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Department of Computer Science and EngineeringAs deep learning has grown fast, so did the desire to interpret deep learning black boxes. As a result, many analysis tools have emerged to interpret it. Interpretation in deep learning has in fact popularized the use of deep learning in many areas including research, manufacturing, finance, and healthcare which needs relatively accurate and reliable decision making process. However, there is something we should not overlook. It is uncertainty. Uncertainties of models are directly reflected in the results of interpretations of model decision as explaining tools are dependent to models. Therefore, uncertainties of interpreting output from deep learning models should be also taken into account as quality and cost are directly impacted by measurement uncertainty. This attempt has not been made yet. Therefore, we suggest Bayesian input attribution rather than discrete input attribution by approximating Bayesian inference in deep Gaussian process through dropout to input attribution in this paper. Then we extract candidates that can sufficiently affect the output of the model, taking into account both input attribution itself and uncertainty of it.clos

Bayesian Deep Net GLM and GLMM

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The consideration of neural networks with random effects is not widely used in the literature, perhaps because of the computational challenges of incorporating subject specific parameters into already complex models. Efficient computational methods for high-dimensional Bayesian inference are developed using Gaussian variational approximation, with a parsimonious but flexible factor parametrization of the covariance matrix. We implement natural gradient methods for the optimization, exploiting the factor structure of the variational covariance matrix in computation of the natural gradient. Our flexible DFNN models and Bayesian inference approach lead to a regression and classification method that has a high prediction accuracy, and is able to quantify the prediction uncertainty in a principled and convenient way. We also describe how to perform variable selection in our deep learning method. The proposed methods are illustrated in a wide range of simulated and real-data examples, and the results compare favourably to a state of the art flexible regression and classification method in the statistical literature, the Bayesian additive regression trees (BART) method. User-friendly software packages in Matlab, R and Python implementing the proposed methods are available at https://github.com/VBayesLabComment: 35 pages, 7 figure, 10 table

Towards a Multi-Subject Analysis of Neural Connectivity

Directed acyclic graphs (DAGs) and associated probability models are widely used to model neural connectivity and communication channels. In many experiments, data are collected from multiple subjects whose connectivities may differ but are likely to share many features. In such circumstances it is natural to leverage similarity between subjects to improve statistical efficiency. The first exact algorithm for estimation of multiple related DAGs was recently proposed by Oates et al. 2014; in this letter we present examples and discuss implications of the methodology as applied to the analysis of fMRI data from a multi-subject experiment. Elicitation of tuning parameters requires care and we illustrate how this may proceed retrospectively based on technical replicate data. In addition to joint learning of subject-specific connectivity, we allow for heterogeneous collections of subjects and simultaneously estimate relationships between the subjects themselves. This letter aims to highlight the potential for exact estimation in the multi-subject setting.Comment: to appear in Neural Computation 27:1-2

Gaussian process regression for virtual metrology of microchip quality and the resulting strategic sampling scheme

Manufacturing of integrated circuits involves many sequential processes, often ex- ecuted to nanoscale tolerances, and the yield depends on the often unmeasured quality of intermediate steps. In the high-throughput industry of fabricating microelectronics on semi-conducting wafers, scheduling measurements of product quality before the electrical test of the complete IC can be expensive. We therefore seek to predict metrics of product quality based on sensor readings describing the environment within the relevant tool during the processing of each wafer, or to apply the concept of virtual metrology (VM) to monitor these intermediate steps. We model the data using Gaussian process regression (GPR), adapted to simultaneously learn the nonlinear dynamics that govern the quality characteristic, as well as their operating space, expressed by a linear embedding of the sensor traces’ features. Such Bayesian models predict a distribution for the target metric, such as a critical dimension, so one may assess the model’s credibility through its predictive uncertainty. Assuming measurements of the quality characteristic of interest are budgeted, we seek to hasten convergence of the GPR model to a credible form through an active sampling scheme, whereby the predictive uncertainty informs which wafer’s quality to measure next. We evaluate this convergence when predicting and updating online, as if in a factory, using a large dataset for plasma-enhanced chemical vapor deposition (PECVD), with measured thicknesses for ~32,000 wafers. By approximately optimizing the information extracted from this seemingly repetitive data describing a tightly controlled process, GPR achieves ~10% greater accuracy on average than a baseline linear model based on partial least squares (PLS). In a derivative study, we seek to discern the degree of drift in the process over the several months the data spans. We express this drift by how unusual the relevant features, as embedded by the GPR model, appear as the in- puts compensate for degrading conditions. This method detects the onset of consistently unusual behavior that extends to a bimodal thickness fault, anticipating its flagging by as much as two days.Mechanical Engineerin

Online Tool Condition Monitoring Based on Parsimonious Ensemble+

Accurate diagnosis of tool wear in metal turning process remains an open challenge for both scientists and industrial practitioners because of inhomogeneities in workpiece material, nonstationary machining settings to suit production requirements, and nonlinear relations between measured variables and tool wear. Common methodologies for tool condition monitoring still rely on batch approaches which cannot cope with a fast sampling rate of metal cutting process. Furthermore they require a retraining process to be completed from scratch when dealing with a new set of machining parameters. This paper presents an online tool condition monitoring approach based on Parsimonious Ensemble+, pENsemble+. The unique feature of pENsemble+ lies in its highly flexible principle where both ensemble structure and base-classifier structure can automatically grow and shrink on the fly based on the characteristics of data streams. Moreover, the online feature selection scenario is integrated to actively sample relevant input attributes. The paper presents advancement of a newly developed ensemble learning algorithm, pENsemble+, where online active learning scenario is incorporated to reduce operator labelling effort. The ensemble merging scenario is proposed which allows reduction of ensemble complexity while retaining its diversity. Experimental studies utilising real-world manufacturing data streams and comparisons with well known algorithms were carried out. Furthermore, the efficacy of pENsemble was examined using benchmark concept drift data streams. It has been found that pENsemble+ incurs low structural complexity and results in a significant reduction of operator labelling effort.Comment: this paper has been published by IEEE Transactions on Cybernetic