Learning how to predict future events from patterns of past events is difficult when the set of possible event types is large. Training an unrestricted neural model might overfit to spurious patterns. To exploit domain-specific knowledge of how past events might affect an event's present probability, we propose using a temporal deductive database to track structured facts over time. Rules serve to prove facts from other facts and from past events. Each fact has a time-varying state---a vector computed by a neural net whose topology is determined by the fact's provenance, including its experience of past events. The possible event types at any time are given by special facts, whose probabilities are neurally modeled alongside their states. In both synthetic and real-world domains, we show that neural probabilistic models derived from concise Datalog programs improve prediction by encoding appropriate domain knowledge in their architecture.

Despite deep neural network (DNN)'s impressive prediction performance in various domains, it is well known now that a set of DNN models trained with the same model specification and the same data can produce very different prediction results. Ensemble method is one state-of-the-art benchmark for prediction uncertainty estimation. However, ensembles are expensive to train and serve for web-scale traffic. In this paper, we seek to advance the understanding of prediction variation estimated by the ensemble method. Through empirical experiments on two widely used benchmark datasets MovieLens and Criteo in recommender systems, we observe that prediction variations come from various randomness sources, including training data shuffling, and parameter random initialization. By introducing more randomness into model training, we notice that ensemble's mean predictions tend to be more accurate while the prediction variations tend to be higher. Moreover, we propose to infer prediction variation from neuron activation strength and demonstrate the strong prediction power from activation strength features. Our experiment results show that the average R squared on MovieLens is as high as 0.56 and on Criteo is 0.81. Our method performs especially well when detecting the lowest and highest variation buckets, with 0.92 AUC and 0.89 AUC respectively. Our approach provides a simple way for prediction variation estimation, which opens up new opportunities for future work in many interesting areas (e.g.,model-based reinforcement learning) without relying on serving expensive ensemble models.

Every year, around 1.3 million people all over the world are killed by road mishaps with approximately 20 to 50 million life-threatening injuries(International Transport Forum, 2018; World Health Organisation, 2018). Notwithstanding, there is a disparity in road traffic death from 9.3 to 26.6 per 100,000 population among countries based on their income level, while the global rate is still 18.2 per 100,000 population (World Health Organisation, 2018). Moreover, traffic collision at intersections is a significant threat to upholding road safety. As a whole, 45% of severe injuries occur at intersections, including 22% of fatal crashes (Li, Jia, et al., 2016). Drivers often inadvertently fail to break immediately at the onset of red light or deliberately run through the red light signal and also miscalculate the motif of the right angle vehicle [in a right-hand driving condition] while crossing the intersection (Zhang et al., 2018). Especially at the onset of yellow signal, drivers get confused with decision measurement either to stop or to run and to get involved in rear-end collision or right-angle collision or uncomfortable hard brake, often resulting in injuries or death (Gazis et al., 1960; Majhi & Senathipathi, 2019).

This paper proposed a new estimation and control strategy to control the satellite attitude. As the attitude control strategy plays an essential role in the different kinds of space missions, scientists try to improve the performance of the satellite attitude system, regardless of the expense. In this study, we proposed an adaptive neuro-fuzzy integrated (ANFIS) satellite attitude estimation and control system. A pulse modulator is used to generate the right ON/OFF commands of the thruster actuator. To evaluate the performance of the ANFIS controller in closed-loop simulation, an ANFIS observer is used to estimate the attitude and angular velocities of the satellite using a magnetometer, sun sensor, and rate gyro data. Besides, a new ANFIS system will be proposed and evaluated that can simultaneously control and estimate the system. The performance of the ANFIS controller is compared with the optimal PID controller in a Monte Carlo simulation using different initial conditions, disturbance, and noise. The simulations are performed to verify the ANFIS controller's ability to decrease settling time and fuel consumption in comparison with the optimal PID controller. Also, examine the ANFIS estimator, and the results demonstrate the high skill of these designated observers. Moreover, we proposed an integrated ANFIS estimator and controller for satellite attitude control and estimation in the presence of noise and uncertainty, which can reduce the computational effort and offer smooth actuator actions.

In this paper we study weighted first-order model counting (WFOMC), which is an important problem (not only) because it can be used for probabilistic inference in most statistical relational learning models [Van den Broeck et al., 2011; Getoor and Taskar, 2007]. Probabilistic inference is in general intractable and the same holds for probabilistic inference in relational domains and therefore also for WFOMC. Lifted inference refers to a set of methods developed in the probabilistic inference literature which exploit structure and symmetries of the problems for making inference more tractable, e.g.

Due to data protection laws sensitive personal data cannot be released or shared among businesses as well as scientific institutions. While anonymization techniques are becoming increasingly popular, they often raise security concerns and have been re-identified in some cases Narayanan and Shmatikov (2010). To be on the safe side, big data collecting organisation such as Eurostat (statistical office of the European Union) or the World Bank only release aggregated summaries of their data. E.g.: Instead of individual salary data only selected quantiles of the population distribution are available. Thus, for exploratory analysis as well as statistical modeling, the need for methods which work on aggregated data is there.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem.

We propose VarFA, a variational inference factor analysis framework that extends existing factor analysis models for educational data mining to efficiently output uncertainty estimation in the model's estimated factors. Such uncertainty information is useful, for example, for an adaptive testing scenario, where additional tests can be administered if the model is not quite certain about a students' skill level estimation. Traditional Bayesian inference methods that produce such uncertainty information are computationally expensive and do not scale to large data sets. VarFA utilizes variational inference which makes it possible to efficiently perform Bayesian inference even on very large data sets. We use the sparse factor analysis model as a case study and demonstrate the efficacy of VarFA on both synthetic and real data sets. VarFA is also very general and can be applied to a wide array of factor analysis models.

To get Bayesian neural networks to perform comparably to standard neural networks it is usually necessary to artificially reduce uncertainty using a "tempered" or "cold" posterior. This is extremely concerning: if the prior is accurate, Bayes inference/decision theory is optimal, and any artificial changes to the posterior should harm performance. While this suggests that the prior may be at fault, here we argue that in fact, BNNs for image classification use the wrong likelihood. In particular, standard image benchmark datasets such as CIFAR-10 are carefully curated. We develop a generative model describing curation which gives a principled Bayesian account of cold posteriors, because the likelihood under this new generative model closely matches the tempered likelihoods used in past work.

Networks can describe the structure of a wide variety of complex systems by specifying how pairs of nodes interact. This choice of representation is flexible, but not necessarily appropriate when joint interactions between groups of nodes are needed to explain empirical phenomena. Networks remain the de facto standard, however, as relational datasets often fail to include higher-order interactions. Here, we introduce a Bayesian approach to reconstruct these missing higher-order interactions, from pairwise network data. Our method is based on the principle of parsimony and only includes higher-order structures when there is sufficient statistical evidence for them.