Exact Inference Algorithm Research Articles

The Normal-Generalised Gamma-Pareto Process: A Novel Pure-Jump Lévy Process with Flexible Tail and Jump-Activity Properties

We propose a novel family of self-decomposable Lévy processes where one can control separately the tail behavior and the jump activity of the process, via two different parameters. Crucially, we show that one can sample exactly increments of this process, at any time scale; this allows the implementation of likelihood-free Markov chain Monte Carlo algorithms for (asymptotically) exact posterior inference. We use this novel process in Lévy-based stochastic volatility models to predict the returns of stock market data, and show that the proposed class of models leads to superior predictive performances compared to classical alternatives.

미디어 사용 행태 토픽 분석을 통한 추천모델링

As online shopping and mobile media are recently activated, various feedbacks are built on users' preferences and purchases. Various approaches are being studied to improve the performance of recommendation considering individual characteristics. This study carries out clustering from media panel data through LDA topic modeling to imply the meaning of user's media use behavior, and applies a new rating, calculated by combining the existing rating and sentiment analysis on media use by cluster, to the recommendation system. We select households living with their children, and make a recommendation 31 smart devices that could be helpful for the members. We utilize the SAMC algorithm for exact inference of LDA topic modeling, and set the optimal number of topics through coherence and perplexity. We use BPR and collaborative filtering for the recommendation algorithm, and BPR provides the best performance by comparing with three performance indicators. It is indicated that the recommendation process suggested by this study provides a reasonable recommendation considering individual characteristics.

Hierarchical Dynamic Bayesian Network-Based Fatigue Crack Propagation Modeling Considering Initial Defects.

Orthotropic steel decks (OSDs) are inevitably subjected to fatigue damage caused by cycled vehicle loads in long-span bridges. This study establishes a probabilistic analysis framework integrating the dynamic Bayesian network (DBN) and fracture mechanics to model the fatigue crack propagation considering mutual correlations among multiple fatigue details. Both the observations of fatigue crack length from field inspection and monitoring data of vehicle loads from the weight-in-motion (WIM) system are utilized. First, fracture mechanics-based uncertainty analysis is performed to determine the multiple uncertainty sources in the Paris crack propagation model, material property, and observation data of crack length. The uncertainty of monitoring data of vehicle loads is ignored because of its high accuracy; consequently, the vehicle-load-related uncertainty is spontaneously ignored, which is also demonstrated to be very small on the investigated actual bridges. Second, a hierarchical DBN model is introduced to construct mutual dependencies among various uncertainties and intra-correlations in the propagation process of multiple fatigue cracks at different components. Third, a stochastic traffic model is established based on the WIM monitoring data and multi-scale finite element analysis via substructure techniques to determine the probability distribution of vehicle-load-related parameters. After variable discretization, a refined exact inference algorithm in a forward–backward–forward manner is adopted to estimate the posterior distribution of equivalent initial crack length and update the established DBN model. Finally, the proposed method is demonstrated by a numerical case study and a typical application on an actual cable-stayed bridge with steel box girders using OSDs in China. The results show that the probability distribution of equivalent initial crack size can be spontaneously derived with a larger mean value than the results of conventional empirical analysis. Furthermore, the component-level fatigue reliability is tracked and predicted based on the established crack propagation model.

Using Survey Sampling Algorithms For Exact Inference in Logistic Regression

SummarySeveral exact inference procedures for logistic regression require the simulation of a 0‐1 dependent vector according to its conditional distribution, given the sufficient statistics for some nuisance parameters. This is viewed, in this work, as a sampling problem involving a population of units, unequal selection probabilities and balancing constraints. The basis for this reformulation of exact inference is a proposition deriving the limit, as goes to infinity, of the conditional distribution of the dependent vector given the logistic regression sufficient statistics. It is proposed to sample from this distribution using the cube sampling algorithm. The interest of this approach to exact inference is illustrated by tackling new problems. First it allows to carry out exact inference with continuous covariates. It is also useful for the investigation of a partial correlation between several 0‐1 vectors. This is illustrated in an example dealing with presence‐absence data in ecology.

Efficient Decomposition of Bayesian Networks With Non-graded Variables

Elicitation, estimation and exact inference in Bayesian Networks (BNs) are often difficult because the dimension of each Conditional Probability Table (CPT) grows exponentially with the increase in the number of parent variables. The Noisy-MAX decomposition has been proposed to break down a large CPT into several smaller CPTs exploiting the assumption of causal independence, i.e., absence of causal interaction among parent variables. In this way, the number of conditional probabilities to be elicited or estimated and the computational burden of the joint tree algorithm for exact inference are reduced. Unfortunately, the Noisy-MAX decomposition is suited to graded variables only, i.e., ordinal variables with the lowest state as reference, but real-world applications of BNs may also involve a number of non-graded variables, like the ones with reference state in the middle of the sample space (double-graded variables) and with two or more unordered non-reference states (multi-valued nominal variables). In this paper, we propose the causal independence decomposition, which includes the Noisy-MAX and two generalizations suited to double-graded and multi-valued nominal variables. While the general definition of BN implicitly assumes the presence of all the possible causal interactions, our proposal is based on causal independence, and causal interaction is a feature that can be added upon need. The impact of our proposal is investigated on a published BN for the diagnosis of acute cardiopulmonary diseases.

Inference in Bayesian Proxy-SVARs

Motivated by the increasing use of external instruments to identify structural vector autoregressions (SVARs), we develop an algorithm for exact finite sample inference in this class of time series models, commonly known as Proxy-SVARs. Our algorithm makes independent draws from any posterior distribution over the structural parameterization of a Proxy-SVAR. Our approach allows researchers to simultaneously use proxies and traditional zero and sign restrictions to identify structural shocks. We illustrate our methods with two applications. In particular, we show how to generalize the counterfactual analysis in Mertens and Montiel-Olea (2018) to identified structural shocks.

Truncated simulation and inference in edge-exchangeable networks

Edge-exchangeable probabilistic network models generate edges as an i.i.d.~sequence from a discrete measure, providing a simple means for statistical inference of latent network properties. The measure is often constructed using the self-product of a realization from a Bayesian nonparametric (BNP) discrete prior; but unlike in standard BNP models, the self-product measure prior is not conjugate the likelihood, hindering the development of exact simulation and inference algorithms. Approximation via finite truncation of the discrete measure is a straightforward alternative, but incurs an unknown approximation error. In this paper, we develop methods for forward simulation and posterior inference in random self-product-measure models based on truncation, and provide theoretical guarantees on the quality of the results as a function of the truncation level. The techniques we present are general and extend to the broader class of discrete Bayesian nonparametric models.

Safety evaluation of truss structures using nested discrete Bayesian networks

Truss structures have been widely adopted for civil structures such as long-span buildings and bridges. An actual truss system is usually statically indeterminate having numerous members and high redundancy. It is practically difficult to evaluate the truss safety through traditional reliability-based approaches in view of complex failure modes and uncertainties. Moreover, monitoring data are generally insufficient in reality due to limited sensors under cost consideration. Therefore, a nested discrete Bayesian network has been developed for safety evaluation of truss structures. A concept of member risk coefficient is first proposed based on the mechanical relationship between load effects and member resistance. According to the coefficients of all members, member risk sequences are found as the basis for establishing the topology of a member-level Bayesian network. Each network node represents a truss member and a nodal variable having three states: elasticity, plasticity, and failure. Two relevant member nodes are connected by a directed edge whose causality strength is expressed by a conditional probability table. Meanwhile, a system-level network topology is established to reflect the effects of member states on the truss system. The system is assigned with a node having two states: safety and failure. The directed edge of each member node directly points to the system node. Then, the two networks are combined to form a nested network topology. By this means, direct topology learning is avoided in order to find rational and concise topologies satisfying the mechanical characteristics of civil structures. After that, the conditional probability tables for the nested network are obtained through parameter learning on complete numerical observation data. The data acquirement procedure takes into account uncertainties by defining the randomness of cross-sectional areas and external loads. With the conditional probability tables, the nested network is ready for use. When new evidence from limited monitored members is input into the nested network, the state probabilities of the other members, as well as the system, are simultaneously updated using exact inference algorithms. The inference ability using insufficient information well accords with the demand of engineering practice. Finally, the proposed method has been successfully verified against both numerical and experimental truss structures. It was found that the network estimations could be further confirmed with more evidence.

