Deep learning is actively used in the area of sparse coding. In current deep sparse coding methods uncertainty of predictions is rarely estimated, thus providing the results that lack the quantitative justification. Bayesian learning provides the way to estimate the uncertainty of predictions in neural networks (NNs) by imposing the prior distributions on weights, propagating the resulting uncertainty through the layers and computing the posterior distributions of predictions. We propose a novel method of propagating the uncertainty through the sparsity-promoiting layers of NNs for the first time. We design a Bayesian Learned Iterative Shrinkage-Thresholding network (BayesLIsTA). An efficient posterior inference algorithm based on probabilistic backpropagation is developed. Experiments on sparse coding show that the proposed framework provides both accurate predictions and sensible estimates of uncertainty in these predictions.

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.

This paper proposes a flame detection framework based on the color, dynamics, and flickering properties of flames. The distribution of flame colors is modeled by a Gaussian mixture model whose number of Gaussian components is estimated by a Dirichlet process from training data rather than set empirically. The proposed approach estimates the flame color distribution more accurately as it can determine the number of Gaussian components of the mixture model automatically. Additionally, a probabilistic saliency analysis method and a one-dimensional wavelet transform are used to extract motion saliency and filtered temporal series as features, describing the dynamics and flickering properties of flames. The developed Dirichlet process Gaussian mixture model based approach for autonomous flame detection is tested on various videos and achieves framewise accuracy higher than 95%.

Semisupervised 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 paper proposes new learning algorithms for activity analysis in video. The activities and behaviors are described by a dynamic topic model. Two novel learning algorithms based on the expectation maximization approach and variational Bayes inference are proposed. Theoretical derivations of the posterior estimates 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 localization procedure, elegantly embedded in the topic modeling framework. It is shown that the developed learning algorithms can achieve 95% success rate. The proposed framework can be applied to a number of areas, including transportation systems, security, and surveillance.

Vehicle logo recognition is an important part of vehicle identification in intelligent transportation systems. State-of-the-art vehicle logo recognition approaches typically consider training models on large datasets. However, there might only be a small training dataset to start with and more images can be obtained during the real-time applications. This paper proposes an online image recognition framework which provides solutions for both small and large datasets. Using this recognition framework, models are built efficiently using a weight updating scheme. Another novelty of this work is that the Cauchy prior logistic regression with conjugate gradient descent is proposed to deal with the multinomial classification tasks. The Cauchy prior results in a quicker convergence speed for the weight updating process which could decrease the computational cost for both online and offline methods. By testing with a publicly available dataset, the Cauchy prior logistic regression deceases the classification time by 59%. An accuracy of up to 98.80% is achieved when the proposed framework is applied.