Lyudmila Mihaylova

Xingchi Liu, Lyudmila Mihaylova, Jemin George et al.

Uncertainty quantification plays a key role in the development of autonomous systems, decision-making, and tracking over wireless sensor networks (WSNs). However, there is a need of providing uncertainty confidence bounds, especially for distributed machine learning-based tracking, dealing with different volumes of data collected by sensors. This paper aims to fill in this gap and proposes a distributed Gaussian process (DGP) approach for point target tracking and derives upper confidence bounds (UCBs) of the state estimates. A unique contribution of this paper includes the derived theoretical guarantees on the proposed approach and its maximum accuracy for tracking with and without clutter measurements. Particularly, the developed approaches with uncertainty bounds are generic and can provide trustworthy solutions with an increased level of reliability. A novel hybrid Bayesian filtering method is proposed to enhance the DGP approach by adopting a Poisson measurement likelihood model. The proposed approaches are validated over a WSN case study, where sensors have limited sensing ranges. Numerical results demonstrate the tracking accuracy and robustness of the proposed approaches. The derived UCBs constitute a tool for trustworthiness evaluation of DGP approaches. The simulation results reveal that the proposed UCBs successfully encompass the true target states with 88% and 42% higher probability in X and Y coordinates, respectively, when compared to the confidence interval-based method.

Tianhao Zhang, Shenglin Wang, Nidhal Bouaynaya et al.

The superior performance of object detectors is often established under the condition that the test samples are in the same distribution as the training data. However, in many practical applications, out-of-distribution (OOD) instances are inevitable and usually lead to uncertainty in the results. In this paper, we propose a novel, intuitive, and scalable probabilistic object detection method for OOD detection. Unlike other uncertainty-modeling methods that either require huge computational costs to infer the weight distributions or rely on model training through synthetic outlier data, our method is able to distinguish between in-distribution (ID) data and OOD data via weight parameter sampling from proposed Gaussian distributions based on pre-trained networks. We demonstrate that our Bayesian object detector can achieve satisfactory OOD identification performance by reducing the FPR95 score by up to 8.19% and increasing the AUROC score by up to 13.94% when trained on BDD100k and VOC datasets as the ID datasets and evaluated on COCO2017 dataset as the OOD dataset.

Usman Muhammad, Jorma Laaksonen, Lyudmila Mihaylova

Deep neural networks have demonstrated highly competitive performance in super-resolution (SR) for natural images by learning mappings from low-resolution (LR) to high-resolution (HR) images. However, hyperspectral super-resolution remains an ill-posed problem due to the high spectral dimensionality of the data and the scarcity of available training samples. Moreover, existing methods often rely on large models with a high number of parameters or require the fusion with panchromatic or RGB images, both of which are often impractical in real-world scenarios. Inspired by the MobileNet architecture, we introduce a lightweight depthwise separable dilated convolutional network (DSDCN) to address the aforementioned challenges. Specifically, our model leverages multiple depthwise separable convolutions, similar to the MobileNet architecture, and further incorporates a dilated convolution fusion block to make the model more flexible for the extraction of both spatial and spectral features. In addition, we propose a custom loss function that combines mean squared error (MSE), an L2 norm regularization-based constraint, and a spectral angle-based loss, ensuring the preservation of both spectral and spatial details. The proposed model achieves very competitive performance on two publicly available hyperspectral datasets, making it well-suited for hyperspectral image super-resolution tasks. The source codes are publicly available at: \href{https://github.com/Usman1021/lightweight}{https://github.com/Usman1021/lightweight}.

Alex George, Lyudmila Mihaylova, Sean Anderson

Most explainable anomaly detection methods often identify anomalies but lack the capability to differentiate the type of anomaly. Furthermore, they often require the costly training and maintenance of separate models for each object category. The lack of specificity is a significant research gap, as identifying the type of anomaly (e.g., "Crack" vs. "Scratch") is crucial for accurate diagnosis that facilitates cost-saving operational decisions across diverse application domains. While some recent large-scale Vision-Language Models (VLMs) have begun to address this, they are computationally intensive and memory-heavy, restricting their use in real-time or embedded systems. We propose MultiTypeFCDD, a simple and lightweight convolutional framework designed as a practical alternative for explainable multi-type anomaly detection. MultiTypeFCDD uses only image-level labels to learn and produce multi-channel heatmaps, where each channel is trained to correspond to a specific anomaly type. The model functions as a single, unified framework capable of differentiating anomaly types across multiple object categories, eliminating the need to train and manage separate models for each object category. We evaluated our proposed method on the Real-IAD dataset and it delivers results competitive with state-of-the-art complex models at significantly reduced parametric load and inference times. This makes it a highly practical and viable solution for real-world applications where computational resources are tightly constrained.

