Approximate Inference Algorithm Research Articles

Machine learning-assisted exploration of thermally conductive polymers based on high-throughput molecular dynamics simulations

Finding amorphous polymers with higher thermal conductivity is important, as they are ubiquitous in a wide range of applications where heat transfer is important. With recent progress in material informatics, machine learning approaches have been increasingly adopted for finding or designing materials with desired properties. However, limited effort has been put on finding thermally conductive polymers using machine learning, mainly due to the lack of polymer thermal conductivity databases with reasonable data volume. In this work, we combine high-throughput molecular dynamics (MD) simulations and machine learning to explore polymers with relatively high thermal conductivity (>0.300 W/m-K) – a statistically important threshold as most neat polymers have thermal conductivity lower than this value under normal conditions. We first randomly select 365 polymers from the existing PoLyInfo database and calculate their thermal conductivity using MD simulations. The data are then employed to train a machine learning regression model to quantify the structure-thermal conductivity relation, which is further leveraged to screen polymer candidates in the PoLyInfo database with thermal conductivity >0.300 W/m-K. 121 polymers with MD-calculated thermal conductivity above this threshold are eventually identified. Polymers with a wide range of thermal conductivity values are selected for re-calculation under different simulation conditions, and those polymers found with thermal conductivity above 0.300 W/m-K are mostly calculated to maintain values above this threshold despite fluctuation in the exact values. Given the observed uncertainties in the MD-calculated TC, we have also constructed a Bayesian neural network to evaluate the epistemic and aleatoric prediction uncertainties, where a state-of-the-art approximate Bayesian inference algorithm is used for scalable training. The strategy and results from this work may contribute to automating the design of polymers with high thermal conductivity.

Analysis of random sequential message passing algorithms for approximate inference

We analyze the dynamics of a random sequential message passing algorithm for approximate inference with large Gaussian latent variable models in a student–teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices drawn from rotation invariant ensembles. Moreover, we consider a model mismatching setting, where the teacher model and the one used by the student may be different. By means of dynamical functional approach, we obtain exact dynamical mean-field equations characterizing the dynamics of the inference algorithm. We also derive a range of model parameters for which the sequential algorithm does not converge. The boundary of this parameter range coincides with the de Almeida Thouless (AT) stability condition of the replica-symmetric ansatz for the static probabilistic model.

Span-Based Semantic Role Labeling with Argument Pruning and Second-Order Inference

We study graph-based approaches to span-based semantic role labeling. This task is difficult due to the need to enumerate all possible predicate-argument pairs and the high degree of imbalance between positive and negative samples. Based on these difficulties, high-order inference that considers interactions between multiple arguments and predicates is often deemed beneficial but has rarely been used in span-based semantic role labeling. Because even for second-order inference, there are already O(n^5) parts for a sentence of length n, and exact high-order inference is intractable. In this paper, we propose a framework consisting of two networks: a predicate-agnostic argument pruning network that reduces the number of candidate arguments to O(n), and a semantic role labeling network with an optional second-order decoder that is unfolded from an approximate inference algorithm. Our experiments show that our framework achieves significant and consistent improvement over previous approaches.

Fast inference for time-varying quantiles via flexible dynamic models with application to the characterization of atmospheric rivers

Atmospheric rivers (ARs) are elongated regions of water vapor in the atmosphere that play a key role in global water cycles, particularly in western U.S. precipitation. The primary component of many AR detection schemes is the thresholding of the integrated water vapor transport (IVT) magnitude at a single quantile over time. Utilizing a recently developed family of parametric distributions for quantile regression, this paper develops a flexible dynamic quantile linear model (exDQLM) which enables versatile, structured, and informative estimation of the IVT quantile threshold. A simulation study illustrates our exDQLM to be more robust than the standard Bayesian parametric quantile regression approach for nonstandard distributions, performing better in both quantile estimation and predictive accuracy. In addition to a Markov chain Monte Carlo (MCMC) algorithm, we develop an efficient importance sampling variational Bayes (ISVB) algorithm for fast approximate Bayesian inference which is found to produce comparable results to the MCMC in a fraction of the computation time. Further, we develop a transfer function extension to our exDQLM as a method for quantifying nonlinear relationships between a quantile of a climatological response and an input. The utility of our transfer function exDQLM is demonstrated in capturing both the immediate and lagged effects of El Niño Southern Oscillation Longitude Index on the estimation of the 0.85 quantile IVT.

