Kernel Belief Propagation

We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (Rd, strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results

Evaluation of the mechatronic systems reliability under parametric uncertainties

The main research intent of this paper is to evaluate the predicted reliability of mechatronic system, with take into account the epistemic uncertainties, The work reported here presents a new methodology based on integrating the petri network with the belief functions, in order to create a belief network, and to show how to propagate the parametric uncertainties in reliability models, Some notions of uncertainty related to the reliability systems are presented, subsequently a brief definition of the belief function and its application in reliability studies are detailed and how we integrate it in petri network. To take into account the interactive aspect of mechatronic systems, we introduce the uncertainties associated to this interaction, by implementing the new method proposed by using belief network. Secondly, we study the propagation of these interaction uncertainties in system reliability. Finally, in regard to applicate the methodology, an industrial example "intelligent actuator" is developed

Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)

We propose parametric constructive Kripke-semantics for multi-agent KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions of two basic functional building blocks, namely bias (or viewpoint) and visibility, functioning also as the parameters of the doxastic and epistemic accessibility relation. The doxastic accessibility relates two possible worlds whenever the application of the composition of bias with visibility to the first world is equal to the application of visibility to the second world. The epistemic accessibility is the transitive closure of the union of our doxastic accessibility and its converse. Therefrom, accessibility relations for common and distributed belief and knowledge can be constructed in a standard way. As a result, we obtain a general definition of knowledge in terms of belief that enables us to view S5-knowledge as accurate (unbiased and thus true) KD45-belief, negation-complete belief and knowledge as exact KD45-belief and S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and accurate) KD45-belief, and all this generically for arbitrary functions of bias and visibility. Our results can be seen as a semantic complement to previous foundational results by Halpern et al. about the (un)definability and (non-)reducibility of knowledge in terms of and to belief, respectively

Non Parametric Distributed Inference in Sensor Networks Using Box Particles Messages

This paper deals with the problem of inference in distributed systems where the probability model is stored in a distributed fashion. Graphical models provide powerful tools for modeling this kind of problems. Inspired by the box particle filter which combines interval analysis with particle filtering to solve temporal inference problems, this paper introduces a belief propagation-like message-passing algorithm that uses bounded error methods to solve the inference problem defined on an arbitrary graphical model. We show the theoretic derivation of the novel algorithm and we test its performance on the problem of calibration in wireless sensor networks. That is the positioning of a number of randomly deployed sensors, according to some reference defined by a set of anchor nodes for which the positions are known a priori. The new algorithm, while achieving a better or similar performance, offers impressive reduction of the information circulating in the network and the needed computation times

Semiparametric identification of structural dynamic optimal stopping time models

This paper presents new identification results for the class of structural dynamic optimal stopping time models that are built upon the framework of the structural discrete Markov decision processes proposed by Rust (1994). We demonstrate how to semiparametrically identify the deep structural parameters of interest in the case where the utility function of an absorbing choice in the model is parametric but the distribution of unobserved heterogeneity is nonparametric. Our identification strategy depends on availability of a continuous observed state variable that satisfies certain exclusion restrictions. If such excluded variable is accessible, we show that the dynamic optimal stopping model is semiparametrically identified using control function approaches

Parameter-Independent Strategies for pMDPs via POMDPs

Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition probabilities to account for stochastic uncertainties of the environment such as noise or input disturbances. We study pMDPs with reachability objectives where the parameter values are unknown and impossible to measure directly during execution, but there is a probability distribution known over the parameter values. We study for the first time computing parameter-independent strategies that are expectation optimal, i.e., optimize the expected reachability probability under the probability distribution over the parameters. We present an encoding of our problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem to computing optimal strategies in POMDPs. We evaluate our method experimentally on several benchmarks: a motivating (repeated) learner model; a series of benchmarks of varying configurations of a robot moving on a grid; and a consensus protocol.Comment: Extended version of a QEST 2018 pape

An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation

In this work we design a receiver that iteratively passes soft information between the channel estimation and data decoding stages. The receiver incorporates sparsity-based parametric channel estimation. State-of-the-art sparsity-based iterative receivers simplify the channel estimation problem by restricting the multipath delays to a grid. Our receiver does not impose such a restriction. As a result it does not suffer from the leakage effect, which destroys sparsity. Communication at near capacity rates in high SNR requires a large modulation order. Due to the close proximity of modulation symbols in such systems, the grid-based approximation is of insufficient accuracy. We show numerically that a state-of-the-art iterative receiver with grid-based sparse channel estimation exhibits a bit-error-rate floor in the high SNR regime. On the contrary, our receiver performs very close to the perfect channel state information bound for all SNR values. We also demonstrate both theoretically and numerically that parametric channel estimation works well in dense channels, i.e., when the number of multipath components is large and each individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin