Mean-field variational approximate Bayesian inference for latent variable models

The ill-posed nature of missing variable models offers a challenging testing ground for new computational techniques. This is the case for the mean-field variational Bayesian inference. The behavior of this approach in the setting of the Bayesian probit model is illustrated. It is shown that the mean-field variational method always underestimates the posterior variance and, that, for small sample sizes, the mean-field variational approximation to the posterior location could be poor.     

Convex multi-task feature learning

We present a method for learning sparse representations shared across multiple tasks. This method is a generalization of the well-known single-task 1-norm regularization. It is based on a novel non-convex regularizer which controls the number of learned features common across the tasks. We prove that the method is equivalent to solving a convex optimization problem for which there is an iterative algorithm which converges to an optimal solution. The algorithm has a simple interpretation: it alternately performs a supervised and an unsupervised step, where in the former step it learns task-specific functions and in the latter step it learns common-across-tasks sparse representations for these functions. We also provide an extension of the algorithm which learns sparse nonlinear representations using kernels. We report experiments on simulated and real data sets which demonstrate that the proposed method can both improve the performance relative to learning each task independently and lead to a few learned features common across related tasks. Our algorithm can also be used, as a special case, to simply select—not learn—a few common variables across the tasks. Editors: Daniel Silver, Kristin Bennett, Richard Caruana. This is a longer version of the conference paper (Argyriou et al. in Advances in neural information processing systems, vol. 19, 2007a). It includes new theoretical and experimental results.     

Simulation-based approach to estimation of latent variable models

We propose a simulation-based method for calculating maximum likelihood estimators in latent variable models. The proposed method integrates a recently developed sampling strategy, the so-called Sample Average Approximation method, to efficiently compute high quality solutions of the estimation problem. Theoretical and algorithmic properties of the method are discussed. A computational study, involving two numerical examples, is presented to highlight a significant improvement of the proposed approach over existing methods.     

MultiTL-KELM: A multi-task learning algorithm for multi-step-ahead time series prediction

Time series prediction for higher future horizons is of great importance and has increasingly aroused interest among both scholars and practitioners. Compared to one-step-ahead prediction, multi-step-ahead prediction encounters higher dose of uncertainty arising from various facets, including accumulation of errors and lack of information. Many existing studies draw attention to the former issue, while relatively overlook the latter one. Inspired by this discovery, a new multi-task learning algorithm, called the MultiTL-KELM algorithm for short, is proposed for multi-step-ahead time series prediction in this work, where the long-ago data is utilized to provide more information for the current prediction task. The time-varying quality of time-series data usually gives rise to a wide variability between data over long time span, making it difficult to ensure the assumption of identical distribution. How to make the most of, rather than discard the abundant old data, and transfer more useful knowledge to current prediction is one of the main concerns of our proposed MultiTL-KELM algorithm. Besides, unlike typical iterated or direct strategies, MultiTL-KELM regards predictions of different horizons as different tasks. Knowledge from one task can benefit others, enabling it to explore the relatedness among horizons. Based upon its design scheme, MultiTL-KELM alleviates the accumulation error problem of iterated strategy and the time consuming of direct strategies. The proposed MultiTL-KELM algorithm has been compared with several other state-of-the-art algorithms, and its effectiveness has been numerically confirmed by the experiments we conducted on four synthetic and two real-world benchmark time series datasets.     

Adaptive sampling design for multi-task learning of Gaussian processes in manufacturing

Approximation models (or surrogate models) have been widely used in engineering problems to mitigate the cost of running expensive experiments or simulations. Gaussian processes (GPs) are a popular tool used to construct these models due to their flexibility and computational tractability. The accuracy of these models is a strong function of the density and locations of the sampled points in the parametric space used for training. Previously, multi-task learning (MTL) has been used to learn similar-but-not-identical tasks together, thus increasing the effective density of training points. Also, several adaptive sampling strategies have been developed to identify regions of interest for intelligent sampling in single-task learning of GPs. While both these methods have addressed the density and location constraint separately, sampling design approaches for MTL are lacking. In this paper, we formulate an adaptive sampling strategy for MTL of GPs, thereby further improving data efficiency and modeling performance in GP. To this end, we develop variance measures for an MTL framework to effectively identify optimal sampling locations while learning multiple tasks simultaneously. We demonstrate the effectiveness of the proposed method using a case study on a real-world engine surface dataset. We observe that the proposed method leverages both MTL and intelligent sampling to significantly outperform state-of-the-art methods which use either approach separately. The developed sampling design strategy is readily applicable to many problems in various fields.     

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.     