Giuseppina Carannante, Dimah Dera, Ghulam Rasool et al.

Learning in uncertain, noisy, or adversarial environments is a challenging task for deep neural networks (DNNs). We propose a new theoretically grounded and efficient approach for robust learning that builds upon Bayesian estimation and Variational Inference. We formulate the problem of density propagation through layers of a DNN and solve it using an Ensemble Density Propagation (EnDP) scheme. The EnDP approach allows us to propagate moments of the variational probability distribution across the layers of a Bayesian DNN, enabling the estimation of the mean and covariance of the predictive distribution at the output of the model. Our experiments using MNIST and CIFAR-10 datasets show a significant improvement in the robustness of the trained models to random noise and adversarial attacks.

Youngjoo Kim, Peng Wang, Lyudmila Mihaylova

This paper presents a scalable deep learning approach for short-term traffic prediction based on historical traffic data in a vehicular road network. Capturing the spatio-temporal relationship of the big data often requires a significant amount of computational burden or an ad-hoc design aiming for a specific type of road network. To tackle the problem, we combine a road network graph with recurrent neural networks (RNNs) to construct a structural RNN (SRNN). The SRNN employs a spatio-temporal graph to infer the interaction between adjacent road segments as well as the temporal dynamics of the time series data. The model is scalable thanks to two key aspects. First, the proposed SRNN architecture is built by using the semantic similarity of the spatio-temporal dynamic interactions of all segments. Second, we design the architecture to deal with fixed-length tensors regardless of the graph topology. With the real traffic speed data measured in the city of Santander, we demonstrate the proposed SRNN outperforms the image-based approaches using the capsule network (CapsNet) by 14.1% and the convolutional neural network (CNN) by 5.87%, respectively, in terms of root mean squared error (RMSE). Moreover, we show that the proposed model is scalable. The SRNN model trained with data of a road network is able to predict traffic speed of different road networks, with the fixed number of parameters to train.

Komlan Atitey, Pavel Loskot, Lyudmila Mihaylova

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such scenarios. In particular, a random process generated by the autoregressive moving average (ARMA) linear model is inferred from non-linearity noise observations. The posterior distribution of hidden states are approximated by a set of weighted particles generated by the sequential Monte carlo (SMC) algorithm involving sampling with importance sampling resampling (SISR). Numerical efficiency and estimation accuracy of the proposed inference method are evaluated by computer simulations. Furthermore, the proposed inference method is demonstrated on a practical problem of estimating the missing values in the gene expression time series assuming vector autoregressive (VAR) data model.

Youngjoo Kim, Peng Wang, Lyudmila Mihaylova

Deep neural networks have recently demonstrated the traffic prediction capability with the time series data obtained by sensors mounted on road segments. However, capturing spatio-temporal features of the traffic data often requires a significant number of parameters to train, increasing computational burden. In this work we demonstrate that embedding topological information of the road network improves the process of learning traffic features. We use a graph of a vehicular road network with recurrent neural networks (RNNs) to infer the interaction between adjacent road segments as well as the temporal dynamics. The topology of the road network is converted into a spatio-temporal graph to form a structural RNN (SRNN). The proposed approach is validated over traffic speed data from the road network of the city of Santander in Spain. The experiment shows that the graph-based method outperforms the state-of-the-art methods based on spatio-temporal images, requiring much fewer parameters to train.

Danil Kuzin, Olga Isupova, Lyudmila Mihaylova

A novel method to propagate uncertainty through the soft-thresholding nonlinearity is proposed in this paper. At every layer the current distribution of the target vector is represented as a spike and slab distribution, which represents the probabilities of each variable being zero, or Gaussian-distributed. Using the proposed method of uncertainty propagation, the gradients of the logarithms of normalisation constants are derived, that can be used to update a weight distribution. A novel Bayesian neural network for sparse coding is designed utilising both the proposed method of uncertainty propagation and Bayesian inference algorithm.