System Reliability Estimation of Divert Attitude Control System of a Launch Vehicle using Bayesian Networks

Divert attitude and control system (DACS) is a one-shot system and provides attitude correction and translation of the Launch vehicle. DACS consists of many flight critical sub systems which are arranged in a series configuration. The traditional Reliability block diagram and Fault tree diagram methods are unsuitable for reliability modelling, when considering uncertainty among the components and system. Bayesian network is the natural choice to model dependencies among the components and system. DACS being one shot system, it is very expensive and time consuming to test more number of systems during the design and development. Hence the data is drawn from component level, subsystem level and expert opinion is used for reliability estimation. In this paper, Bayesian network modelling of DAC system was carried out for estimating the reliability using multi-level data. An algorithm is developed for computation of Conditional probabilities in Bayesian network. Posterior probability distribution of components is calculated using Markov Chain Monte Carlo (MCMC) simulations and results are compared with Junction tree based exact inference algorithm. MATLAB code is developed to estimate the reliability of DAC system.

Structured Bayesian Networks: From Inference to Learning with Routes

Structured Bayesian networks (SBNs) are a recently proposed class of probabilistic graphical models which integrate background knowledge in two forms: conditional independence constraints and Boolean domain constraints. In this paper, we propose the first exact inference algorithm for SBNs, based on compiling a given SBN to a Probabilistic Sentential Decision Diagram (PSDD). We further identify a tractable subclass of SBNs, which have PSDDs of polynomial size. These SBNs yield a tractable model of route distributions, whose structure can be learned from GPS data, using a simple algorithm that we propose. Empirically, we demonstrate the utility of our inference algorithm, showing that it can be an order-ofmagnitude more efficient than more traditional approaches to exact inference. We demonstrate the utility of our learning algorithm, showing that it can learn more accurate models and classifiers from GPS data.

Dynamic Bayesian network-based system-level evaluation on fatigue reliability of orthotropic steel decks

Fatigue fractures can be frequently observed in welded joints in orthotropic steel decks (OSDs) after just a few decades of operation, which become the major deterioration mechanism deterring the serviceability of OSDs. In this paper, a novel dynamic Bayesian network (DBN) model has been established for the fatigue reliability analysis of OSDs at system-level. The exact inference algorithm is applied in the DBN model with discrete variables. Special modifications have been made on the existing algorithm to improve the computational efficiency in dealing with the deck system consisting of a considerable number of joints. Using the DBN model, the fatigue reliability of welded joints can be predicted and updated with the inspection and monitoring results at system-level. At the same time, a framework is established for the system-level reliability considering the fatigue fracture of rib-to-deck (RD) joints, the dominant cracking pattern affecting the serviceability of OSDs. For illustration, a typical OSD bridge in China has been selected to carry out a case study. To derive the stress spectrum required by the DBN model, the stochastic traffic model is employed, and the influence-based Monte Carlo simulations have been carried out. As a result, the fatigue reliability can be predicted at both component- and system-levels. Meanwhile, the observation of the traffic and the inspection result has been fused into the DBN model to update the deteriorating state of the deck system. Besides, the effect of enhancement and maintenance has been highlighted, including the enhancement in fatigue strength at the construction stage, and the repair and traffic control during the operation stage.