A mixture of generalized latent variable models for mixed mode and heterogeneous data

In the behavioral, biomedical, and social-psychological sciences, mixed data types such as continuous, ordinal, count, and nominal are common. Subpopulations also often exist and contribute to heterogeneity in the data. In this paper, we propose a mixture of generalized latent variable models (GLVMs) to handle mixed types of heterogeneous data. Different link functions are specified to model data of multiple types. A Bayesian approach, together with the Markov chain Monte Carlo (MCMC) method, is used to conduct the analysis. A modified DIC is used for model selection of mixture components in the GLVMs. A simulation study shows that our proposed methodology performs satisfactorily. An application of mixture GLVM to a data set from the National Longitudinal Surveys of Youth (NLSY) is presented.     

Latent variable iterative learning model predictive control for multivariable control of batch processes

A latent variable iterative learning model predictive control (LV-ILMPC) method is presented for trajectory tracking in batch processes. Different from the iterative learning model predictive control (ILMPC) model built from the original variable space, LV-ILMPC develops a latent variable model based on dynamic partial least squares (DyPLS) to capture the dominant features of each batch. In each latent variable space, we use a state–space model to describe the dynamic characteristics of the internal model, and an LV-ILMPC controller is designed. Each LV-ILMPC controller tracks the set points of the current batch projection in the corresponding latent variable space, and the optimal control law is determined and the persistent process disturbances is rejected along both time and batch horizons. The proposed LV-ILMPC formulation is based on general LV-MPC and incorporates an iterative learning function into LV-MPC. In addition, the real physical input that drives the process can be reconstructed from the latent variable space. Therefore, this algorithm is particularly suitable for multiple-input, multiple-output (MIMO) systems with strong coupling and serious collinearity. Three studies are used to illustrate the effectiveness of the proposed LV-ILMPC .     

Object tracking via collaborative multi-task learning and appearance model updating

In this paper, we propose a novel visual tracking algorithm using the collaboration of generative and discriminative trackers under the particle filter framework. Each particle denotes a single task, and we encode all the tasks simultaneously in a structured multi-task learning manner. Then, we implement generative and discriminative trackers, respectively. The discriminative tracker considers the overall information of object to represent the object appearance; while the generative tracker takes the local information of object into account for handling partial occlusions. Therefore, two models are complementary during the tracking. Furthermore, we design an effective dictionary updating mechanism. The dictionary is composed of fixed and variational parts. The variational parts are progressively updated using Metropolis–Hastings strategy. Experiments on different challenging video sequences demonstrate that the proposed tracker performs favorably against several state-of-the-art trackers.     

Parameter constraints in generalized linear latent variable models

Parameter constraints in generalized linear latent variable models are discussed. Both linear equality and inequality constraints are considered. Maximum likelihood estimators for the parameters of the constrained model and corrected standard errors are derived. A significant reduction in the dimension of the optimization problem is achieved with the proposed methodology for fitting models subject to linear equality constraints.     

Refined instrumental variable methods for identification of LPV Box-Jenkins models

The identification of linear parameter-varying systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive colored noise. In the Box-Jenkins and output-error cases, it is shown that the currently available linear regression and instrumental variable methods from the literature are far from being optimal in terms of bias and variance of the estimates. To overcome the underlying problems, a refined instrumental variable method is introduced. The proposed approach is compared to the existing methods via a representative simulation example.     

Constrained latent variable model predictive control for trajectory tracking and economic optimization in batch processes

A constrained latent variable model predictive control (LV-MPC) technique is proposed for trajectory tracking and economic optimization in batch processes. The controller allows the incorporation of constraints on the process variables and is designed on the basis of multi-way principal component analysis (MPCA) of a batch data array rearranged by means of a regularized batch-wise unfolding. The main advantages of LV-MPC over other MPC techniques are: (i) requirements for the dataset are rather modest (only around 10–20 batch runs are necessary), (ii) nonlinear processes can efficiently be handled algebraically through MPCA models, and (iii) the tuning procedure is simple. The LV-MPC for tracking is tested through a benchmark process used in previous LV-MPC formulations. The extension to economic LV-MPC includes an economic cost and it is based on model and trajectory updating from batch to batch to drive the process to the economic optimal region. A data-driven model validity indicator is used to ensure the prediction’s validity while the economic cost drives the process to regions with higher profit. This technique is validated through simulations in a case study.     

