Complex Probabilistic Modeling with Recursive Relational Bayesian Networks

A number of representation systems have been proposed that extend the purely propositional Bayesian network paradigm with representation tools for some types of first-order probabilistic dependencies. Examples of such systems are dynamic Bayesian networks and systems for knowledge based model construction. We can identify the representation of probabilistic relational models as a common well-defined semantic core of such systems.Recursive relational Bayesian networks (RRBNs) are a framework for the representation of probabilistic relational models. A main design goal for RRBNs is to achieve greatest possible expressiveness with as few elementary syntactic constructs as possible. The advantage of such an approach is that a system based on a small number of elementary constructs will be much more amenable to a thorough mathematical investigation of its semantic and algorithmic properties than a system based on a larger number of high-level constructs. In this paper we show that with RRBNs we have achieved our goal, by showing, first, how to solve within that framework a number of non-trivial representation problems. In the second part of the paper we show how to construct from a RRBN and a specific query, a standard Bayesian network in which the answer to the query can be computed with standard inference algorithms. Here the simplicity of the underlying representation framework greatly facilitates the development of simple algorithms and correctness proofs. As a result we obtain a construction algorithm that even for RRBNs that represent models for complex first-order and statistical dependencies generates standard Bayesian networks of size polynomial in the size of the domain given in a specific application instance.     

Generic causal probabilistic networks: a solution to a problem of transferability in medical decision support

Causal probabilistic networks provide a natural framework for representation of medical knowledge, allowing clinical experts to encode assumptions about causal dependencies between stochastic variables. Application in medical decision support has produced promising results. However, model features and parameters may vary geo- or demographically. Therefore methods are needed that allow for easy adjustment of the model to a change in conditions. We present a method to represent causal probabilistic networks generically that maximizes the transferability of a models relevance and completeness, when moved from one environment to another, and illustrate application of the method with an example from a medical decision support system.     

概率生成模型变分推理方法综述

概率生成模型是知识表示的重要方法,在该模型上计算似然函数的概率推理问题一般是难解的.变分推理是重要的确定性近似推理方法,具有较快的收敛速度、坚实的理论基础．尤其随着大数据时代的到来,概率生成模型变分推理方法受到工业界和学术界的极大关注.综述了多种概率生成模型变分推理框架及最新进展,具体包括：首先综述了概率生成模型变分推理一般框架及基于变分推理的生成模型参数学习过程;然后对于条件共轭指数族分布,给出了具有解析优化式的变分推理框架及该框架下可扩展的随机化变分推理;进一步,对于一般概率分布,给出了基于随机梯度的黑盒变分推理框架,并简述了该框架下多种变分推理算法的具体实现;最后分析了结构化变分推理,通过不同方式丰富变分分布提高推理精度并改善近似推理一致性.此外,展望了概率生成模型变分推理的发展趋势.     

概率逻辑模型与学习研究进展

近年来,概率逻辑学习研究取得了很大进展,已经提出各种不同的形式化方法和学习方法,包括概率关系模（PRMs）、贝叶斯逻辑程序（BLPs）、逻辑贝叶斯网络（LBNs）和随机逻辑程序（SLPs）等。文章重点介绍了贝叶斯网络与一阶逻辑的结合,并以PRMs、BLPs和LBNs为例,描述了基于贝叶斯网络的概率逻辑模型（PLMs）的知识表示方法,给出了此类PLMs一般使用的参数估计方法和结构学习方法,并给出了建议的研究方向。     

Factorial Hidden Markov Models

Hidden Markov models (HMMs) have proven to be one of the most widely used tools for learning probabilistic models of time series data. In an HMM, information about the past is conveyed through a single discrete variable—the hidden state. We discuss a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. We describe an exact algorithm for inferring the posterior probabilities of the hidden state variables given the observations, and relate it to the forward–backward algorithm for HMMs and to algorithms for more general graphical models. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or variational methods. Within the variational framework, we present a structured approximation in which the the state variables are decoupled, yielding a tractable algorithm for learning the parameters of the model. Empirical comparisons suggest that these approximations are efficient and provide accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach's chorales and show that factorial HMMs can capture statistical structure in this data set which an unconstrained HMM cannot.     

Generalized ordering-search for learning directed probabilistic logical models

Recently, there has been an increasing interest in directed probabilistic logical models and a variety of formalisms for describing such models has been proposed. Although many authors provide high-level arguments to show that in principle models in their formalism can be learned from data, most of the proposed learning algorithms have not yet been studied in detail. We introduce an algorithm, generalized ordering-search, to learn both structure and conditional probability distributions (CPDs) of directed probabilistic logical models. The algorithm is based on the ordering-search algorithm for Bayesian networks. We use relational probability trees as a representation for the CPDs. We present experiments on a genetics domain, blocks world domains and the Cora dataset. Editors: Stephen Muggleton, Ramon Otero, Simon Colton.     