Inverse reinforcement learning from summary data

Inverse reinforcement learning (IRL) aims to explain observed strategic behavior by fitting reinforcement learning models to behavioral data. However, traditional IRL methods are only applicable when the observations are in the form of state-action paths. This assumption may not hold in many real-world modeling settings, where only partial or summarized observations are available. In general, we may assume that there is a summarizing function $\sigma$, which acts as a filter between us and the true state-action paths that constitute the demonstration. Some initial approaches to extending IRL to such situations have been presented, but with very specific assumptions about the structure of $\sigma$, such as that only certain state observations are missing. This paper instead focuses on the most general case of the problem, where no assumptions are made about the summarizing function, except that it can be evaluated. We demonstrate that inference is still possible. The paper presents exact and approximate inference algorithms that allow full posterior inference, which is particularly important for assessing parameter uncertainty in this challenging inference situation. Empirical scalability is demonstrated to reasonably sized problems, and practical applicability is demonstrated by estimating the posterior for a cognitive science RL model based on an observed user's task completion time only.

Inference in Bayesian Proxy-SVARs

Motivated by the increasing use of external instruments to identify structural vector autoregressions (SVARs), we develop algorithms for exact finite sample inference in this class of time series models, commonly known as proxy-SVARs. Our algorithms make independent draws from the normal-generalized-normal family of conjugate posterior distributions over the structural parameterization of a proxy-SVAR. Importantly, our techniques can handle the case of set identification and hence they can be used to relax the additional exclusion restrictions unrelated to the external instruments often imposed to facilitate inference when more than one instrument are used to identify more than one equation, as in Mertens and Montiel-Olea (2018).

An empirical study of Bayesian network inference with simple propagation

We propose Simple Propagation (SP) as a new join tree propagation algorithm for exact inference in discrete Bayesian networks. We establish the correctness of SP. The striking feature of SP is that its message construction exploits the factorization of potentials at a sending node, but without the overhead of building and examining graphs as done in Lazy Propagation (LP). Experimental results on optimal (or close to optimal) join trees built from numerous benchmark Bayesian networks show that SP is often faster than LP.

On Darwinian Networks

We suggest Darwinian Networks (DNs) as a simplification of working with Bayesian networks (BNs). DNs adapt a handful of well‐known concepts in biology into a single framework that is surprisingly simple yet remarkably robust. With respect to modeling, on one hand, DNs not only represent BNs but also faithfully represent the testing of independencies in a more straightforward fashion. On the other hand, with respect to three exact inference algorithms in BNs, DNs simplify each of them while unifying all of them. DNs can determine good elimination orderings using the same platform as used for modeling and inference. Finally, we demonstrate how DNs can represent two additional frameworks. Practical benefits of DNs include faster algorithms for inference and modeling.

Network inference in the nonequilibrium steady state.

Nonequilibrium systems lack an explicit characterization of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of the parameters of a model when its dynamics lacks detailed balance. Such nonequilibrium systems occur naturally in applications like neural networks and gene regulatory networks. Here, we focus on the paradigmatic asymmetric Ising model and show that we can learn its parameters from independent samples of the nonequilibrium steady state. We present both an exact inference algorithm and a computationally more efficient, approximate algorithm for weak interactions based on a systematic expansion around mean-field theory. Obtaining expressions for magnetizations and two- and three-point spin correlations, we establish that these observables are sufficient to infer the model parameters. Further, we discuss the symmetries characterizing the different orders of the expansion around the mean field and show how different types of dynamics can be distinguished on the basis of samples from the nonequilibrium steady state.

