Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related problem, that is, the problem of finding a set of sufficiently dissimilar, yet all plausible, explanations. Applications of this problem are, e.g., in search query results (you won't want 10 results that all link to the same website) or in decision support systems. We show that the problem of finding a 'good enough' explanation that differs in structure from the best explanation is at least as hard as finding the best explanation itself.

Abstract--In this paper we consider the problem of modelbased learningof turbulent flows using mobile robots. The key idea is to use empirical data to improve on numerical estimates of time-averaged flow properties that can be obtained using Reynolds-Averaged Navier Stokes (RANS) models. RANS models are computationally efficient and provide global knowledge of the flow but they also rely on simplifying assumptions and require experimental validation. In this paper, we instead construct statistical models of the flow properties using Gaussian Processes (GPs) and rely on the numerical solutions obtained from RANS models to inform their mean. We then utilize Bayesian inference to incorporate empirical measurements of the flow into these GPs, specifically, measurements of the time-averaged velocity and turbulent intensity fields. Moreover, it accounts for measurement noise by systematically incorporating it in the GP models. To obtain the velocity and turbulent intensity measurements, we design a cost-effective mobile robot sensor that collects and analyzes instantaneous velocity readings. We control this mobile robot through a sequence of waypoints that maximize the information content of the corresponding measurements. The end result is a posterior distribution of the flow field that better approximates the real flow and also quantifies the uncertainty in the flow properties. We present experimental results that demonstrate considerable improvement in the prediction of the flow properties compared to pure numerical simulations. I. INTRODUCTION Knowledge of turbulent flow properties, e.g., velocity and turbulent intensity, is of paramount importance for many engineering applications.At larger scales, these properties are used for the study of ocean currents and their effects on aquatic life, [1], [2], [3], meteorology, [4], bathymetry, [5], and localization of atmospheric pollutants, [6], to name a few. At smaller scales, knowledge of flow fields is important in applications ranging from optimal HVAC of residential buildings for human comfort, [7], to design of drag-efficient bodies in aerospace and automotive industries, [8]. At even smaller scales, the characteristics of velocity fluctuations in vessels are important for vascular pathology and diagnosis, [9] or for the control of bacteria-inspired uniflagellar robots, [10]. Another important application that requires global knowledge of the velocity field is chemical source identification in advection-diffusion transport systems, [11], [12], [13].

Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The field's progression is hampered by the lack of robust software to estimate the numerous parameters of the speciation process. In this work we present an R package, pcmabc, based on Approximate Bayesian Computations, that implements three novel phylogenetic algorithms for trait-dependent speciation modelling. Our phylogenetic comparative methodology takes into account both the simulated traits and phylogeny, attempting to estimate the parameters of the processes generating the phenotype and the trait. The user is not restricted to a predefined set of models and can specify a variety of evolutionary and branching models. We illustrate the software with a simulation-reestimation study focused around the branching Ornstein-Uhlenbeck process, where the branching rate depends non-linearly on the value of the driving Ornstein-Uhlenbeck process. Included in this work is a tutorial on how to use the software.

Robots are increasingly used to carry out critical missions in extreme environments that are hazardous for humans. This requires a high degree of operational autonomy under uncertain conditions, and poses new challenges for assuring the robot's safety and reliability. In this paper, we develop a framework for probabilistic model checking on a layered Markov model to verify the safety and reliability requirements of such robots, both at pre-mission stage and during runtime. Two novel estimators based on conservative Bayesian inference and imprecise probability model with sets of priors are introduced to learn the unknown transition parameters from operational data. We demonstrate our approach using data from a real-world deployment of unmanned underwater vehicles in extreme environments.

Tasks such as social network analysis, human behavior recognition, or modeling biochemical reactions, can be solved elegantly by using the probabilistic inference framework. However, standard probabilistic inference algorithms work at a propositional level, and thus cannot capture the symmetries and redundancies that are present in these tasks. Algorithms that exploit those symmetries have been devised in different research fields, for example by the lifted inference-, multiple object tracking-, and modeling and simulation-communities. The common idea, that we call state space abstraction, is to perform inference over compact representations of sets of symmetric states. Although they are concerned with a similar topic, the relationship between these approaches has not been investigated systematically. This survey provides the following contributions. We perform a systematic literature review to outline the state of the art in probabilistic inference methods exploiting symmetries. From an initial set of more than 4,000 papers, we identify 116 relevant papers. Furthermore, we provide new high-level categories that classify the approaches, based on common properties of the approaches. The research areas underlying each of the categories are introduced concisely. Researchers from different fields that are confronted with a state space explosion problem in a probabilistic system can use this classification to identify possible solutions. Finally, based on this conceptualization, we identify potentials for future research, as some relevant application domains are not addressed by current approaches.

