Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforward to implement. There are a number of limitations in existing approaches to marginalize over multiplicative errors, such as positivity of the multiplicative noise term. The focus in this paper is in large dimensional (inverse) problems for which sampling type approaches have too high computational complexity. In this paper, we propose an alternative approach to carry out approximative marginalization over the multiplicative error by embedding the statistics in an additive error term. The approach is essentially a Bayesian one in that the statistics of the additive error is induced by the statistics of the other unknowns. As an example, we consider a deconvolution problem on random fields with different statistics of the multiplicative noise. Furthermore, the approach allows for correlated multiplicative noise. We show that the proposed approach provides feasible error estimates in the sense that the posterior models support the actual image.

We report a procedure that, in one step from continuous data with minimal preparation, recovers the graph found by Sachs et al. \cite{sachs2005causal}, with only a few edges different. The algorithm, Fast Adjacency Skewness (FASK), relies on a mixture of linear reasoning and reasoning from the skewness of variables; the Sachs data is a good candidate for this procedure since the skewness of the variables is quite pronounced. We review the ground truth model from Sachs et al. as well as some of the fluctuations seen in the protein abundances in the system, give the Sachs model and the FASK model, and perform a detailed comparison. Some variation in hyper-parameters is explored, though the main result uses values at or near the defaults learned from work modeling fMRI data.

The system's ability to adapt and self-organize are two key factors when it comes to how well the system can survive the changes to the environment and the plant they work within. Intelligent control improves these two factors in controllers. Considering the increasing complexity of dynamic systems along with their need for feedback controls, using more complicated controls has become necessary and intelligent control can be a suitable response to this necessity. This paper briefly describes the structure of intelligent control and provides a review on fuzzy logic and neural networks which are some of the base methods for intelligent control. The different aspects of these two methods are then compared together and an example of a combined method is presented.

Conceptual formalism supported by typical ontologies may not be sufficient to represent uncertainty information which is caused due to the lack of clear cut boundaries between concepts of a domain. Fuzzy ontologies are proposed to offer a way to deal with this uncertainty. This paper describes the state of the art in developing fuzzy ontologies. The survey is produced by studying about 35 works on developing fuzzy ontologies from a batch of 100 articles in the field of fuzzy ontologies. 1. Introduction Ontology is an explicit, formal specification of a shared conceptualization in a human understandable, machinereadable format. Ontologies are the knowledge backbone for many intelligent and knowledge based systems [1, 2].

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian standpoint, we investigate the MAP (maximum a posteriori) estimator from a penalized likelihood perspective that gives rise to a new non-convex penalty approximating the $\ell_0$ penalty. Optimal error rates for estimation consistency in terms of various matrix norms along with selection consistency for sparse structure recovery are shown for the unique MAP estimator under mild conditions. For fast and efficient computation, an EM algorithm is proposed to compute the MAP estimator of the precision matrix and (approximate) posterior probabilities on the edges of the underlying sparse structure. Through extensive simulation studies and a real application to a call center data, we have demonstrated the fine performance of our method compared with existing alternatives.

Semi-supervised learning (SSL) has become important in current data analysis applications, where the amount of unlabeled data is growing exponentially and user input remains limited by logistics and expense. Constrained clustering, as a subclass of SSL, makes use of user input in the form of relationships between data points (e.g., pairs of data points belonging to the same class or different classes) and can remarkably improve the performance of unsupervised clustering in order to reflect user-defined knowledge of the relationships between particular data points. Existing algorithms incorporate such user input, heuristically, as either hard constraints or soft penalties, which are separate from any generative or statistical aspect of the clustering model; this results in formulations that are suboptimal and not sufficiently general. In this paper, we propose a principled, generative approach to probabilistically model, without ad hoc penalties, the joint distribution given by user-defined pairwise relations. The proposed model accounts for general underlying distributions without assuming a specific form and relies on expectation-maximization for model fitting. For distributions in a standard form, the proposed approach results in a closed-form solution for updated parameters.

Causal processes in nature may contain cycles, and real datasets may violate causal sufficiency as well as contain selection bias. No constraint-based causal discovery algorithm can currently handle cycles, latent variables and selection bias (CLS) simultaneously. I therefore introduce an algorithm called Cyclic Causal Inference (CCI) that makes sound inferences with a conditional independence oracle under CLS, provided that we can represent the cyclic causal process as a non-recursive linear structural equation model with independent errors. Empirical results show that CCI outperforms CCD in the cyclic case as well as rivals FCI and RFCI in the acyclic case. 1. The Problem Scientists often infer causation using data collected from randomized controlled experiments. However, randomized experiments can be slow, nongeneralizable, unethical or expensive. Consider for example trying to discover the causes of a human illness, a common scenario in modern medical science. Performing interventions with possibly harmful consequences on humans is unethical, so scientists often perform experiments on animals instead knowing full well that the causal relationships discovered in animals may not generalize to humans. Moreover, many possible causes for an illness often exist, so scientists typically perform numerous animal experiments in order to discover the causes.

We propose a generic, Bayesian, information geometric approach to the exploration--exploitation trade-off in multi-armed bandit problems. Our approach, BelMan, uniformly supports pure exploration, exploration--exploitation, and two-phase bandit problems. The knowledge on bandit arms and their reward distributions is summarised by the barycentre of the joint distributions of beliefs and rewards of the arms, the \emph{pseudobelief-reward}, within the beliefs-rewards manifold. BelMan alternates \emph{information projection} and \emph{reverse information projection}, i.e., projection of the pseudobelief-reward onto beliefs-rewards to choose the arm to play, and projection of the resulting beliefs-rewards onto the pseudobelief-reward. It introduces a mechanism that infuses an exploitative bias by means of a \emph{focal distribution}, i.e., a reward distribution that gradually concentrates on higher rewards. Comparative performance evaluation with state-of-the-art algorithms shows that BelMan is not only competitive but can also outperform other approaches in specific setups, for instance involving many arms and continuous rewards.

Several recently proposed methods aim to learn conceptual space representations from large text collections. These learned representations asso- ciate each object from a given domain of interest with a point in a high-dimensional Euclidean space, but they do not model the concepts from this do- main, and can thus not directly be used for catego- rization and related cognitive tasks. A natural solu- tion is to represent concepts as Gaussians, learned from the representations of their instances, but this can only be reliably done if sufficiently many in- stances are given, which is often not the case. In this paper, we introduce a Bayesian model which addresses this problem by constructing informative priors from background knowledge about how the concepts of interest are interrelated with each other. We show that this leads to substantially better pre- dictions in a knowledge base completion task.

One principle way to measure the uncertainty or confidence of the prediction is based on the statistic such as predictive mean, entropy and variance, using Bayesian machine learning, i.e. BNN if our model is a DNN[Nea12]. Beside capturing the parameters uncertainty, other methods works with modifying the loss function [DT18], [KG17], by which the model attempts to learn the heteroscedastic aleatoric uncertainty, i.e. uncertainty that depends on the input data (e.g. if there is an occlusion on the image object, our model will less likely to produce accurate prediction so we train our model such that it recognize "occlusion"). Experiments in previous paper [RBB18], [LPB17], the estimated predictive posterior is used to detect out-of-distribution data, or data from unknown class by measuring the its statistics. In other words, they expect data from unknown class to have high entropy and variance by using BNN.