Negative probabilities in probabilistic logic programs

We consider probabilistic logic programs (PLPs) for non-extreme distributions. We show that in the relational case with fixed populations, PLPs cannot represent many non-extreme distributions, even using negations. We introduce negative rule probabilities in PLPs, and show they make the language strictly more expressive. In addition, they render negations unnecessary: negations in PLPs can be translated to rules with negative probabilities, thus avoiding the problem of logical inconsistency. Furthermore, this translation keeps the PLP size compact (assuming the number of negations per rule is small). This translation algorithm also allows algorithms for exact inference that do not support negations to be applicable to PLPs with negations.The noise probabilities for non-exclusive rules are difficult to interpret and unintuitive to manipulate. To alleviate this we define “probability-strengths”, an alternative representation for probabilistic values, which results in an intuitive additive algebra for combining rules.For acyclic propositional PLPs we prove what constraints on the strengths allow for proper distributions on the non-noise variables and allow for all non-extreme distributions to be represented. We show how arbitrary CPDs can be converted into this form in a canonical way.

An extended depth-first search algorithm for optimal triangulation of Bayesian networks

The junction tree algorithm is currently the most popular algorithm for exact inference on Bayesian networks. To improve the time complexity of the junction tree algorithm, we need to find a triangulation with the optimal total table size. For this purpose, Ottosen and Vomlel have proposed a depth-first search (DFS) algorithm. They also introduced several techniques to improve the DFS algorithm, including dynamic clique maintenance and coalescing map pruning. Nevertheless, the efficiency and scalability of that algorithm leave much room for improvement. First, the dynamic clique maintenance allows to recompute some cliques. Second, in the worst case, the DFS algorithm explores the search space of all elimination orders, which has size n!, where n is the number of variables in the Bayesian network. To mitigate these problems, we propose an extended depth-first search (EDFS) algorithm. The new EDFS algorithm introduces the following two techniques as improvements to the DFS algorithm: (1) a new dynamic clique maintenance algorithm that computes only those cliques that contain a new edge, and (2) a new pruning rule, called pivot clique pruning. The new dynamic clique maintenance algorithm explores a smaller search space and runs faster than the Ottosen and Vomlel approach. This improvement can decrease the overhead cost of the DFS algorithm, and the pivot clique pruning reduces the size of the search space by a factor of O(n2). Our empirical results show that our proposed algorithm finds an optimal triangulation markedly faster than the state-of-the-art algorithm does.

Recursive prediction algorithm for non-stationary Gaussian Process

The original exact inference algorithm of the GP model runs very slow.We developed a recursive inference algorithm as an improvement.The new algorithm can obtain the same result in a shorter time.It works well for the real-time online prediction problems. Gaussian Process is a theoretically rigorous model for prediction problems. One of the deficiencies of this model is that its original exact inference algorithm is computationally intractable. Therefore, its applications are limited in the field of real-time online predictions. In this paper, a recursive prediction algorithm based on the Gaussian Process model is proposed. In recursive algorithms, the computational time of the next step can be greatly reduced by utilizing the intermediate results of the current step. The proposed recursive algorithm accelerates the prediction and avoids the loss of accuracy at the same time. Experiments are done on an ultra-short term electric load data set and the results are demonstrated to show the accuracy and efficiency of the new algorithm.

Efficient Exact Inference With Loss Augmented Objective in Structured Learning.

Structural support vector machine (SVM) is an elegant approach for building complex and accurate models with structured outputs. However, its applicability relies on the availability of efficient inference algorithms--the state-of-the-art training algorithms repeatedly perform inference to compute a subgradient or to find the most violating configuration. In this paper, we propose an exact inference algorithm for maximizing nondecomposable objectives due to special type of a high-order potential having a decomposable internal structure. As an important application, our method covers the loss augmented inference, which enables the slack and margin scaling formulations of structural SVM with a variety of dissimilarity measures, e.g., Hamming loss, precision and recall, Fβ-loss, intersection over union, and many other functions that can be efficiently computed from the contingency table. We demonstrate the advantages of our approach in natural language parsing and sequence segmentation applications.