpretation which we argue is due to the nature of the SoftMax layer. To reduce the overconfidence without compromising the classification performance, we introduce a CNN probabilistic approach based on distributions calculated in the network's Logit layer. The approach enables Bayesian inference by means of ML and MAP layers. Experiments with calibrated and the proposed prediction layers are carried out on object classification using data from the KITTI database. Results are reported for camera (RGB) and LiDAR (range-view) modalities, where the new approach shows promising performance compared to SoftMax. Keywords: Probabilistic inference, Perception systems, CNN probabilistic layer, object classification.

Understanding data and reaching valid conclusions are of paramount importance in the present era of big data. Machine learning and probability theory methods have widespread application for this purpose in different fields. One critically important yet less explored aspect is how data and model uncertainties are captured and analyzed. Proper quantification of uncertainty provides valuable information for optimal decision making. This paper reviewed related studies conducted in the last 30 years (from 1991 to 2020) in handling uncertainties in medical data using probability theory and machine learning techniques. Medical data is more prone to uncertainty due to the presence of noise in the data. So, it is very important to have clean medical data without any noise to get accurate diagnosis. The sources of noise in the medical data need to be known to address this issue. Based on the medical data obtained by the physician, diagnosis of disease, and treatment plan are prescribed. Hence, the uncertainty is growing in healthcare and there is limited knowledge to address these problems. We have little knowledge about the optimal treatment methods as there are many sources of uncertainty in medical science. Our findings indicate that there are few challenges to be addressed in handling the uncertainty in medical raw data and new models. In this work, we have summarized various methods employed to overcome this problem. Nowadays, application of novel deep learning techniques to deal such uncertainties have significantly increased.

This paper presents a cognitive behavioral-based driver mood repairment platform in intelligent transportation cyber-physical systems (IT-CPS) for road safety. In particular, we propose a driving safety platform for distracted drivers, namely \emph{drive safe}, in IT-CPS. The proposed platform recognizes the distracting activities of the drivers as well as their emotions for mood repair. Further, we develop a prototype of the proposed drive safe platform to establish proof-of-concept (PoC) for the road safety in IT-CPS. In the developed driving safety platform, we employ five AI and statistical-based models to infer a vehicle driver's cognitive-behavioral mining to ensure safe driving during the drive. Especially, capsule network (CN), maximum likelihood (ML), convolutional neural network (CNN), Apriori algorithm, and Bayesian network (BN) are deployed for driver activity recognition, environmental feature extraction, mood recognition, sequential pattern mining, and content recommendation for affective mood repairment of the driver, respectively. Besides, we develop a communication module to interact with the systems in IT-CPS asynchronously. Thus, the developed drive safe PoC can guide the vehicle drivers when they are distracted from driving due to the cognitive-behavioral factors. Finally, we have performed a qualitative evaluation to measure the usability and effectiveness of the developed drive safe platform. We observe that the P-value is 0.0041 (i.e., < 0.05) in the ANOVA test. Moreover, the confidence interval analysis also shows significant gains in prevalence value which is around 0.93 for a 95% confidence level. The aforementioned statistical results indicate high reliability in terms of driver's safety and mental state.

A large family of score-based methods are developed recently to solve unsupervised learning problems including density estimation, statistical testing and variational inference. These methods are attractive because they exploit the derivative of the log density, which is independent of the normaliser, and are thus suitable for tasks involving unnormalised densities. Despite the theoretical guarantees on the performance, here we illustrate a common practical issue suffered by these methods when the unnormalised distribution of interest has isolated components. In particular, we study the behaviour of some popular score-based methods on tasks involving 1-D mixture of Gaussian. These methods fail to identify appropriate mixing proportions when the unnormalised distribution is multimodal. Finally, some directions for finding a remedy are discussed in light of recent successes in specific tasks. We hope to bring the attention of theoreticians and practitioners to this issue when developing new algorithms and applications.

In stochastic systems, informative approaches select key measurement or decision variables that maximize information gain to enhance the efficacy of model-related inferences. Neural Learning also embodies stochastic dynamics, but informative Learning is less developed. Here, we propose Informative Ensemble Kalman Learning, which replaces backpropagation with an adaptive Ensemble Kalman Filter to quantify uncertainty and enables maximizing information gain during Learning. After demonstrating Ensemble Kalman Learning's competitive performance on standard datasets, we apply the informative approach to neural structure learning. In particular, we show that when trained from the Lorenz-63 system's simulations, the efficaciously learned structure recovers the dynamical equations. To the best of our knowledge, Informative Ensemble Kalman Learning is new. Results suggest that this approach to optimized Learning is promising.