Sparse linear mixed model selection via streamlined variational Bayes

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is of interest to select a parsimonious subset of those being effectively relevant for predicting the response variable. Variational approximations facilitate fast approximate Bayesian inference for the parameters of a variety of statistical models, including linear mixed models. However, for models having a high number of fixed or random effects, simple application of standard variational inference principles does not lead to fast approximate inference algorithms, due to the size of model design matrices and inefficient treatment of sparse matrix problems arising from the required approximating density parameters updates. We illustrate how recently developed streamlined variational inference procedures can be generalized to make fast and accurate inference for the parameters of linear mixed models with nested random effects and global-local priors for Bayesian fixed effects selection. Our variational inference algorithms achieve convergence to the same optima of their standard implementations, although with significantly lower computational effort, memory usage and time, especially for large numbers of random effects. Using simulated and real data examples, we assess the quality of automated procedures for fixed effects selection that are free from hyperparameters tuning and only rely upon variational posterior approximations. Moreover, we show high accuracy of variational approximations against model fitting via Markov Chain Monte Carlo sampling.

Advances in Lifted Importance Sampling

We consider lifted importance sampling (LIS), a previously proposed approximate inference algorithm for statistical relational learning (SRL) models. LIS achieves substantial variance reduction over conventional importance sampling by using various lifting rules that take advantage of the symmetry in the relational representation. However, it suffers from two drawbacks. First, it does not take advantage of some important symmetries in the relational representation and may exhibit needlessly high variance on models having these symmetries. Second, it uses an uninformative proposal distribution which adversely affects its accuracy. We propose two improvements to LIS that address these limitations. First, we identify a new symmetry in SRL models and define a lifting rule for taking advantage of this symmetry. The lifting rule reduces the variance of LIS. Second, we propose a new, structured approach for constructing and dynamically updating the proposal distribution via adaptive sampling. We demonstrate experimentally that our new, improved LIS algorithm is substantially more accurate than the LIS algorithm.

The Inverse G‐Wishart distribution and variational message passing

SummaryMessage passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily large graphical models. The notion of a factor graph fragment allows for compartmentalisation of algebra and computer code. We show that the Inverse G‐Wishart family of distributions enables fundamental variational message passing factor graph fragments to be expressed elegantly and succinctly. Such fragments arise in models for which approximate inference concerning covariance matrix or variance parameters is made, and are ubiquitous in contemporary statistics and machine learning.

An empirical evaluation of active inference in multi-armed bandits

A key feature of sequential decision making under uncertainty is a need to balance between exploiting—choosing the best action according to the current knowledge, and exploring—obtaining information about values of other actions. The multi-armed bandit problem, a classical task that captures this trade-off, served as a vehicle in machine learning for developing bandit algorithms that proved to be useful in numerous industrial applications. The active inference framework, an approach to sequential decision making recently developed in neuroscience for understanding human and animal behaviour, is distinguished by its sophisticated strategy for resolving the exploration–exploitation trade-off. This makes active inference an exciting alternative to already established bandit algorithms. Here we derive an efficient and scalable approximate active inference algorithm and compare it to two state-of-the-art bandit algorithms: Bayesian upper confidence bound and optimistic Thompson sampling. This comparison is done on two types of bandit problems: a stationary and a dynamic switching bandit. Our empirical evaluation shows that the active inference algorithm does not produce efficient long-term behaviour in stationary bandits. However, in the more challenging switching bandit problem active inference performs substantially better than the two state-of-the-art bandit algorithms. The results open exciting venues for further research in theoretical and applied machine learning, as well as lend additional credibility to active inference as a general framework for studying human and animal behaviour.

Stein variational gradient descent with local approximations

Bayesian computation plays an important role in modern machine learning and statistics to reason about uncertainty. A key computational challenge in Bayesian inference is to develop efficient techniques to approximate, or draw samples from posterior distributions. Stein variational gradient decent (SVGD) has been shown to be a powerful approximate inference algorithm for this issue. However, the vanilla SVGD requires calculating the gradient of the target density and cannot be applied when the gradient is unavailable or too expensive to evaluate. In this paper we explore one way to address this challenge by the construction of a local surrogate for the target distribution in which the gradient can be obtained in a much more computationally feasible manner. More specifically, we approximate the forward model using a deep neural network (DNN) which is trained on a carefully chosen training set, which also determines the quality of the surrogate. To this end, we propose a general adaptation procedure to refine the local approximation online without destroying the convergence of the resulting SVGD. This significantly reduces the computational cost of SVGD and leads to a suite of algorithms that are straightforward to implement. The new algorithm is illustrated on a set of challenging Bayesian inverse problems, and numerical experiments demonstrate a clear improvement in performance and applicability of standard SVGD.