Youngjoo Kim, Peng Wang, Yifei Zhu et al.

This paper proposes a deep learning approach for traffic flow prediction in complex road networks. Traffic flow data from induction loop sensors are essentially a time series, which is also spatially related to traffic in different road segments. The spatio-temporal traffic data can be converted into an image where the traffic data are expressed in a 3D space with respect to space and time axes. Although convolutional neural networks (CNNs) have been showing surprising performance in understanding images, they have a major drawback. In the max pooling operation, CNNs are losing important information by locally taking the highest activation values. The inter-relationship in traffic data measured by sparsely located sensors in different time intervals should not be neglected in order to obtain accurate predictions. Thus, we propose a neural network with capsules that replaces max pooling by dynamic routing. This is the first approach that employs the capsule network on a time series forecasting problem, to our best knowledge. Moreover, an experiment on real traffic speed data measured in the Santander city of Spain demonstrates the proposed method outperforms the state-of-the-art method based on a CNN by 13.1% in terms of root mean squared error.

Danil Kuzin, Olga Isupova, Lyudmila Mihaylova

This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies between the components of the sparse signal of interest. A hierarchical Gaussian process describes such structure and the interdependencies are represented via the covariance matrices of the prior distributions. The inference is based on the expectation propagation method and the theoretical derivation of the posterior distribution is provided in the paper. The inference framework is thoroughly evaluated over synthetic, real video and electroencephalography (EEG) data where the spatio-temporal evolving patterns need to be reconstructed with high accuracy. It is shown that it achieves 15% improvement of the F-measure compared with the alternating direction method of multipliers, spatio-temporal sparse Bayesian learning method and one-level Gaussian process model. Additionally, the required memory for the proposed algorithm is less than in the one-level Gaussian process model. This structured sparse regression framework is of broad applicability to source localisation and object detection problems with sparse signals.

Danil Kuzin, Le Yang, Olga Isupova et al.

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically with the number of observations. Several approaches based on inducing points were proposed to handle this problem in a static context. These methods though face challenges with real-time tasks and when the data is received sequentially over time. In this paper, a novel online algorithm for training sparse Gaussian process models is presented. It treats the mean and hyperparameters of the Gaussian process as the state and parameters of the ensemble Kalman filter, respectively. The online evaluation of the parameters and the state is performed on new upcoming samples of data. This procedure iteratively improves the accuracy of parameter estimates. The ensemble Kalman filter reduces the computational complexity required to obtain predictions with Gaussian processes preserving the accuracy level of these predictions. The performance of the proposed method is demonstrated on the synthetic dataset and real large dataset of UK house prices.

Danil Kuzin, Olga Isupova, Lyudmila Mihaylova

Video analytics requires operating with large amounts of data. Compressive sensing allows to reduce the number of measurements required to represent the video using the prior knowledge of sparsity of the original signal, but it imposes certain conditions on the design matrix. The Bayesian compressive sensing approach relaxes the limitations of the conventional approach using the probabilistic reasoning and allows to include different prior knowledge about the signal structure. This paper presents two Bayesian compressive sensing methods for autonomous object detection in a video sequence from a static camera. Their performance is compared on the real datasets with the non-Bayesian greedy algorithm. It is shown that the Bayesian methods can provide the same accuracy as the greedy algorithm but much faster; or if the computational time is not critical they can provide more accurate results.

Danil Kuzin, Olga Isupova, Lyudmila Mihaylova

In this paper a new Bayesian model for sparse linear regression with a spatio-temporal structure is proposed. It incorporates the structural assumptions based on a hierarchical Gaussian process prior for spike and slab coefficients. We design an inference algorithm based on Expectation Propagation and evaluate the model over the real data.

Olga Isupova, Danil Kuzin, Lyudmila Mihaylova

Semi-supervised and unsupervised systems provide operators with invaluable support and can tremendously reduce the operators load. In the light of the necessity to process large volumes of video data and provide autonomous decisions, this work proposes new learning algorithms for activity analysis in video. The activities and behaviours are described by a dynamic topic model. Two novel learning algorithms based on the expectation maximisation approach and variational Bayes inference are proposed. Theoretical derivations of the posterior of model parameters are given. The designed learning algorithms are compared with the Gibbs sampling inference scheme introduced earlier in the literature. A detailed comparison of the learning algorithms is presented on real video data. We also propose an anomaly localisation procedure, elegantly embedded in the topic modeling framework. The proposed framework can be applied to a number of areas, including transportation systems, security and surveillance.

