Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time series are limited: Gaussian DLMs require continuous data, while Poisson-based alternatives often lack sufficient modeling flexibility. We introduce a novel semiparametric methodology for count time series by warping a Gaussian DLM. The warping function has two components: a (nonparametric) transformation operator that provides distributional flexibility and a rounding operator that ensures the correct support for the discrete data-generating process. We develop conjugate inference for the warped DLM, which enables analytic and recursive updates for the state space filtering and smoothing distributions. We leverage these results to produce customized and efficient algorithms for inference and forecasting, including Monte Carlo simulation for offline analysis and an optimal particle filter for online inference. This framework unifies and extends a variety of discrete time series models and is valid for natural counts, rounded values, and multivariate observations. Simulation studies illustrate the excellent forecasting capabilities of the warped DLM. The proposed approach is applied to a multivariate time series of daily overdose counts and demonstrates both modeling and computational successes.
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This paper pushes further the intrinsic capabilities of the GFEM$^{gl}$ global-local approach introduced initially in [1]. We develop a distributed computing approach using MPI (Message Passing Interface) both for the global and local problems. Regarding local problems, a specific scheduling strategy is introduced. Then, to measure correctly the convergence of the iterative process, we introduce a reference solution that revisits the product of classical and enriched functions. As a consequence, we are able to propose a purely matrix-based implementation of the global-local problem. The distributed approach is then compared to other parallel solvers either direct or iterative with domain decomposition. The comparison addresses the scalability as well as the elapsed time. Numerical examples deal with linear elastic problems: a polynomial exact solution problem, a complex micro-structure, and, finally, a pull-out test (with different crack extent). 1: C. A. Duarte, D.-J. Kim, and I. Babu\v{s}ka. A global-local approach for the construction of enrichment functions for the generalized fem and its application to three-dimensional cracks. In Advances in Meshfree Techniques, Dordrecht, 2007. Springer
Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient inference algorithms due to the high computational cost of inferring many model parameters based on random sampling. Although Markov Chain Monte Carlo (MCMC) algorithms have been widely used for Bayesian inference, sampling using this class of algorithms is time-consuming for applications with large-scale data and time-sensitive decision-making, partially due to the non-conjugacy of many models. To overcome this limitation, this research develops an approximate Gibbs sampler (AGS) to efficiently learn the HBPRMs while maintaining the inference accuracy. In the proposed sampler, the data likelihood is approximated with Gaussian distribution such that the conditional posterior of the coefficients has a closed-form solution. Numerical experiments using real and synthetic datasets with small and large counts demonstrate the superior performance of AGS in comparison to the state-of-the-art sampling algorithm, especially for large datasets.
We introduce a Loss Discounting Framework for model and forecast combination which generalises and combines Bayesian model synthesis and generalized Bayes methodologies. We use a loss function to score the performance of different models and introduce a multilevel discounting scheme which allows a flexible specification of the dynamics of the model weights. This novel and simple model combination approach can be easily applied to large scale model averaging/selection, can handle unusual features such as sudden regime changes, and can be tailored to different forecasting problems. We compare our method to both established methodologies and state of the art methods for a number of macroeconomic forecasting examples. We find that the proposed method offers an attractive, computationally efficient alternative to the benchmark methodologies and often outperforms more complex techniques.
The generative adversarial networks (GANs) have recently been applied to estimating the distribution of independent and identically distributed data, and got excellent performances. In this paper, we use the blocking technique to demonstrate the effectiveness of GANs for estimating the distribution of stationary time series. Theoretically, we obtain a non-asymptotic error bound for the Deep Neural Network (DNN)-based GANs estimator for the stationary distribution of the time series. Based on our theoretical analysis, we put forward an algorithm for detecting the change-point in time series. We simulate in our first experiment a stationary time series by the multivariate autoregressive model to test our GAN estimator, while the second experiment is to use our proposed algorithm to detect the change-point in a time series sequence. Both perform very well. The third experiment is to use our GAN estimator to learn the distribution of a real financial time series data, which is not stationary, we can see from the experiment results that our estimator cannot match the distribution of the time series very well but give the right changing tendency.
