The distribution semantics for normal programs with function symbols

The distribution semantics integrates logic programming and probability theory using a possible worlds approach. Its intuitiveness and simplicity have made it the most widely used semantics for probabilistic logic programming, with successful applications in many domains. When the program has function symbols, the semantics was defined for special cases: either the program has to be definite or the queries must have a finite number of finite explanations. In this paper we show that it is possible to define the semantics for all programs. We also show that this definition coincides with that of Sato and Kameya on positive programs. Moreover, we highlight possible approaches for inference, both exact and approximate.     

Optimal greedy policies for stochastic control models

We introduce the notion of a greedy policy for general stochastic control models. Sufficient conditions for the optimality of the greedy policy for finite and infinite horizon are given. Moreover, we derive error bounds if the greedy policy is not optimal. The main results are illustrated by Bayesian information models, discounted Bayesian search problems, stochastic scheduling problems, single-server queueing networks and deterministic dynamic programs.     

Imprecise probability models for learning multinomial distributions from data. Applications to learning credal networks

This paper considers the problem of learning multinomial distributions from a sample of independent observations. The Bayesian approach usually assumes a prior Dirichlet distribution about the probabilities of the different possible values. However, there is no consensus on the parameters of this Dirichlet distribution. Here, it will be shown that this is not a simple problem, providing examples in which different selection criteria are reasonable. To solve it the Imprecise Dirichlet Model (IDM) was introduced. But this model has important drawbacks, as the problems associated to learning from indirect observations. As an alternative approach, the Imprecise Sample Size Dirichlet Model (ISSDM) is introduced and its properties are studied. The prior distribution over the parameters of a multinomial distribution is the basis to learn Bayesian networks using Bayesian scores. Here, we will show that the ISSDM can be used to learn imprecise Bayesian networks, also called credal networks when all the distributions share a common graphical structure. Some experiments are reported on the use of the ISSDM to learn the structure of a graphical model and to build supervised classifiers.     

Bayesian Inference via Filtering for a Class of Counting Processes: Application to the Micromovement of Asset Price

This paper highlights recent developments in a rich class of counting process models for the micromovement of asset price and in the Bayesian inference (estimation and model selection) via filtering for the class of models. A specific micromovement model built upon linear Brownian motion with jumping stochastic volatility is used to demonstrate the procedure to develop a micromovement model with specific tick-level sample characteristics. The model is further used to demonstrate the procedure to implement Bayes estimation via filtering, namely, to construct a recursive algorithm for computing the trade-by-trade Bayes parameter estimates, especially for the stochastic volatility. The consistency of the recursive algorithm model is proven. Simulation and real-data examples are provided as well as a brief example of Bayesian model selection via filtering.     

Probabilistic abductive logic programming using Dirichlet priors

Probabilistic programming is an area of research that aims to develop general inference algorithms for probabilistic models expressed as probabilistic programs whose execution corresponds to inferring the parameters of those models. In this paper, we introduce a probabilistic programming language (PPL) based on abductive logic programming for performing inference in probabilistic models involving categorical distributions with Dirichlet priors. We encode these models as abductive logic programs enriched with probabilistic definitions and queries, and show how to execute and compile them to boolean formulas. Using the latter, we perform generalized inference using one of two proposed Markov Chain Monte Carlo (MCMC) sampling algorithms: an adaptation of uncollapsed Gibbs sampling from related work and a novel collapsed Gibbs sampling (CGS). We show that CGS converges faster than the uncollapsed version on a latent Dirichlet allocation (LDA) task using synthetic data. On similar data, we compare our PPL with LDA-specific algorithms and other PPLs. We find that all methods, except one, perform similarly and that the more expressive the PPL, the slower it is. We illustrate applications of our PPL on real data in two variants of LDA models (Seed and Cluster LDA), and in the repeated insertion model (RIM). In the latter, our PPL yields similar conclusions to inference with EM for Mallows models.     

Upper Limitation of Kolmogorov Complexity and Universal P. Martin-Löf Tests

In this paper we study the Kolmogorov complexity of initial strings in infinite sequences (being inspired by [9]), and we relate it with the theory of P. Martin-Lof random sequences. Working with partial recursive functions instead of recursive functions we can localize on an apriori given recursive set the points where the complexity is small. The relation between Kolmogorov's complexity and P. Martin-Lof's universal tests enables us to show that the randomness theories for finite strings and infinite sequences are not compatible (e.g.because no universal test is sequential).We lay stress upon the fact that we work within the general framework of a non-necessarily binary alphabet.     

