我们提出一个随机在线凸优化的通用框架，以获得快速率的随机遗憾界。我们证明，诸如 online newton steps（在线牛顿步）和 Bernstein online aggregation 的无尺度 10 版本等算法，在无界随机环境中可达到已知最优速率。我们将该方法用于校准非平稳次高斯时间序列的参数化概率预测器。我们的快速率随机遗憾界在任意时刻均有效。证明在随机指数凹性假设下，分别结合了鞅的自界不等式与次高斯随机变量的泊松型不等式。
英文摘要：
We introduce a general framework of stochastic online convex optimization to obtain fast-rate stochastic regret bounds. We prove that algorithms such as online newton steps and a scale-free 10 version of Bernstein online aggregation achieve best-known rates in unbounded stochastic settings. We apply our approach to calibrate parametric probabilistic forecasters of non-stationary sub-gaussian time series. Our fast-rate stochastic regret bounds are any-time valid. Our proofs combine self-bounded and Poissonnian inequalities for martingales and sub-gaussian random variables, respectively, under a stochastic exp-concavity assumption.
Probabilistic forecasting, i.e. estimating the probability distribution of a time series' future given its past, is a key enabler for optimizing business processes. In retail businesses, for example, forecasting demand is crucial for having the right inventory available at the right time at the right place. In this paper we propose DeepAR, a methodology for producing accurate probabilistic forecasts, based on training an auto regressive recurrent network model on a large number of related time series. We demonstrate how by applying deep learning techniques to forecasting, one can overcome many…
AI Institute（人工智能研究院）；Shanghai Jiao Tong University（上海交通大学）
Probabilistic time series forecasting involves estimating the distribution of future based on its history, which is essential for risk management in downstream decision-making. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks and the dependency is modeled by recurrent neural nets. We take the automatic relevance determination (ARD) view and devise a network to exploit the exogenous variables in addition to time series. In particular, our ARD network can incorporate the uncertai…
Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications -- the goal is to obtain coherent probabilistic predictions for a large number of time series arranged in a pre-specified tree hierarchy. In this paper, we present an end-to-end deep probabilistic model for hierarchical forecasting that is motivated by a classical top-down strategy. It jointly learns the distribution of the root time series, and the (dirichlet) proportions according to which each parent time-series is split among its children at any point in time. The resulting foreca…
University of Kaiserslautern（凯泽斯劳滕大学）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心（DFKI））
Time series forecasting is one of the challenging problems for humankind. Traditional forecasting methods using mean regression models have severe shortcomings in reflecting real-world fluctuations. While new probabilistic methods rush to rescue, they fight with technical difficulties like quantile crossing or selecting a prior distribution. To meld the different strengths of these fields while avoiding their weaknesses as well as to push the boundary of the state-of-the-art, we introduce ForGAN - one step ahead probabilistic forecasting with generative adversarial networks. ForGAN utilizes th…
ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations
Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
National Technical University of Athens（雅典国立技术大学）；Hellenic Air Force（希腊空军）
Probabilistic forecasting is receiving growing attention nowadays in a variety of applied fields, including hydrology. Several machine learning concepts and methods are notably relevant towards addressing the major challenges of formalizing and optimizing probabilistic forecasting implementations, as well as the equally important challenge of identifying the most useful ones among these implementations. Nonetheless, practically-oriented reviews focusing on such concepts and methods, and on how these can be effectively exploited in the above-outlined essential endeavour, are currently missing f…
Toronto Metropolitan University（多伦多都会大学）；University of Toronto（多伦多大学）
Despite the high performance of neural network-based time series forecasting methods, the inherent challenge in explaining their predictions has limited their applicability in certain application areas. Due to the difficulty in identifying causal relationships between the input and output of such black-box methods, they rarely have been adopted in domains such as legal and medical fields in which the reliability and interpretability of the results can be essential. In this paper, we propose \model, a novel deep learning-based probabilistic time series forecasting architecture that is intrinsic…
Point forecasting of univariate time series is a challenging problem with extensive work having been conducted. However, nonparametric probabilistic forecasting of time series, such as in the form of quantiles or prediction intervals is an even more challenging problem. In an effort to expand the possible forecasting paradigms we devise and explore an extrapolation-based approach that has not been applied before for probabilistic forecasting. We present a novel quantile Fourier neural network is for nonparametric probabilistic forecasting of univariate time series. Multi-step predictions are p…
We discuss an approach to probabilistic forecasting based on two chained machine-learning steps: a dimensional reduction step that learns a reduction map of predictor information to a low-dimensional space in a manner designed to preserve information about forecast quantities; and a density estimation step that uses the probabilistic machine learning technique of normalizing flows to compute the joint probability density of reduced predictors and forecast quantities. This joint density is then renormalized to produce the conditional forecast distribution. In this method, probabilistic calibrat…
Probabilistic time-series models become popular in the forecasting field as they help to make optimal decisions under uncertainty. Despite the growing interest, a lack of thorough analysis hinders choosing what is worth applying for the desired task. In this paper, we analyze the performance of three prominent probabilistic time-series models for sales forecasting. To remove the role of random chance in architecture's performance, we make two experimental principles; 1) Large-scale dataset with various cross-validation sets. 2) A standardized training and hyperparameter selection. The experime…
Department of Computer Science, ETH Zürich（苏黎世联邦理工学院计算机科学系）；Department of Computer Science, ETH Zürich, Switzerland（苏黎世联邦理工学院计算机科学系）
We develop an effective generation of adversarial attacks on neural models that output a sequence of probability distributions rather than a sequence of single values. This setting includes the recently proposed deep probabilistic autoregressive forecasting models that estimate the probability distribution of a time series given its past and achieve state-of-the-art results in a diverse set of application domains. The key technical challenge we address is effectively differentiating through the Monte-Carlo estimation of statistics of the joint distribution of the output sequence. Additionally,…
We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is expanded from a set of fixed quantiles to the whole Quantile Function by a univariate mapping from a latent uniform distribution to the target distribution. Then the multivariate case is solved by learning such quantile functions for each dimension's marginal distribution, followed by estimating a conditional Copula to associate these latent uniform random va…
Sharif University of Technology（谢里夫理工大学）；Institute of Science and Technology Austria (IST Austria)（奥地利科学技术研究所（IST Austria））
We introduce a spatio-temporal convolutional neural network model for trajectory forecasting from visual sources. Applied in an auto-regressive way it provides an explicit probability distribution over continuations of a given initial trajectory segment. We discuss it in relation to (more complicated) existing work and report on experiments on two standard datasets for trajectory forecasting: MNISTseq and Stanford Drones, achieving results on-par with or better than previous methods.