Maneuvering target tracking is a challenging problem for sensor systems because of the unpredictability of the targets' motions. This paper proposes a novel data-driven method for learning the dynamical motion model of a target. Non-parametric Gaussian process regression (GPR) is used to learn a target's naturally shift invariant motion (NSIM) behavior, which is translationally invariant and does not need to be constantly updated as the target moves. The learned Gaussian processes (GPs) can be applied to track targets within different surveillance regions from the surveillance region of the training data by being incorporated into the particle filter (PF) implementation. The performance of our proposed approach is evaluated over different maneuvering scenarios by being compared with commonly used interacting multiple model (IMM)-PF methods and provides around $90\%$ performance improvement for a multi-target tracking (MTT) highly maneuvering scenario.
Local search has been demonstrated as an efficient approach for two practical generalizations of the MaxSAT problem, namely Partial MaxSAT (PMS) and Weighted PMS (WPMS). In this work, we observe that most local search (W)PMS solvers usually flip a single variable per iteration. Such a mechanism may lead to relatively low-quality local optimal solutions, and may limit the diversity of search directions to escape from local optima. To address this issue, we propose a general strategy, called farsighted probabilistic sampling (FPS), to replace the single flipping mechanism so as to boost the local search (W)PMS algorithms. FPS considers the benefit of continuously flipping a pair of variables in order to find higher-quality local optimal solutions. Moreover, FPS proposes an effective approach to escape from local optima by preferring the best to flip among the best sampled single variable and the best sampled variable pair. Extensive experiments demonstrate that our proposed FPS strategy significantly improves the state-of-the-art (W)PMS solvers, and FPS has an excellent generalization capability to various local search MaxSAT solvers.
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.
Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also intrigues great interests in the time series community. Among multiple advantages of transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling, leading to exciting progress in various time series applications. In this paper, we systematically review transformer schemes for time series modeling by highlighting their strengths as well as limitations through a new taxonomy to summarize existing time series transformers in two perspectives. From the perspective of network modifications, we summarize the adaptations of module level and architecture level of the time series transformers. From the perspective of applications, we categorize time series transformers based on common tasks including forecasting, anomaly detection, and classification. Empirically, we perform robust analysis, model size analysis, and seasonal-trend decomposition analysis to study how Transformers perform in time series. Finally, we discuss and suggest future directions to provide useful research guidance. To the best of our knowledge, this paper is the first work to comprehensively and systematically summarize the recent advances of Transformers for modeling time series data. We hope this survey will ignite further research interests in time series Transformers.
The essence of multivariate sequential learning is all about how to extract dependencies in data. These data sets, such as hourly medical records in intensive care units and multi-frequency phonetic time series, often time exhibit not only strong serial dependencies in the individual components (the "marginal" memory) but also non-negligible memories in the cross-sectional dependencies (the "joint" memory). Because of the multivariate complexity in the evolution of the joint distribution that underlies the data generating process, we take a data-driven approach and construct a novel recurrent network architecture, termed Memory-Gated Recurrent Networks (mGRN), with gates explicitly regulating two distinct types of memories: the marginal memory and the joint memory. Through a combination of comprehensive simulation studies and empirical experiments on a range of public datasets, we show that our proposed mGRN architecture consistently outperforms state-of-the-art architectures targeting multivariate time series.
Aspect based sentiment analysis (ABSA) can provide more detailed information than general sentiment analysis, because it aims to predict the sentiment polarities of the given aspects or entities in text. We summarize previous approaches into two subtasks: aspect-category sentiment analysis (ACSA) and aspect-term sentiment analysis (ATSA). Most previous approaches employ long short-term memory and attention mechanisms to predict the sentiment polarity of the concerned targets, which are often complicated and need more training time. We propose a model based on convolutional neural networks and gating mechanisms, which is more accurate and efficient. First, the novel Gated Tanh-ReLU Units can selectively output the sentiment features according to the given aspect or entity. The architecture is much simpler than attention layer used in the existing models. Second, the computations of our model could be easily parallelized during training, because convolutional layers do not have time dependency as in LSTM layers, and gating units also work independently. The experiments on SemEval datasets demonstrate the efficiency and effectiveness of our models.
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