Probabilistic time series forecasting is crucial in many application domains such as retail, ecommerce, finance, or biology. With the increasing availability of large volumes of data, a number of neural architectures have been proposed for this problem. In particular, Transformer-based methods achieve state-of-the-art performance on real-world benchmarks. However, these methods require a large number of parameters to be learned, which imposes high memory requirements on the computational resources for training such models. To address this problem, we introduce a novel Bidirectional Temporal Convolutional Network (BiTCN), which requires an order of magnitude less parameters than a common Transformer-based approach. Our model combines two Temporal Convolutional Networks (TCNs): the first network encodes future covariates of the time series, whereas the second network encodes past observations and covariates. We jointly estimate the parameters of an output distribution via these two networks. Experiments on four real-world datasets show that our method performs on par with four state-of-the-art probabilistic forecasting methods, including a Transformer-based approach and WaveNet, on two point metrics (sMAPE, NRMSE) as well as on a set of range metrics (quantile loss percentiles) in the majority of cases. Secondly, we demonstrate that our method requires significantly less parameters than Transformer-based methods, which means the model can be trained faster with significantly lower memory requirements, which as a consequence reduces the infrastructure cost for deploying these models.
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Reliable probability estimation is of crucial importance in many real-world applications where there is inherent uncertainty, such as weather forecasting, medical prognosis, or collision avoidance in autonomous vehicles. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the important difference that the objective is to estimate probabilities rather than predicting the specific outcome. The goal of this work is to investigate probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on classification problems where the probabilities are related to model uncertainty. In the case of problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.
As a traditional and widely-adopted mortality rate projection technique, by representing the log mortality rate as a simple bilinear form $\log(m_{x,t})=a_x+b_xk_t$. The Lee-Carter model has been extensively studied throughout the past 30 years, however, the performance of the model in the presence of outliers has been paid little attention, particularly for the parameter estimation of $b_x$. In this paper, we propose a robust estimation method for Lee-Carter model by formulating it as a probabilistic principal component analysis (PPCA) with multivariate $t$-distributions, and an efficient expectation-maximization (EM) algorithm for implementation. The advantages of the method are threefold. It yields significantly more robust estimates of both $b_x$ and $k_t$, preserves the fundamental interpretation for $b_x$ as the first principal component as in the traditional approach and is flexible to be integrated into other existing time series models for $k_t$. The parameter uncertainties are examined by adopting a standard residual bootstrap. A simulation study based on Human Mortality Database shows superior performance of the proposed model compared to other conventional approaches.
Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.
Time series forecasting is widely used in business intelligence, e.g., forecast stock market price, sales, and help the analysis of data trend. Most time series of interest are macroscopic time series that are aggregated from microscopic data. However, instead of directly modeling the macroscopic time series, rare literature studied the forecasting of macroscopic time series by leveraging data on the microscopic level. In this paper, we assume that the microscopic time series follow some unknown mixture probabilistic distributions. We theoretically show that as we identify the ground truth latent mixture components, the estimation of time series from each component could be improved because of lower variance, thus benefitting the estimation of macroscopic time series as well. Inspired by the power of Seq2seq and its variants on the modeling of time series data, we propose Mixture of Seq2seq (MixSeq), an end2end mixture model to cluster microscopic time series, where all the components come from a family of Seq2seq models parameterized by different parameters. Extensive experiments on both synthetic and real-world data show the superiority of our approach.
Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the art point forecasting methods.
Personalized recommender systems are playing an increasingly important role as more content and services become available and users struggle to identify what might interest them. Although matrix factorization and deep learning based methods have proved effective in user preference modeling, they violate the triangle inequality and fail to capture fine-grained preference information. To tackle this, we develop a distance-based recommendation model with several novel aspects: (i) each user and item are parameterized by Gaussian distributions to capture the learning uncertainties; (ii) an adaptive margin generation scheme is proposed to generate the margins regarding different training triplets; (iii) explicit user-user/item-item similarity modeling is incorporated in the objective function. The Wasserstein distance is employed to determine preferences because it obeys the triangle inequality and can measure the distance between probabilistic distributions. Via a comparison using five real-world datasets with state-of-the-art methods, the proposed model outperforms the best existing models by 4-22% in terms of recall@K on Top-K recommendation.
Markov Logic Networks (MLNs), which elegantly combine logic rules and probabilistic graphical models, can be used to address many knowledge graph problems. However, inference in MLN is computationally intensive, making the industrial-scale application of MLN very difficult. In recent years, graph neural networks (GNNs) have emerged as efficient and effective tools for large-scale graph problems. Nevertheless, GNNs do not explicitly incorporate prior logic rules into the models, and may require many labeled examples for a target task. In this paper, we explore the combination of MLNs and GNNs, and use graph neural networks for variational inference in MLN. We propose a GNN variant, named ExpressGNN, which strikes a nice balance between the representation power and the simplicity of the model. Our extensive experiments on several benchmark datasets demonstrate that ExpressGNN leads to effective and efficient probabilistic logic reasoning.
Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is the Markov Logic Network (MLN), which is able to leverage domain knowledge with first-order logic and meanwhile handle their uncertainty. However, the inference of MLNs is usually very difficult due to the complicated graph structures. Different from MLNs, knowledge graph embedding methods (e.g. TransE, DistMult) learn effective entity and relation embeddings for reasoning, which are much more effective and efficient. However, they are unable to leverage domain knowledge. In this paper, we propose the probabilistic Logic Neural Network (pLogicNet), which combines the advantages of both methods. A pLogicNet defines the joint distribution of all possible triplets by using a Markov logic network with first-order logic, which can be efficiently optimized with the variational EM algorithm. In the E-step, a knowledge graph embedding model is used for inferring the missing triplets, while in the M-step, the weights of logic rules are updated based on both the observed and predicted triplets. Experiments on multiple knowledge graphs prove the effectiveness of pLogicNet over many competitive baselines.
Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.
We propose a temporally coherent generative model addressing the super-resolution problem for fluid flows. Our work represents a first approach to synthesize four-dimensional physics fields with neural networks. Based on a conditional generative adversarial network that is designed for the inference of three-dimensional volumetric data, our model generates consistent and detailed results by using a novel temporal discriminator, in addition to the commonly used spatial one. Our experiments show that the generator is able to infer more realistic high-resolution details by using additional physical quantities, such as low-resolution velocities or vorticities. Besides improvements in the training process and in the generated outputs, these inputs offer means for artistic control as well. We additionally employ a physics-aware data augmentation step, which is crucial to avoid overfitting and to reduce memory requirements. In this way, our network learns to generate advected quantities with highly detailed, realistic, and temporally coherent features. Our method works instantaneously, using only a single time-step of low-resolution fluid data. We demonstrate the abilities of our method using a variety of complex inputs and applications in two and three dimensions.
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