小数据集情况下基于变权重融合的BN参数学习算法

针对小数据集情况下贝叶斯网络（BN）参数学习结果精度较低的问题,分析了小数据集情况下BN参数变权重设计的必要性,提出一种基于变权重融合的BN参数学习算法VWPL。首先根据专家经验确定不等式约束条件,计算参数学习最小样本数据集阈值,设计了随样本量变化的变权重因子函数;然后根据样本计算出初始参数集,通过Bootstrap方法进行参数扩展得到满足约束条件的候选参数集,将其代入BN变权重参数计算模型即可获取最终的BN参数。实验结果表明,当学习数据量较小时,VWPL算法的学习精度高于MLE算法和QMAP算法的,也优于定权重学习算法的。另外,将VWPL算法成功应用到了轴承故障诊断实验中,为在小数据集上进行BN参数估计提供了一种方法。     

Agglomerative independent variable group analysis

Independent variable group analysis (IVGA) is a method for grouping dependent variables together while keeping mutually independent or weakly dependent variables in separate groups. In this paper two variants of an agglomerative method for learning a hierarchy of IVGA groupings are presented. The method resembles hierarchical clustering, but the choice of clusters to merge is based on variational Bayesian model comparison. This is approximately equivalent to using a distance measure based on a model-based approximation of mutual information between groups of variables. The approach also allows determining optimal cutoff points for the hierarchy. The method is demonstrated to find sensible groupings of variables that can be used for feature selection and ease construction of a predictive model.     

Bayesian projection approaches to variable selection in generalized linear models

A Bayesian approach to variable selection which is based on the expected Kullback-Leibler divergence between the full model and its projection onto a submodel has recently been suggested in the literature. For generalized linear models an extension of this idea is proposed by considering projections onto subspaces defined via some form of L₁ constraint on the parameter in the full model. This leads to Bayesian model selection approaches related to the lasso. In the posterior distribution of the projection there is positive probability that some components are exactly zero and the posterior distribution on the model space induced by the projection allows exploration of model uncertainty. Use of the approach in structured variable selection problems such as ANOVA models is also considered, where it is desired to incorporate main effects in the presence of interactions. Projections related to the non-negative garotte are able to respect the hierarchical constraints. A consistency result is given concerning the posterior distribution on the model induced by the projection, showing that for some projections related to the adaptive lasso and non-negative garotte the posterior distribution concentrates on the true model asymptotically.     

A random-effect model approach for group variable selection

We consider regression models with a group structure in explanatory variables. This structure is commonly seen in practice, but it is only recently realized that taking the information into account in the modeling process may improve both the interpretability and accuracy of the model. In this paper, we study a new approach to group variable selection using random-effect models. Specific distributional assumptions on random effects pertaining to a given structure lead to a new class of penalties that include some existing penalties. We also develop an efficient computational algorithm. Numerical studies are provided to demonstrate better sensitivity and specificity properties without sacrificing the prediction accuracy. Finally, we present some real-data applications of the proposed approach.     

Multi-label,multi-task CNN approach for context-based emotion recognition

This paper proposes a new deep learning architecture for context-based multi-label multi-task emotion recognition. The architecture is built from three main modules: (1) a body features extraction module, which is a pre-trained Xception network, (2) a scene features extraction module, based on a modified VGG16 network, and (3) a fusion-decision module. Moreover, three categorical and three continuous loss functions are compared in order to point out the importance of the synergy between loss functions when it comes to multi-task learning. Then, we propose a new loss function, the multi-label focal loss (MFL), based on the focal loss to deal with imbalanced data. Experimental results on EMOTIC dataset show that MFL with the Huber loss gave better results than any other combination and outperformed the current state of art on the less frequent labels.     

Transfer in variable-reward hierarchical reinforcement learning

Transfer learning seeks to leverage previously learned tasks to achieve faster learning in a new task. In this paper, we consider transfer learning in the context of related but distinct Reinforcement Learning (RL) problems. In particular, our RL problems are derived from Semi-Markov Decision Processes (SMDPs) that share the same transition dynamics but have different reward functions that are linear in a set of reward features. We formally define the transfer learning problem in the context of RL as learning an efficient algorithm to solve any SMDP drawn from a fixed distribution after experiencing a finite number of them. Furthermore, we introduce an online algorithm to solve this problem, Variable-Reward Reinforcement Learning (VRRL), that compactly stores the optimal value functions for several SMDPs, and uses them to optimally initialize the value function for a new SMDP. We generalize our method to a hierarchical RL setting where the different SMDPs share the same task hierarchy. Our experimental results in a simplified real-time strategy domain show that significant transfer learning occurs in both flat and hierarchical settings. Transfer is especially effective in the hierarchical setting where the overall value functions are decomposed into subtask value functions which are more widely amenable to transfer across different SMDPs.