Olga Isupova, Danil Kuzin, Lyudmila Mihaylova

This paper proposes a novel dynamic Hierarchical Dirichlet Process topic model that considers the dependence between successive observations. Conventional posterior inference algorithms for this kind of models require processing of the whole data through several passes. It is computationally intractable for massive or sequential data. We design the batch and online inference algorithms, based on the Gibbs sampling, for the proposed model. It allows to process sequential data, incrementally updating the model by a new observation. The model is applied to abnormal behaviour detection in video sequences. A new abnormality measure is proposed for decision making. The proposed method is compared with the method based on the non- dynamic Hierarchical Dirichlet Process, for which we also derive the online Gibbs sampler and the abnormality measure. The results with synthetic and real data show that the consideration of the dynamics in a topic model improves the classification performance for abnormal behaviour detection.

Olga Isupova, Danil Kuzin, Lyudmila Mihaylova

A novel dynamic Bayesian nonparametric topic model for anomaly detection in video is proposed in this paper. Batch and online Gibbs samplers are developed for inference. The paper introduces a new abnormality measure for decision making. The proposed method is evaluated on both synthetic and real data. The comparison with a non-dynamic model shows the superiority of the proposed dynamic one in terms of the classification performance for anomaly detection.

Ata-ur-Rehman, Syed Mohsen Naqvi, Lyudmila Mihaylova et al.

This paper considers the problem of multiple human target tracking in a sequence of video data. A solution is proposed which is able to deal with the challenges of a varying number of targets, interactions and when every target gives rise to multiple measurements. The developed novel algorithm comprises variational Bayesian clustering combined with a social force model, integrated within a particle filter with an enhanced prediction step. It performs measurement-to-target association by automatically detecting the measurement relevance. The performance of the developed algorithm is evaluated over several sequences from publicly available data sets: AV16.3, CAVIAR and PETS2006, which demonstrates that the proposed algorithm successfully initializes and tracks a variable number of targets in the presence of complex occlusions. A comparison with state-of-the-art techniques due to Khan et al., Laet et al. and Czyz et al. shows improved tracking performance.

Matthew Hawes, Lyudmila Mihaylova, Francois Septier et al.

In this paper, we look to address the problem of estimating the dynamic direction of arrival (DOA) of a narrowband signal impinging on a sensor array from the far field. The initial estimate is made using a Bayesian compressive sensing (BCS) framework and then tracked using a Bayesian compressed sensing Kalman filter (BCSKF). The BCS framework splits the angular region into N potential DOAs and enforces a belief that only a few of the DOAs will have a non-zero valued signal present. A BCSKF can then be used to track the change in the DOA using the same framework. There can be an issue when the DOA approaches the endfire of the array. In this angular region current methods can struggle to accurately estimate and track changes in the DOAs. To tackle this problem, we propose changing the traditional sparse belief associated with BCS to a belief that the estimated signals will match the predicted signals given a known DOA change. This is done by modelling the difference between the expected sparse received signals and the estimated sparse received signals as a Gaussian distribution. Example test scenarios are provided and comparisons made with the traditional BCS based estimation method. They show that an improvement in estimation accuracy is possible without a significant increase in computational complexity.

Christopher Nemeth, Paul Fearnhead, Lyudmila Mihaylova

Poyiadjis et al. (2011) show how particle methods can be used to estimate both the score and the observed information matrix for state space models. These methods either suffer from a computational cost that is quadratic in the number of particles, or produce estimates whose variance increases quadratically with the amount of data. This paper introduces an alternative approach for estimating these terms at a computational cost that is linear in the number of particles. The method is derived using a combination of kernel density estimation, to avoid the particle degeneracy that causes the quadratically increasing variance, and Rao-Blackwellisation. Crucially, we show the method is robust to the choice of bandwidth within the kernel density estimation, as it has good asymptotic properties regardless of this choice. Our estimates of the score and observed information matrix can be used within both online and batch procedures for estimating parameters for state space models. Empirical results show improved parameter estimates compared to existing methods at a significantly reduced computational cost. Supplementary materials including code are available.