Mixed Memory Markov Models: Decomposing Complex Stochastic Processes as Mixtures of Simpler Ones

We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combination—or mixture—of simpler dynamical models. The parameters in these models admit a simple probabilistic interpretation and can be fitted iteratively by an Expectation-Maximization (EM) procedure. We derive a set of generalized Baum-Welch updates for factorial hidden Markov models that make use of this parameterization. We also describe a simple iterative procedure for approximately computing the statistics of the hidden states. Throughout, we give examples where mixed memory models provide a useful representation of complex stochastic processes.     

A Hybrid Framework for Mobile Robot Localization: Formulation Using Switching State-Space Models

In this paper we address one of the most important issues for autonomous mobile robots, namely their ability to localize themselves safely and reliably within their environments. We propose a probabilistic framework for modelling the robot's state and sensory information based on a Switching State-Space Model. The proposed framework generalizes two of the most successful probabilistic model families currently used for this purpose: the Kalman filter Linear models and the Hidden Markov Models. The proposed model combines the advantages of both models, relaxing at the same time inherent assumptions made individually in each of these existing models.     

一种实数编码多目标贝叶斯优化算法

提出了一种采用基于决策树概率模型表示各变量之间条件相关性的分布估算算法:实数编码多目标贝叶斯优化算法(RCMBOA)。通过构建这样的概率模型,继而对模型进行抽样以产生新个体。再对生成的新个体进行变异操作,以提高算法的搜索能力,增加种群的多样性。这种生成新个体的方法结合非劣分层与截断选择机制,可以很好地逼近多目标问题的Pareto前沿。同时,在进行截断选择时,每次只删除一个排挤距离小的个体,之后重新估算个体的排挤距离,以获得分布均匀的非劣解集。对于约束多目标优化问题,算法采用带约束支配关系判别个体的优劣。用该算法对8个较难的测试问题进行了优化计算,获得的非劣解集与NSGA-II算法得到的相比,非劣解集的质量更高,分布更为均匀。计算结果说明RCMBOA是一种有效、鲁棒的多目标优化算法。     

概率图模型学习技术研究进展

概率图模型能有效处理不确定性推理,从样本数据中准确高效地学习概率图模型是其在实际应用中的关键问题.概率图模型的表示由参数和结构两部分组成,其学习算法也相应分为参数学习与结构学习.本文详细介绍了基于概率图模型网络的参数学习与结构学习算法,并根据数据集是否完备而分别讨论各种情况下的参数学习算法,还针对结构学习算法特点的不同把结构学习算法归纳为基于约束的学习、基于评分搜索的学习、混合学习、动态规划结构学习、模型平均结构学习和不完备数据集的结构学习.并总结了马尔科夫网络的参数学习与结构学习算法.最后指出了概率图模型学习的开放性问题以及进一步的研究方向.     

Data-efficient learning of robotic clothing assistance using Bayesian Gaussian process latent variable model

ABSTRACT

Motor-skill learning for complex robotic tasks is a challenging problem due to the high task variability. Robotic clothing assistance is one such challenging problem that can greatly improve the quality-of-life for the elderly and disabled. In this study, we propose a data-efficient representation to encode task-specific motor-skills of the robot using Bayesian nonparametric latent variable models. The effectivity of the proposed motor-skill representation is demonstrated in two ways: (1) through a real-time controller that can be used as a tool for learning from demonstration to impart novel skills to the robot and (2) by demonstrating that policy search reinforcement learning in such a task-specific latent space outperforms learning in the high-dimensional joint configuration space of the robot. We implement our proposed framework in a practical setting with a dual-arm robot performing clothing assistance tasks.     

OctoMap: an efficient probabilistic 3D mapping framework based on octrees

Three-dimensional models provide a volumetric representation of space which is important for a variety of robotic applications including flying robots and robots that are equipped with manipulators. In this paper, we present an open-source framework to generate volumetric 3D environment models. Our mapping approach is based on octrees and uses probabilistic occupancy estimation. It explicitly represents not only occupied space, but also free and unknown areas. Furthermore, we propose an octree map compression method that keeps the 3D models compact. Our framework is available as an open-source C++ library and has already been successfully applied in several robotics projects. We present a series of experimental results carried out with real robots and on publicly available real-world datasets. The results demonstrate that our approach is able to update the representation efficiently and models the data consistently while keeping the memory requirement at a minimum.     