Partially observable multistage stochastic programming

We propose a class of partially observable multistage stochastic programs and describe an algorithm for solving this class of problems. We provide a Bayesian update of a belief-state vector, extend the stochastic programming formulation to incorporate the belief state, and characterize saddle-function properties of the corresponding cost-to-go function. Our algorithm is a derivative of the stochastic dual dynamic programming method.     

Gated Bayesian networks for algorithmic trading

This paper introduces a new probabilistic graphical model called gated Bayesian network (GBN). This model evolved from the need to represent processes that include several distinct phases. In essence, a GBN is a model that combines several Bayesian networks (BNs) in such a manner that they may be active or inactive during queries to the model. We use objects called gates to combine BNs, and to activate and deactivate them when predefined logical statements are satisfied. In this paper we also present an algorithm for semi-automatic learning of GBNs. We use the algorithm to learn GBNs that output buy and sell decisions for use in algorithmic trading systems. We show how the learnt GBNs can substantially lower risk towards invested capital, while they at the same time generate similar or better rewards, compared to the benchmark investment strategy buy-and-hold. We also explore some differences and similarities between GBNs and other related formalisms.     

Multiagent bayesian forecasting of structural time-invariant dynamic systems with graphical models

Time series are found widely in engineering and science. We study forecasting of stochastic, dynamic systems based on observations from multivariate time series. We model the domain as a dynamic multiply sectioned Bayesian network (DMSBN) and populate the domain by a set of proprietary, cooperative agents. We propose an algorithm suite that allows the agents to perform one-step forecasts with distributed probabilistic inference. We show that as long as the DMSBN is structural time-invariant (possibly parametric time-variant), the forecast is exact and its time complexity is exponentially more efficient than using dynamic Bayesian networks (DBNs). In comparison with independent DBN-based agents, multiagent DMSBNs produce more accurate forecasts. The effectiveness of the framework is demonstrated through experiments on a supply chain testbed.     

An interactive approach for Bayesian network learning using domain/expert knowledge

Using domain/expert knowledge when learning Bayesian networks from data has been considered a promising idea since the very beginning of the field. However, in most of the previously proposed approaches, human experts do not play an active role in the learning process. Once their knowledge is elicited, they do not participate any more. The interactive approach for integrating domain/expert knowledge we propose in this work aims to be more efficient and effective. In contrast to previous approaches, our method performs an active interaction with the expert in order to guide the search based learning process. This method relies on identifying the edges of the graph structure which are more unreliable considering the information present in the learning data. Another contribution of our approach is the integration of domain/expert knowledge at different stages of the learning process of a Bayesian network: while learning the skeleton and when directing the edges of the directed acyclic graph structure.     

概率约束规划逼近最优解集的上半收敛性

本文讨论了概率约束规划目标函数的连续收敛性,并利用概率测度弱收敛的特征给出了概率约束规划可行集的收敛性条件,得到了概率约束规划逼近最优解集的上半收敛性.     

Towards a new theory of confirmation

Any sequence of events can be “explained” by any of an infinite number of hypotheses. Popper describes the “logic of discovery” as a process of choosing from a hierarchy of hypotheses the first hypothesis which is not at variance with the observed facts. Blum and Blum formalized these hierarchies of hypotheses as hierarchies of infinite binary sequences and imposed on them certain decidability conditions. In this paper we also consider hierarchies of infinite binary sequences but we impose only the most elementary Bayesian considerations. We use the structure of such hierarchies to define “confirmation”. We then suggest a definition of probability based on the amount of confirmation a particular hypothesis (i.e. pattern) has received. We show that hypothesis confirmation alone is a sound basis for determining probabilities and in particular that Carnap’s logical and empirical criteria for determining probabilities are consequences of the confirmation criterion in appropriate limiting cases.     

Ergodicity of Jackson-type queueing networks

This paper gives a pathwise construction of Jackson-type queueing networks allowing the derivation of stability and convergence theorems under general probabilistic assumptions on the driving sequences; namely, it is only assumed that the input process, the service sequences and the routing mechanism are jointly stationary and ergodic in a sense that is made precise in the paper. The main tools for these results are the subadditive ergodic theorem, which is used to derive a strong law of large numbers, and basic theorems on monotone stochastic recursive sequences. The techniques which are proposed here apply to other and more general classes of discrete event systems, like Petri nets or GSMPs. The paper also provides new results on the Jackson-type networks with i.i.d. driving sequences which were studied in the past.The work of this author was supported in part by a grant from the European Commission DG XIII, under the BRA Qmips contract.The work of this author was supported by a sabbatical grant from INRIA Sophia Antipolis.     