Query Training: Learning a Worse Model to Infer Better Marginals in Undirected Graphical Models with Hidden Variables

Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model once, new probabilistic queries can be answered at test time without retraining. However, when using undirected PGMS with hidden variables, two sources of error typically compound in all but the simplest models (a) learning error (both computing the partition function and integrating out the hidden variables is intractable); and (b) prediction error (exact inference is also intractable). Here we introduce query training (QT), a mechanism to learn a PGM that is optimized for the approximate inference algorithm that will be paired with it. The resulting PGM is a worse model of the data (as measured by the likelihood), but it is tuned to produce better marginals for a given inference algorithm. Unlike prior works, our approach preserves the querying flexibility of the original PGM: at test time, we can estimate the marginal of any variable given any partial evidence. We demonstrate experimentally that QT can be used to learn a challenging 8-connected grid Markov random field with hidden variables and that it consistently outperforms the state-of-the-art AdVIL when tested on three undirected models across multiple datasets.

Shadow Simulated Annealing: A new algorithm for approximate Bayesian inference of Gibbs point processes

This paper presents a new algorithm for statistical inference and analysis of spatial patterns assumed to be realisations of Gibbs point processes. This approach has a general character and it contributes to the existing methods based on Approximate Bayesian Computation, by providing control properties of the proposed solution. Results on simulated data and real data are presented. The real data application fits an inhomogeneous area interaction point process to cosmological data. The obtained results validate two important aspects of the galaxies distribution in our Universe: proximity of the galaxies from the cosmic filament network together with territorial clustering at given range of interactions. Finally, conclusions and perspectives are depicted.

Assessment and Adjustment of Approximate Inference Algorithms Using the Law of Total Variance

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated parameter values for corresponding posterior distributions are uniformly distributed. Checking for uniformity when a posterior density is approximated numerically provides a diagnostic for algorithm validity. Furthermore, adjustments to achieve uniformity can improve the quality of approximate inference methods. The present article develops a moment-based alternative to the conventional checking and adjustment methods using quantiles. The new approach relates prior and posterior expectations and covariances through the tower property of conditional expectation and the law of total variance. For adjustment, approximate inferences are modified so that the correct prior to posterior relationships hold. We illustrate the method in three examples. The first uses an auxiliary model in a likelihood-free inference problem. The second considers corrections for variational Bayes approximations in a deep neural network generalized linear mixed model. Our final application considers a deep neural network surrogate for approximating Gaussian process regression predictive inference. Supplementary files for this article are available online.

Approximate Inference and Learning of State Space Models With Laplace Noise

State space models have been extensively applied to model and control dynamical systems in disciplines including neuroscience, target tracking, and audio processing. A common modeling assumption is that both the state and data noise are Gaussian because it simplifies the estimation of the system's state and model parameters. However, in many real-world scenarios where the noise is heavy-tailed or includes outliers, this assumption does not hold, and the performance of the model degrades. In this paper, we present a new approximate inference algorithm for state space models with Laplace-distributed multivariate data that is robust to a wide range of non-Gaussian noise. Exact inference is combined with an expectation propagation algorithm, leading to filtering and smoothing that outperforms existing approximate inference methods for Laplace-distributed data, while retaining a fast speed similar to the Kalman filter. Further, we present a maximum posterior expectation-maximization (EM) algorithm that learns the parameters of the model in an unsupervised way, automatically avoids over-fitting the data, and provides better model estimation than existing methods for the Gaussian model. The quality of the inference and learning algorithms are exemplified through a diverse set of experiments and an application to non-linear tracking of audio frequency.

Deep Medical Image Reconstruction with Autoencoders using Deep Boltzmann Machine Training

INTRODUCTION: Deep learning-based Image compression achieves a promising result in recent years as compared with the traditional transform coding methodology. Autoencoder, an unsupervised learning algorithm with the input value as same as that of the output value, is considered in this research work for effective medical image reconstruction. OBJECTIVES: Medical data needs to be reconstructed without distorting the details present over it. A deep neural network that accepts the data and processes it to the other several layers and reconstructs that data is achieved by autoencoder. METHODS: Deep Autoencoder is implemented in this methodology as it has been considered for high dimensionality reduction. Layer by layer pretraining is achieved using an approximate inference algorithm called Deep Boltzmann Machine. RESULTS: The proposed method proves to be efficient when compared with the performance of the other autoencoders such as Deep Autoencoder with multiple Backpropagation (DA-MBP), Deep Autoencoder with RBM (DA-RBM) and Deep Convolutional Autoencoder with RBM (DCA-RBM). CONCLUSION: Performance metrics are measured in terms of Mean Square Error, Structural similarity Index and PSNR.

