The 5G system should be flexible to cope with diversity of functions and infrastructure, in an efficient way while supporting a wide range of services associated with a set of requirements through Service Function Chaining (SFC). Fault management plays a paramount role to fulfill the SFC requirements towards reliability of telecommunication networks. Model-based (MB) approaches are knowledge-based systems that reason about a system from an explicit representation of its structure and functional behavior through a dependency model. MB techniques solve novel diagnosis problems and provide explanations for their decisions. However, current MB methods suffer from some limitations due to network virtualization challenges: lack of network visibility and dynamic topologies. To tackle those limitations, we propose a self-modeling approach and an active diagnosis process for virtual networks that considers two types of knowledge to build the model: acquired knowledge and learned knowledge provided by fault injection to expand and validate the proposed model. The experimental results from their application to a real-world virtual IP Multimedia Subsystem (vIMS) use case show that the self-modeling and the active diagnosis procedures are effective in determining the root cause(s) of a failure and explaining fault propagation.

Virtualization technologies become pervasive in networking, as a way to better exploit hardware capabilities and to quickly deploy tailored networking solutions for customers. But these new programmability abilities of networks also come with new management challenges: it is critical to quickly detect performance degradation, before they impact Quality of Service (QoS) or produce outages and alarms, as this takes part in the closed loop that adapts resources to services. This paper addresses the early detection, localization and identification of faults, before alarms are produced. We rely on the abundance of metrics available on virtualized networks, and explore various data preprocessing and classification techniques. As all Machine Learning approaches must be fed with large datasets, we turn to our advantage the softwarization of networks: one can easily deploy in a cloud the very same software that is used in production, and analyze its behaviour under stress, by fault injection.

We are interested in studying the evolution of large homogeneous populations of cells, where each cell is assumed to be composed of a group of biological players (species) whose dynamics is governed by a complex biological pathway, identical for all cells. Modeling the inherent variability of the species concentrations in different cells is crucial to understand the dynamics of the population. In this work, we focus on handling this variability by modeling each species by a random variable that evolves over time. This appealing approach runs into the curse of dimensionality since exactly representing a joint probability distribution involving a large set of random variables quickly becomes intractable as the number of variables grows. To make this approach amenable to biopathways, we explore different techniques to (i) approximate the exact joint distribution at a given time point, and (ii) to track its evolution as time elapses. We start with the problem of approximating the probability distribution of biological species in a population of cells at some given time point. Data come from different fine-grained models of biological pathways of increasing complexities, such as (perturbed) Ordinary Differential Equations (ODEs). Classical approximations rely on the strong and unrealistic assumption that variables/species are independent, or that they can be grouped into small independent clusters. We propose instead to use the Chow-Liu tree representation, based on overlapping clusters of two variables, which better captures correlations between variables. Our experiments show that the proposed approximation scheme is more accurate than existing ones to model probability distributions deriving from biopathways. Then we address the problem of tracking the dynamics of a population of cells, that is computing from an initial distribution the evolution of the (approximate) joint distribution of species over time, called the inference problem. We evaluate several approximate inference algorithms (e.g., [14] , [17] ) for coarse-grained abstractions [12], [16] of biological pathways. Using the Chow-Liu tree approximation, we develop a new inference algorithm which is very accurate according to the experiments we report, for a minimal computation overhead. Our implementation is available at https://codeocean.com/capsule/6491669/tree.

An important task in AI is one of classifying an observation as belonging to one class among several (e.g. image classification). We revisit this problem in a verification context: given k partially observable systems modeled as Hidden Markov Models (also called labeled Markov chains), and an execution of one of them, can we eventually classify which system performed this execution, just by looking at its observations? Interestingly, this problem generalizes several problems in verification and control, such as fault diagnosis and opacity. Also, classification has strong connections with different notions of distances between stochastic models. In this paper, we study a general and practical notion of classifiers, namely limit-sure classifiers, which allow misclassification, i.e. errors in classification, as long as the probability of misclassification tends to 0 as the length of the observation grows. To study the complexity of several notions of classification, we develop techniques based on a simple but powerful notion of stationary distributions for HMMs. We prove that one cannot classify among HMMs iff there is a finite separating word from their stationary distributions. This provides a direct proof that classifiability can be checked in PTIME, as an alternative to existing proofs using separating events (i.e. sets of infinite separating words) for the total variation distance. Our approach also allows us to introduce and tackle new notions of classifiability which are applicable in a security context.

