Robustness analysis of Gaussian process convolutional neural network with uncertainty quantification

This paper presents a novel framework for image classification which comprises a convolutional neural network (CNN) feature map extractor combined with a Gaussian process (GP) classifier. Learning within the CNN-GP involves forward propagating the predicted class labels, then followed by backpropagation of the maximum likelihood function of the GP with a regularization term added. The regularization term takes the form of one of the three loss functions: the Kullback-Leibler divergence, Wasserstein distance, and maximum correntropy. The training and testing are performed in mini batches of images. The forward step (before the regularization) involves replacing the original images in the mini batch with their close neighboring images and then providing these to the CNN-GP to get the new predictive labels. The network performance is evaluated on MNIST, Fashion-MNIST, CIFAR10, and CIFAR100 datasets. Precision-recall and receiver operating characteristics curves are used to evaluate the performance of the GP classifier. The proposed CNN-GP performance is validated with different levels of noise, motion blur, and adversarial attacks. Results are explained using uncertainty analysis and further tests on quantifying the impact on uncertainty with attack strength are carried out. The results show that the testing accuracy improves for networks that backpropagate the maximum likelihood with regularized losses when compared with methods that do not. Moreover, a comparison with a state-of-art CNN Monte Carlo dropout method is presented. The outperformance of the CNN-GP framework with respect to reliability and computational efficiency is demonstrated

BaSIS-Net: From point estimate to predictive distribution in neural networks - a Bayesian sequential importance sampling framework

Data-driven Deep Learning (DL) models have revolutionized autonomous systems, but ensuring their safety and reliability necessitates the assessment of predictive confidence or uncertainty. Bayesian DL provides a principled approach to quantify uncertainty via probability density functions defined over model parameters. However, the exact solution is intractable for most DL models, and the approximation methods, often based on heuristics, suffer from scalability issues and stringent distribution assumptions and may lack theoretical guarantees. This work develops a Sequential Importance Sampling framework that approximates the posterior probability density function through weighted samples (or particles), which can be used to find the mean, variance, or higher-order moments of the posterior distribution. We demonstrate that propagating particles, which capture information about the higher-order moments, through the layers of the DL model results in increased robustness to natural and malicious noise (adversarial attacks). The variance computed from these particles effectively quantifies the model’s decision uncertainty, demonstrating well-calibrated and accurate predictive confidence

A Beamformer-Particle Filter Framework for Localization of Correlated EEG Sources

Abstract—Electroencephalography (EEG)-based brain computer interface (BCI) is the most studied non-invasive interface to build a direct communication pathway between the brain and an external device. However, correlated noises in EEG measurements still constitute a significant challenge. Alternatively, building BCIs based on filtered brain activity source signals instead of using their surface projections, obtained from the noisy EEG signals, is a promising and not well explored direction. In this context, finding the locations and waveforms of inner brain sources represents a crucial task for advancing source-based non-invasive BCI technologies. In this paper, we propose a novel Multi-core Beamformer Particle Filter (Multi-core BPF) to estimate the EEG brain source spatial locations and their corresponding waveforms. In contrast to conventional (single-core) Beamforming spatial filters, the developed Multi-core BPF considers explicitly temporal correlation among the estimated brain sources by suppressing activation from regions with interfering coherent sources. The hybrid Multi-core BPF brings together the advantages of both deterministic and Bayesian inverse problem algorithms in order to improve the estimation accuracy. It solves the brain activity localization problem without prior information about approximate areas of source locations. Moreover, the multi-core BPF reduces the dimensionality of the problem to half compared with the PF solution; thus alleviating the curse of dimensionality problem. The results, based on generated and real EEG data, show that the proposed framework recovers correctly the dominant sources of brain activity

