Deep probabilistic time series forecasting has gained significant attention due to its ability to provide valuable uncertainty quantification for decision-making tasks. However, many existing models oversimplify the problem by assuming the error process is time-independent, thereby overlooking the serial correlation in the error process. This oversight can potentially diminish the accuracy of the forecasts, rendering these models less effective for decision-making purposes. To overcome this limitation, we propose an innovative training method that incorporates error autocorrelation to enhance the accuracy of probabilistic forecasting. Our method involves constructing a mini-batch as a collection of $D$ consecutive time series segments for model training and explicitly learning a covariance matrix over each mini-batch that encodes the error correlation among adjacent time steps. The resulting covariance matrix can be used to improve prediction accuracy and enhance uncertainty quantification. We evaluate our method using DeepAR on multiple public datasets, and the experimental results confirm that our framework can effectively capture the error autocorrelation and enhance probabilistic forecasting.
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Model checking has been proposed as a formal verification approach for analyzing computer-based and cyber-physical systems. The state space explosion problem is the main obstacle for applying this approach for sophisticated systems. Bisimulation minimization is a prominent method for reducing the number of states in a labeled transition system and is used to alleviate the challenges of the state space explosion problem. For systems with stochastic behaviors, probabilistic bisimulation is used to reduce a given model to its minimized equivalent one. In recent years, several techniques have been proposed to reduce the time complexity of the iterative methods for computing probabilistic bisimulation of stochastic systems with nondeterministic behaviors. In this paper, we propose several techniques to accelerate iterative processes to partition the state space of a given probabilistic model to its bisimulation classes. The first technique applies two ordering heuristics for choosing splitter blocks. The second technique uses hash tables to reduce the running time and the average time complexity of the standard iterative method. The proposed approaches are implemented and run on several conventional case studies and reduce the running time by one order of magnitude on average.
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation leverages conventional PDE discretization techniques, deep neural networks, probabilistic modelling, and variational inference to assemble a fully probabilistic coherent framework. In the posited probabilistic model, both the forward and inverse maps are approximated as Gaussian distributions with a mean and covariance parameterized by deep neural networks. The PDE residual is assumed to be an observed random vector of value zero, hence we model it as a random vector with a zero mean and a user-prescribed covariance. The model is trained by maximizing the probability, that is the evidence or marginal likelihood, of observing a residual of zero by maximizing the evidence lower bound (ELBO). Consequently, the proposed methodology does not require any independent PDE solves and is physics-informed at training time, allowing the real-time solution of PDE forward and inverse problems after training. The proposed framework can be easily extended to seamlessly integrate observed data to solve inverse problems and to build generative models. We demonstrate the efficiency and robustness of our method on finite element discretized parametric PDE problems such as linear and nonlinear Poisson problems, elastic shells with complex 3D geometries, and time-dependent nonlinear and inhomogeneous PDEs using a physics-informed neural network (PINN) discretization. We achieve up to three orders of magnitude speed-up after training compared to traditional finite element method (FEM), while outputting coherent uncertainty estimates.
Load forecasting is of great significance in the power industry as it can provide a reference for subsequent tasks such as power grid dispatch, thus bringing huge economic benefits. However, there are many differences between load forecasting and traditional time series forecasting. On the one hand, load forecasting aims to minimize the cost of subsequent tasks such as power grid dispatch, rather than simply pursuing prediction accuracy. On the other hand, the load is largely influenced by many external factors, such as temperature or calendar variables. In addition, the scale of predictions (such as building-level loads and aggregated-level loads) can also significantly impact the predicted results. In this paper, we provide a comprehensive load forecasting archive, which includes load domain-specific feature engineering to help forecasting models better model load data. In addition, different from the traditional loss function which only aims for accuracy, we also provide a method to customize the loss function based on the forecasting error, integrating it into our forecasting framework. Based on this, we conducted extensive experiments on load data at different levels, providing a reference for researchers to compare different load forecasting models.