基于贝叶斯网络的多态故障树分析方法

针对多态系统故障树分析的难点,通过一个多态雷达系统的实例给出了一种基于贝叶斯网络的多态故障树分析方法.首先根据多态故障树的结构建立贝叶斯网络的拓扑结构,然后根据多态逻辑算子对其进行定量化,进而利用贝叶斯网络分析多态故障树顶事件概率、部件重要度及其它结果.最后通过对实例的分析说明了基于贝叶斯网络的多态故障树分析方法有更强的建模分析能力.     

Action-timing problem with sequential Bayesian belief revision process

We consider the problem of deciding the best action time when observations are made sequentially. Specifically we address a special type of optimal stopping problem where observations are made from state-contingent distributions and there exists uncertainty on the state. In this paper, the decision-maker's belief on state is revised sequentially based on the previous observations. By using the independence property of the observations from a given distribution, the sequential Bayesian belief revision process is represented as a simple recursive form. The methodology developed in this paper provides a new theoretical framework for addressing the uncertainty on state in the action-timing problem context. By conducting a simulation analysis, we demonstrate the value of applying Bayesian strategy which uses sequential belief revision process. In addition, we evaluate the value of perfect information to gain more insight on the effects of using Bayesian strategy in the problem.     

近似Bayes计算前沿研究进展及应用

在大数据和人工智能时代,建立能够有效处理复杂数据的模型和算法,以从数据中获取有用的信息和知识是应用数学、统计学和计算机科学面临的共同难题.为复杂数据建立生成模型并依据这些模型进行分析和推断是解决上述难题的一种有效手段.从一种宏观的视角来看,无论是应用数学中常用的微分方程和动力系统,或是统计学中表现为概率分布的统计模型,还是机器学习领域兴起的生成对抗网络和变分自编码器,都可以看作是一种广义的生成模型.随着所处理的数据规模越来越大,结构越来越复杂,在实际问题中所需要的生成模型也变得也越来越复杂,对这些生成模型的数学结构进行精确地解析刻画变得越来越困难.如何对没有精确解析形式（或其解析形式的精确计算非常困难）的生成模型进行有效的分析和推断,逐渐成为一个十分重要的问题.起源于Bayes统计推断,近似Bayes计算是一种可以免于计算似然函数的统计推断技术,近年来在复杂统计模型和生成模型的分析和推断中发挥了重要作用.该文从经典的近似Bayes计算方法出发,对近似Bayes计算方法的前沿研究进展进行了系统的综述,并对近似Bayes计算方法在复杂数据处理中的应用前景及其和前沿人工智能方法的深刻联系进行了分析和讨论.     

A visual programming system for defining behavior in simulation models of manufacturing systems

A visual programming system is described that allows the modeler full flexibility in defining the behavior of a manufacturing system simulation model. Decision-making behavior of objects in the simulation can be viewed by watching an animation of the system layout, viewing function block diagrams of rules that govern behavior, or noting the progress of an object in carrying out sequences of activities that are pictured as operation networks. Rules, elemental operations and operation networks are structured and associated with particular objects, groups of objects, and locations on the manufacturing system layout. The objective of this system is to reduce the time and expense required to construct and modify models, given that manufacturing system data have been collected.     

On categorical time series models with covariates

We study the problem of stationarity and ergodicity for autoregressive multinomial logistic time series models which possibly include a latent process and are defined by a GARCH-type recursive equation. We improve considerably upon the existing conditions about stationarity and ergodicity of those models. Proofs are based on theory developed for chains with complete connections. A useful coupling technique is employed for studying ergodicity of infinite order finite-state stochastic processes which generalize finite-state Markov chains. Furthermore, for the case of finite order Markov chains, we discuss ergodicity properties of a model which includes strongly exogenous but not necessarily bounded covariates.     

Convergence rates in monotone separable stochastic networks

We study bounds on the rate of convergence to the stationary distribution in monotone separable networks which are represented in terms of stochastic recursive sequences. Monotonicity properties of this subclass of Markov chains allow us to formulate conditions in terms of marginal network characteristics. Two particular examples, generalized Jackson networks and multiserver queues, are considered.