Time-dependent ARMA modeling of genomic sequences

<p>Abstract</p> <p>Background</p> <p>Over the past decade, many investigators have used sophisticated time series tools for the analysis of genomic sequences. Specifically, the correlation of the nucleotide chain has been studied by examining the properties of the power spectrum. The main limitation of the power spectrum is that it is restricted to stationary time series. However, it has been observed over the past decade that genomic sequences exhibit non-stationary statistical behavior. Standard statistical tests have been used to verify that the genomic sequences are indeed not stationary. More recent analysis of genomic data has relied on time-varying power spectral methods to capture the statistical characteristics of genomic sequences. Techniques such as the evolutionary spectrum and evolutionary periodogram have been successful in extracting the time-varying correlation structure. The main difficulty in using time-varying spectral methods is that they are extremely unstable. Large deviations in the correlation structure results from very minor perturbations in the genomic data and experimental procedure. A fundamental new approach is needed in order to provide a stable platform for the non-stationary statistical analysis of genomic sequences.</p> <p>Results</p> <p>In this paper, we propose to model non-stationary genomic sequences by a time-dependent autoregressive moving average (TD-ARMA) process. The model is based on a classical ARMA process whose coefficients are allowed to vary with time. A series expansion of the time-varying coefficients is used to form a generalized Yule-Walker-type system of equations. A recursive least-squares algorithm is subsequently used to estimate the time-dependent coefficients of the model. The non-stationary parameters estimated are used as a basis for statistical inference and biophysical interpretation of genomic data. In particular, we rely on the TD-ARMA model of genomic sequences to investigate the statistical properties and differentiate between coding and non-coding regions in the nucleotide chain. Specifically, we define a quantitative measure of randomness to assess how far a process deviates from white noise. Our simulation results on various gene sequences show that both the coding and non-coding regions are non-random. However, coding sequences are "whiter" than non-coding sequences as attested by a higher index of randomness.</p> <p>Conclusion</p> <p>We demonstrate that the proposed TD-ARMA model can be used to provide a stable time series tool for the analysis of non-stationary genomic sequences. The estimated time-varying coefficients are used to define an index of randomness, in order to assess the statistical correlations in coding and non-coding DNA sequences. It turns out that the statistical differences between coding and non-coding sequences are more subtle than previously thought using stationary analysis tools: Both coding and non-coding sequences exhibit statistical correlations, with the coding regions being "whiter" than the non-coding regions. These results corroborate the evolutionary periodogram analysis of genomic sequences and revoke the stationary analysis' conclusion that coding DNA behaves like random sequences.</p

Spatially-Variant Directional Mathematical Morphology Operators Based on a Diffused Average Squared Gradient Field

International audienceThis paper proposes an approach for mathematical morphology operators whose structuring element can locally adapt its orientation across the pixels of the image. The orientation at each pixel is extracted by means of a diffusion process of the average squared gradient field. The resulting vector field, the average squared gradient vector flow, extends the orientation information from the edges of the objects to the homogeneous areas of the image. The provided orientation field is then used to perform a spatially variant filtering with a linear structuring element. Results of erosion, dilation, opening and closing spatially-variant on binary images prove the validity of this theoretical sound and novel approach

A deep learning framework for joint image restoration and recognition

Image restoration and recognition are important computer vision tasks representing an inherent part of autonomous systems. These two tasks are often implemented in a sequential manner, in which the restoration process is followed by a recognition. In contrast, this paper proposes a joint framework that simultaneously performs both tasks within a shared deep neural network architecture. This joint framework integrates the restoration and recognition tasks by incorporating: i) common layers, ii) restoration layers and iii) classification layers. The total loss function combines the restoration and classification losses. The proposed joint framework, based on capsules, provides an efficient solution that can cope with challenges due to noise, image rotations and occlusions. The developed framework has been validated and evaluated on a public vehicle logo dataset under various degradation conditions, including Gaussian noise, rotation and occlusion. The results show that the joint framework improves the accuracy compared with the single task networks

Spatially Variant Morphological Image Processing: Theory and Applications

Originally, mathematical morphology was a theory of signal transformations which are invariant under Euclidean translations. An interest in the extension of mathematical morphology to spatially-variant (SV) operators has emerged due to the requirements imposed by numerous applications in adaptive signal (image) processing. This paper presents a general theory of spatially-variant mathematical morphology in the Euclidean space. We define the binary and gray-level spatially-variant basic morphological operators (i.e., erosion, dilation, opening and closing) and study their properties. We subsequently derive kernel representations for a large class of binary and gray-level SV operators in terms of the basic SV morphological operators. The theory of SV mathematical morphology is used to extend and analyze two important image processing applications: morphological image restoration and skeleton representation of binary images. For morphological image restoration, we obtain new realizations of adaptive median filters in terms of the basic SV morphological operators. For skeleton representation, we develop an algorithm to construct the optimal structuring elements, in the sense of minimizing the cardinality of the spatially-variant morphological skeleton representation. Experimental results show the power of the proposed theory of spatially-variant mathematical morphology in practical image processing applications. Keywords: Spatially-Variant Mathematical Morphology, Spatially-variant homomorphism theorem, Kernel representation, Adaptive median filter, Spatially-Variant skeleton representation

Variance guided continual learning in a convolutional neural network Gaussian process single classifier approach for multiple tasks in noisy images

This work provides a continual learning solution in a single-classifier to multiple classification tasks with various data sets. A Gaussian process (GP) is combined with a Convolutional Neural Network (CNN) feature extractor architecture (CNNGP). Post softmax samples are used to estimate the variance. The variance is characterising the impact of uncertainties and is part of the update process for the learning rate parameters. Within the proposed framework two learning approaches are adopted: 1) in the first, the weights of the CNN are deterministic and only the GP learning rate is updated, 2) in the second setting, prior distributions are adopted for the CNN weights. Both the learning rates of the CNN and the GP are updated. The algorithm is trained on two variants of the MNIST dataset, split-MNIST and permuted-MNIST. Results are compared with the Uncertainty Guided Continual Bayesian Networks (UCB) multi-classifier approach [1]. The validation shows that the proposed algorithm in the Bayesian setting outperforms the UCB in tasks subject to Gaussian noise image noises and shows robustness