Model based machine learning (MBML) techniques solve novel diagnosis problems and provide explanations for their decisions. However, current MBMLs suffer some limitations, since virtualization of network brings new challenges such as the dynamic topology and elasticity. Those limitations include the high dependency on previous knowledge and the difficulty to represent the model. To face those limitations, we propose SAKURA: a root cause analysis framework for the virtual Ip Multimedia Subsystem (vIMS). SAKURA is composed of a self-modeling and a constraints solver.

The advent of 5G and the ever increasing stringent requirements in terms of bandwidth, latency, and quality of service pushes the boundaries of what is feasible with legacy Mobile Network Operators' technologies. Network Functions Virtualization (NFV) is a promising attempt at solving some of these challenges that is widely adopted by the industry and specified by the standardization bodies. In essence, NFV is about running Network Functions (NFs) as virtualized workloads on commodity hardware. This may optimize deployment costs and simplify the lifecycle management of NFs, but it introduces new fault management challenges and issues. In this paper, we propose a comprehensive state of the art of fault management techniques. We address the impact of virtualization in fault management. We propose a new classification of the recent fault management research achievements in the network virtualization environments and compare their major contributions and shortcomings.

We study quantitative properties of the response time in stochastic models. For instance, we are interested in quantifying bounds such that a high percentage of the runs answers a query within these bounds. To study such problems, computing probabilities on a state-space blown-up by a factor depending on the bound could be used, but this solution is not satisfactory when the bound is large. In this paper, we propose a new symbolic method to quantify bounds on the response time, using the moments of the distribution of simple stochastic systems. We prove that the distribution (and hence the bounds) is uniquely defined given its moments. We provide optimal bounds for the response time over all distributions having a pair of these moments. We explain how to symbolically compute in polynomial time any moment of the distribution of response times using adequately-defined semirings. This allows us to compute optimal bounds in parametric models and to reduce complexity for computing optimal bounds in hierarchical models. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

MOTIVATION: Quantitative models are increasingly used in systems biology. Usually, these quantitative models involve many molecular species and their associated reactions. When simulating a tissue with thousands of cells, using these large models becomes computationally and time limiting. RESULTS: In this paper, we propose to construct abstractions using information theory notions. Entropy is used to discretize the state space and mutual information is used to select a subset of all original variables and their mutual dependencies. We apply our method to an hybrid model of TRAIL-induced apoptosis in HeLa cell. Our abstraction, represented as a Dynamic Bayesian Network (DBN), reduces the number of variables from 92 to 10, and accelerates numerical simulation by an order of magnitude, yet preserving essential features of cell death time distributions. AVAILABILITY AND IMPLEMENTATION: This approach is implemented in the tool DBNizer, freely available at http://perso.crans.org/genest/DBNizer . CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

This paper proposes an approach to solve cost-optimal factored planning problems. Planning consists in organizing actions in order to reach some predefined goal. In factored planning one considers several interacting planning problems and has to design an action plan for each of them. But one must also guarantee that all these local plans are compatible: actions shared among several problems must be jointly performed or jointly rejected. We enrich the problem with the extra requirement that the global plan computed in this modular manner must also minimize the sum of all action costs. A solution is provided to this problem, based on classical message passing algorithms, known as belief propagation in the setting of Bayesian networks. Here, messages carry complex information under the form of weighted (or (min; +)) automata, and all computations are performed with these objects. At the time our first paper on this topic was published, this method was the only one to solve cost-optimal factored planning problems in a modular way. Since then, new approaches were proposed. Experiments on classical benchmarks show that it is a valuable alternative to existing methods.

Factored planning mitigates the state explosion problem by avoiding the construction of the state space of the whole system and instead working with the system's components. Traditionally, finite automata have been used to represent the components, with the overall system being represented as their product. In this article, we change the representation of components to safe Petri nets. This allows one to use cheap structural operations like transition contractions to reduce the size of the Petri net before its state space is generated, which often leads to substantial savings compared with automata. The proposed approach has been implemented and proved efficient on several factored planning benchmarks. This article is an extended version of our ACSD 2013 paper [Jezequel et al. 2013], with the addition of the proofs and the experimental results of Sections 6 and 7.