Learning the latent structure of collider events

We describe a technique to learn the underlying structure of collider events directly from the data, without having a particular theoretical model in mind. It allows to infer aspects of the theoretical model that may have given rise to this structure, and can be used to cluster or classify the events for analysis purposes. The unsupervised machine-learning technique is based on the probabilistic (Bayesian) generative model of Latent Dirichlet Allocation. We pair the model with an approximate inference algorithm called Variational Inference, which we then use to extract the latent probability distributions describing the learned underlying structure of collider events. We provide a detailed systematic study of the technique using two example scenarios to learn the latent structure of di-jet event samples made up of QCD background events and either toverline{t} or hypothetical W′ → (ϕ → WW)W signal events.

Improved High Dimensional Discrete Bayesian Network Inference using Triplet Region Construction

Performing efficient inference on high dimensional discrete Bayesian Networks (BNs) is challenging. When using exact inference methods the space complexity can grow exponentially with the tree-width, thus making computation intractable. This paper presents a general purpose approximate inference algorithm, based on a new region belief approximation method, called Triplet Region Construction (TRC). TRC reduces the cluster space complexity for factorized models from worst-case exponential to polynomial by performing graph factorization and producing clusters of limited size. Unlike previous generations of region-based algorithms, TRC is guaranteed to converge and effectively addresses the region choice problem that bedevils other region-based algorithms used for BN inference. Our experiments demonstrate that it also achieves significantly more accurate results than competing algorithms.

Semi-analytic approximate stability selection for correlated data in generalized linear models

We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is computationally demanding because it needs to fit GLMs to many re-sampled datasets. We propose a novel approximate inference algorithm that can conduct SS without the repeated fitting. The algorithm is based on the replica method of statistical mechanics and vector approximate message passing of information theory. For datasets characterized by rotation-invariant matrix ensembles, we derive state evolution equations that macroscopically describe the dynamics of the proposed algorithm. We also show that their fixed points are consistent with the replica symmetric solution obtained by the replica method. Numerical experiments indicate that the algorithm exhibits fast convergence and high approximation accuracy for both synthetic and real-world data.

Analysis of Bayesian inference algorithms by the dynamical functional approach

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student–teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices drawn from rotation invariant ensembles. For the case of perfect data-model matching, the knowledge of static order parameters derived from the replica method allows us to obtain efficient algorithmic updates in terms of matrix–vector multiplications with a fixed matrix. Using the dynamical functional approach, we obtain an exact effective stochastic process in the thermodynamic limit for a single node. From this, we obtain closed-form expressions for the rate of the convergence. Analytical results are in excellent agreement with simulations of single instances of large models.

Few-Shot Bayesian Imitation Learning with Logical Program Policies

Humans can learn many novel tasks from a very small number (1–5) of demonstrations, in stark contrast to the data requirements of nearly tabula rasa deep learning methods. We propose an expressive class of policies, a strong but general prior, and a learning algorithm that, together, can learn interesting policies from very few examples. We represent policies as logical combinations of programs drawn from a domain-specific language (DSL), define a prior over policies with a probabilistic grammar, and derive an approximate Bayesian inference algorithm to learn policies from demonstrations. In experiments, we study six strategy games played on a 2D grid with one shared DSL. After a few demonstrations of each game, the inferred policies generalize to new game instances that differ substantially from the demonstrations. Our policy learning is 20–1,000x more data efficient than convolutional and fully convolutional policy learning and many orders of magnitude more computationally efficient than vanilla program induction. We argue that the proposed method is an apt choice for tasks that have scarce training data and feature significant, structured variation between task instances.

Local Variational Feature-Based Similarity Models for Recommending Top- N New Items

The top- N recommendation problem has been studied extensively. Item-based collaborative filtering recommendation algorithms show promising results for the problem. They predict a user’s preferences by estimating similarities between a target and user-rated items. Top- N recommendation remains a challenging task in scenarios where there is a lack of preference history for new items. Feature-based Similarity Models (FSMs) address this particular problem by extending item-based collaborative filtering by estimating similarity functions of item features. The quality of the estimated similarity function determines the accuracy of the recommendation. However, existing FSMs only estimate global similarity functions; i.e., they estimate using preference information across all users. Moreover, the estimated similarity functions are linear ; hence, they may fail to capture the complex structure underlying item features. In this article, we propose to improve FSMs by estimating local similarity functions, where each function is estimated for a subset of like-minded users. To capture global preference patterns, we extend the global similarity function from linear to nonlinear, based on the effectiveness of variational autoencoders. We propose a Bayesian generative model, called the Local Variational Feature-based Similarity Model, to encapsulate local and global similarity functions. We present a variational Expectation Minimization algorithm for efficient approximate inference. Extensive experiments on a large number of real-world datasets demonstrate the effectiveness of our proposed model.