Towards informative sensor-based grasp planning

This paper proposes a probabilistic framework for sensor-based grasping and describes how information about object attributes, such as position and orientation, can be updated using on-line sensor information gained during grasping. This allows learning about the target object even with a failed grasp, leading to replanning with improved performance at each successive attempt. Two grasp planning approaches utilizing the framework are proposed. Firstly, an approach maximizing the expected posterior stability of a grasp is suggested. Secondly, the approach is extended to use an entropy-based explorative procedure, which allows gathering more information when the current belief about the grasp stability does not allow robust grasping. In the framework, both object and grasp attributes as well as the stability of the grasp and on-line sensor information are represented by probabilistic models. Experiments show that the probabilistic treatment of grasping allows improving the probability of success in a series of grasping attempts. Moreover, experimental results on a real platform using the basic stability maximizing approach not only validate the proposed probabilistic framework but also show that under large initial uncertainties, explorative actions help to achieve successful grasps faster.     

Knowledge discovery through directed probabilistic topic models: a survey

Graphical models have become the basic framework for topic based probabilistic modeling. Especially models with latent variables have proved to be effective in capturing hidden structures in the data. In this paper, we survey an important subclass Directed Probabilistic Topic Models (DPTMs) with soft clustering abilities and their applications for knowledge discovery in text corpora. From an unsupervised learning perspective, “topics are semantically related probabilistic clusters of words in text corpora; and the process for finding these topics is called topic modeling”. In topic modeling, a document consists of different hidden topics and the topic probabilities provide an explicit representation of a document to smooth data from the semantic level. It has been an active area of research during the last decade. Many models have been proposed for handling the problems of modeling text corpora with different characteristics, for applications such as document classification, hidden association finding, expert finding, community discovery and temporal trend analysis. We give basic concepts, advantages and disadvantages in a chronological order, existing models classification into different categories, their parameter estimation and inference making algorithms with models performance evaluation measures. We also discuss their applications, open challenges and future directions in this dynamic area of research.     

Flexible latent variable models for multi-task learning

Given multiple prediction problems such as regression or classification, we are interested in a joint inference framework that can effectively share information between tasks to improve the prediction accuracy, especially when the number of training examples per problem is small. In this paper we propose a probabilistic framework which can support a set of latent variable models for different multi-task learning scenarios. We show that the framework is a generalization of standard learning methods for single prediction problems and it can effectively model the shared structure among different prediction tasks. Furthermore, we present efficient algorithms for the empirical Bayes method as well as point estimation. Our experiments on both simulated datasets and real world classification datasets show the effectiveness of the proposed models in two evaluation settings: a standard multi-task learning setting and a transfer learning setting.     

DISCOV: A Framework for Discovering Objects in Video

This paper presents a probabilistic framework for discovering objects in video. The video can switch between different shots, the unknown objects can leave or enter the scene at multiple times, and the background can be cluttered. The framework consists of an appearance model and a motion model. The appearance model exploits the consistency of object parts in appearance across frames. We use maximally stable extremal regions as observations in the model and hence provide robustness to object variations in scale, lighting and viewpoint. The appearance model provides location and scale estimates of the unknown objects through a compact probabilistic representation. The compact representation contains knowledge of the scene at the object level, thus allowing us to augment it with motion information using a motion model. This framework can be applied to a wide range of different videos and object types, and provides a basis for higher level video content analysis tasks. We present applications of video object discovery to video content analysis problems such as video segmentation and threading, and demonstrate superior performance to methods that exploit global image statistics and frequent itemset data mining techniques.     

A derivative-free affine scaling trust region methods based on probabilistic models with new nonmonotone line search technique for linear inequality constrained minimization without strict complementarity

ABSTRACT

In this paper, a derivative-free trust region methods based on probabilistic models with new nonmonotone line search technique is considered for nonlinear programming with linear inequality constraints. The proposed algorithm is designed to build probabilistic polynomial interpolation models for the objective function. We build the affine scaling trust region methods which use probabilistic or random models within a classical trust region framework. The new backtracking linear search technique guarantee the descent of the objective function, and new iterative points are in the feasible region. In order to overcome the strict complementarity hypothesis, under some reasonable conditions which are weaker than strong second order sufficient condition, we give the new and more simple identification function to structure the affine matrix. The global and local fast convergence of the algorithm are shown and the results of numerical experiments are reported to show the effectiveness of the proposed algorithm.     

Hierarchical pose estimation for human gait analysis

Articulated structures like the human body have many degrees of freedom. This makes an evaluation of the configuration's likelihood very challenging. In this work we propose new linked hierarchical graphical models which are able to efficiently evaluate likelihoods of articulated structures by sharing visual primitives. Instead of evaluating all configurations of the human body separately we take advantage of the fact that different configurations of the human body share body parts, and body parts, in turn, share visual primitives. A hierarchical Markov random field is used to integrate the sharing of visual primitives in a probabilistic framework. We propose a scalable hierarchical representation of the human body and show that this representation is especially well suited for human gait analysis from a frontal camera perspective. Furthermore, the results of the evaluation on a gait dataset show that sharing primitives substantially accelerates the evaluation and that our hierarchical probabilistic framework is a robust method for scalable detection of the human body.