This paper considers distributed systems, defined as a collection of components interacting through interfaces. Components, interfaces and distributed systems are modeled as Petri nets. It is well known that the unfolding of such a distributed system factorises, in the sense that it can be expressed as the composition of unfoldings of its components. This factorised form of the unfolding generally provides a more compact representation of the system runs, because each component does not need to represent the possible choices (conflicts) appearing in the other components. Moreover, the unfolding factorisation makes it possible to analyse the system by parts. The paper focuses on the derivation of a finite and complete prefix (FCP) in the unfolding of a distributed system. Specifically, one would like to directly obtain such a FCP in factorised form, without computing first a FCP of the global distributed system and then factorising it. The construction of such a "modular FCP" is based on deriving summaries of component behaviours w.r.t. their interfaces, that are then communicated to the neighbouring components. The latter combine these summaries with their local behaviours, and prepare interface summaries for the next components. This globally takes the form of a message passing algorithm, where the global system is never considered.

In this paper, we present a low complexity code design for the 2-user Gaussian multiple access channels. In order to analyze this multiuser MAC decoder, we formulate density evolution (DE) and study the stability condition of the fixed point corresponding to zero BER.

A multiple description scalar quantization (MDSQ) based coding system can be regarded as a source coder (quantizer) followed by a channel coder, i.e. the combination of index and codeword assignment. The redundancy, or the correlation between the descriptions, is controlled by the number of diagonals covered by the index assignment. In this paper, we analyse dependencies between the variables involved in the MDSQ coding chain and design an estimation strategy making use of part of the global model of dependencies at each time. Inference of the hidden states of the connected models is done by applying belief propagation principles on the resulting Bayesian network. We try to evidence the most appropriate form of redundancy one should introduce in the context of variable length code compressed streams in order to fight against de-synchronizations when impaired by channel noise.

We analyse the dependencies between the variables involved in the source and channel coding chain. This chain is composed of (1) a Markov source of symbols, followed by (2) a variable length source coder, and (3) a channel coder. The output process is analysed in the framework of Bayesian networks, which provide both an intuitive representation of the structure of dependencies, and a way of deriving joint (soft) decoding algorithms. Joint decoding relying on the hidden Markov model (HMM) of the global coding chain is intractable, except in trivial cases, due to the high dimensionality of the state space. We advocate instead an iterative procedure inspired from serial turbo codes, in which the three models of the coding chain are used alternately. This idea of using separately each factor of a big product model inside an iterative procedure usually requires the presence of an interleaver between successive components. We show that only one interleaver is necessary here, placed between the source coder and the channel coder. As a sub-product, we also derive a soft VLC decoder with good (and adjustable) synchronization properties.

We analyze the dependencies between the variables involved in the source and channel coding chain. This analysis is carried out in the framework of Bayesian networks, which provide both an intuitive representation for the global model of the coding chain and a way of deriving joint (soft) decoding algorithms. Three sources of dependencies are involved in the chain: (1) the source model, a Markov chain of symbols; (2) the source coder model, based on a variable length code (VLC), for example a Huffman code; and (3) the channel coder, based on a convolutional error correcting code. Joint decoding relying on the hidden Markov model (HMM) of the global coding chain is intractable, except in trivial cases. We advocate instead an iterative procedure inspired from serial turbo codes, in which the three models of the coding chain are used alternately. This idea of using separately each factor of a big product model inside an iterative procedure usually requires the presence of an interleaver between successive components. We show that only one interleaver is necessary here, placed between the source coder and the channel coder. The decoding scheme we propose can be viewed as a turbo algorithm using alternately the intersymbol correlation due to the Markov source and the redundancy introduced by the channel code. The intermediary element, the source coder model, is used as a translator of soft information from the bit clock to the symbol clock.

This paper presents a class of nonlinear hierarchical algorithms for the fusion of multiresolution image data in low-level vision. The approach combines nonlinear causal Markov models defined on hierarchical graph structures, with standard bayesian estimation theory. Two random processes defined on simple hierarchical graphs (quadtrees or "ternary graphs") are introduced to represent the multiresolution observations at hand and the hidden labels to be estimated. An optimal algorithm (inspired from the Viterbi algorithm) is developed to compute the bayesian estimates on the hierarchical graph structures. Estimates are obtained within two passes on the graph structure. This algorithm is non-iterative and yields a per pixel computational complexity which is independent of image size. This approach is compared to the multiscale algorithm proposed by (Bouman et al., 1994) for single-resolution image segmentation (that we have extended for multiresolution data fusion).>