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the system states and the transition function. We exploit Markov structure in the true posterior, as well as an inducing point approximation to achieve linear time complexity in the length of the time series. Contrary to previous approaches, no Monte Carlo sampling is required: inference is cast as a deterministic optimisation problem. In a number of experiments, we demonstrate the ability to model non-linear dynamics in the presence of both process and observation noise as well as to impute missing information (e.g. velocities from raw positions through time), to de-noise, and to estimate the underlying dimensionality of the system. Finally, we also introduce a closed-form method for multi-step prediction, and a novel criterion for assessing the quality of our approximate posterior.

Traditional model-based RL relies on hand-specified or learned models of transition dynamics of the environment. These methods are sample efficient and facilitate learning in the real world but fail to generalize to subtle variations in the underlying dynamics, e.g., due to differences in mass, friction, or actuators across robotic agents or across time. We propose using variational inference to learn an explicit latent representation of unknown environment properties that accelerates learning and facilitates generalization on novel environments at test time. We use Online Bayesian Inference of these learned latents to rapidly adapt online to changes in environments without retaining large replay buffers of recent data. Combined with a neural network ensemble that models dynamics and captures uncertainty over dynamics, our approach demonstrates positive transfer during training and online adaptation on the continuous control task HalfCheetah.

Faces play a magnificent role in human robot interaction, as they do in our daily life. The inherent ability of the human mind facilitates us to recognize a person by exploiting various challenges such as bad illumination, occlusions, pose variation etc. which are involved in face recognition. But it is a very complex task in nature to identify a human face by humanoid robots. The recent literatures on face biometric recognition are extremely rich in its application on structured environment for solving human identification problem. But the application of face biometric on mobile robotics is limited for its inability to produce accurate identification in uneven circumstances. The existing face recognition problem has been tackled with our proposed component based fragmented face recognition framework. The proposed framework uses only a subset of the full face such as eyes, nose and mouth to recognize a person. It's less searching cost, encouraging accuracy and ability to handle various challenges of face recognition offers its applicability on humanoid robots. The second problem in face recognition is the face spoofing, in which a face recognition system is not able to distinguish between a person and an imposter (photo/video of the genuine user). The problem will become more detrimental when robots are used as an authenticator. A depth analysis method has been investigated in our research work to test the liveness of imposters to discriminate them from the legitimate users. The implication of the previous earned techniques has been used with respect to criminal identification with NAO robot. An eyewitness can interact with NAO through a user interface. NAO asks several questions about the suspect, such as age, height, her/his facial shape and size etc., and then making a guess about her/his face.

Deep neural networks(NNs) have achieved impressive performance, often exceed human performance on many computer vision tasks. However, one of the most challenging issues that still remains is that NNs are overconfident in their predictions, which can be very harmful when this arises in safety critical applications. In this paper, we show that predictive uncertainty can be efficiently estimated when we incorporate the concept of gradients uncertainty into posterior sampling. The proposed method is tested on two different datasets, MNIST for in-distribution confusing examples and notMNIST for out-of-distribution data. We show that our method is able to efficiently represent predictive uncertainty on both datasets.

Abstract-- In an automated search system, similarity is a key concept in solving a human task. Indeed, human process is usually a natural categorization that underlies many natural abilities such as image recovery, language comprehension, decision making, or pattern recognition. In the image search axis, there are several ways to measure the similarity between images in an image database, to a query image. Image search by content is based on the similarity of the visual characteristics of the images. The distance function used to evaluate the similarity between images depends on the criteria of the search but also on the representation of the characteristics of the image; this is the main idea of the near and fuzzy sets approaches. In this article, we introduce a new category of beta type-2 fuzzy sets for the description of image characteristics as well as the near sets approach for image recovery. Finally, we illustrate our work with examples of image recovery problems used in the real world. I. INTRODUCTION He number of daily-generated images by websites and personal archives are constantly growing. Indeed, the effective management of the rapid expansion of visual information has become a major problem and a necessity for strengthening visual search technique based on visual content [3]. This necessity is behind the emergence of new visual search techniques based on visual content. It has been widely identified that the most efficient and intuitive way to research visual information is based on the properties that are extracted from the images themselves. Researchers from different communities ("Computer Vision" [4], "Database Management", "Man-machine Interface", "Information Retrieval") were attracted by this field. Since then, the search for images by content has developed quite rapidly. The intuitive idea of "any system that analyzes or automatically organizes a set of data or knowledge must use, in one form or another, a similarity operator whose purpose is to establish similarities or the relationships that exist between the manipulated information".