Denoising low-dose computed tomography (CT) images is a critical task in medical image computing. Supervised deep learning-based approaches have made significant advancements in this area in recent years. However, these methods typically require pairs of low-dose and normal-dose CT images for training, which are challenging to obtain in clinical settings. Existing unsupervised deep learning-based methods often require training with a large number of low-dose CT images or rely on specially designed data acquisition processes to obtain training data. To address these limitations, we propose a novel unsupervised method that only utilizes normal-dose CT images during training, enabling zero-shot denoising of low-dose CT images. Our method leverages the diffusion model, a powerful generative model. We begin by training a cascaded unconditional diffusion model capable of generating high-quality normal-dose CT images from low-resolution to high-resolution. The cascaded architecture makes the training of high-resolution diffusion models more feasible. Subsequently, we introduce low-dose CT images into the reverse process of the diffusion model as likelihood, combined with the priors provided by the diffusion model and iteratively solve multiple maximum a posteriori (MAP) problems to achieve denoising. Additionally, we propose methods to adaptively adjust the coefficients that balance the likelihood and prior in MAP estimations, allowing for adaptation to different noise levels in low-dose CT images. We test our method on low-dose CT datasets of different regions with varying dose levels. The results demonstrate that our method outperforms the state-of-the-art unsupervised method and surpasses several supervised deep learning-based methods. Codes are available in //github.com/DeepXuan/Dn-Dp.
Breaking safety constraints in control systems can lead to potential risks, resulting in unexpected costs or catastrophic damage. Nevertheless, uncertainty is ubiquitous, even among similar tasks. In this paper, we develop a novel adaptive safe control framework that integrates meta learning, Bayesian models, and control barrier function (CBF) method. Specifically, with the help of CBF method, we learn the inherent and external uncertainties by a unified adaptive Bayesian linear regression (ABLR) model, which consists of a forward neural network (NN) and a Bayesian output layer. Meta learning techniques are leveraged to pre-train the NN weights and priors of the ABLR model using data collected from historical similar tasks. For a new control task, we refine the meta-learned models using a few samples, and introduce pessimistic confidence bounds into CBF constraints to ensure safe control. Moreover, we provide theoretical criteria to guarantee probabilistic safety during the control processes. To validate our approach, we conduct comparative experiments in various obstacle avoidance scenarios. The results demonstrate that our algorithm significantly improves the Bayesian model-based CBF method, and is capable for efficient safe exploration even with multiple uncertain constraints.
Off-policy evaluation (OPE) aims to estimate the benefit of following a counterfactual sequence of actions, given data collected from executed sequences. However, existing OPE estimators often exhibit high bias and high variance in problems involving large, combinatorial action spaces. We investigate how to mitigate this issue using factored action spaces i.e. expressing each action as a combination of independent sub-actions from smaller action spaces. This approach facilitates a finer-grained analysis of how actions differ in their effects. In this work, we propose a new family of "decomposed" importance sampling (IS) estimators based on factored action spaces. Given certain assumptions on the underlying problem structure, we prove that the decomposed IS estimators have less variance than their original non-decomposed versions, while preserving the property of zero bias. Through simulations, we empirically verify our theoretical results, probing the validity of various assumptions. Provided with a technique that can derive the action space factorisation for a given problem, our work shows that OPE can be improved "for free" by utilising this inherent problem structure.
Time series forecasting has received wide interest from existing research due to its broad applications and inherent challenging. The research challenge lies in identifying effective patterns in historical series and applying them to future forecasting. Advanced models based on point-wise connected MLP and Transformer architectures have strong fitting power, but their secondary computational complexity limits practicality. Additionally, those structures inherently disrupt the temporal order, reducing the information utilization and making the forecasting process uninterpretable. To solve these problems, this paper proposes a forecasting model, MPR-Net. It first adaptively decomposes multi-scale historical series patterns using convolution operation, then constructs a pattern extension forecasting method based on the prior knowledge of pattern reproduction, and finally reconstructs future patterns into future series using deconvolution operation. By leveraging the temporal dependencies present in the time series, MPR-Net not only achieves linear time complexity, but also makes the forecasting process interpretable. By carrying out sufficient experiments on more than ten real data sets of both short and long term forecasting tasks, MPR-Net achieves the state of the art forecasting performance, as well as good generalization and robustness performance.
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.
Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of modeling complex patterns or dependencies lying in real word data. To address such concerns, various deep learning models, mainly Recurrent Neural Network (RNN) based methods, are proposed. Nevertheless, capturing extremely long-term patterns while effectively incorporating information from other variables remains a challenge for time-series forecasting. Furthermore, lack-of-explainability remains one serious drawback for deep neural network models. Inspired by Memory Network proposed for solving the question-answering task, we propose a deep learning based model named Memory Time-series network (MTNet) for time series forecasting. MTNet consists of a large memory component, three separate encoders, and an autoregressive component to train jointly. Additionally, the attention mechanism designed enable MTNet to be highly interpretable. We can easily tell which part of the historic data is referenced the most.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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