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 o…
Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE model for representing structured diversity based on shape and time features, ensuring both probable predictions while being sharp and accurate. STRIPE is agnostic to the forecasting model, and we equip it with a diversification mechanism relying on determinantal point processes (DPP). We introduce two DPP kernels for modeling diverse trajectories in terms of…
Middle-term horizon (months to a year) power consumption prediction is a main challenge in the energy sector, in particular when probabilistic forecasting is considered. We propose a new modelling approach that incorporates trend, seasonality and weather conditions, as explicative variables in a shallow Neural Network with an autoregressive feature. We obtain excellent results for density forecast on the one-year test set applying it to the daily power consumption in New England U.S.A.. The quality of the achieved power consumption probabilistic forecasting has been verified, on the one hand, …
Bigo Inc.（Bigo公司）；Beihang University（北京航空航天大学）；IBM China CIC（IBM中国创新中心）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
We present a probabilistic forecasting framework based on convolutional neural network for multiple related time series forecasting. The framework can be applied to estimate probability density under both parametric and non-parametric settings. More specifically, stacked residual blocks based on dilated causal convolutional nets are constructed to capture the temporal dependencies of the series. Combined with representation learning, our approach is able to learn complex patterns such as seasonality, holiday effects within and across series, and to leverage those patterns for more accurate for…
Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization
University of Oxford（牛津大学）；Southern University of Science and Technology（南方科技大学）；University of Warwick（华威大学）；European Centre for Medium-Range Weather Forecasts（欧洲中期天气预报中心）
Artificial Intelligence Department Universidad Nacional de Educación a Distancia — UNED（西班牙马德里开放大学（UNED）人工智能系）
High concentration episodes for NO$_2$ are increasingly dealt with by authorities through traffic restrictions which are activated when air quality deteriorates beyond certain thresholds. Foreseeing the probability that pollutant concentrations reach those thresholds becomes thus a necessity. Probabilistic forecasting is a family of techniques that allow for the prediction of the expected distribution function instead of a single value. In the case of NO$_2$, it allows for the calculation of future chances of exceeding thresholds and to detect pollution peaks. We thoroughly compared 10 state o…
Time-series is ubiquitous across applications, such as transportation, finance and healthcare. Time-series is often influenced by external factors, especially in the form of asynchronous events, making forecasting difficult. However, existing models are mainly designated for either synchronous time-series or asynchronous event sequence, and can hardly provide a synthetic way to capture the relation between them. We propose Variational Synergetic Multi-Horizon Network (VSMHN), a novel deep conditional generative model. To learn complex correlations across heterogeneous sequences, a tailored enc…
Probabilistic forecasting of electricity load curves is of fundamental importance for effective scheduling and decision making in the increasingly volatile and competitive energy markets. We propose a novel approach to construct probabilistic predictors for curves (PPC), which leads to a natural and new definition of quantiles in the context of curve-to-curve linear regression. There are three types of PPC: a predictive set, a predictive band and a predictive quantile, all of which are defined at a pre-specified nominal probability level. In the simulation study, the PPC achieve promising cove…
Multivariate time series prediction has attracted a lot of attention because of its wide applications such as intelligence transportation, AIOps. Generative models have achieved impressive results in time series modeling because they can model data distribution and take noise into consideration. However, many existing works can not be widely used because of the constraints of functional form of generative models or the sensitivity to hyperparameters. In this paper, we propose ScoreGrad, a multivariate probabilistic time series forecasting framework based on continuous energy-based generative m…
We study the estimation of the probability distribution of individual patient waiting times in an emergency department (ED). Our feature-rich modelling allows for dynamic updating and refinement of waiting time estimates as patient- and ED-specific information (e.g., patient condition, ED congestion levels) is revealed during the waiting process. Aspects relating to communicating forecast uncertainty to patients, and implementing this methodology in practice, are also discussed.
The exponential growth of renewable energy capacity has brought much uncertainty to electricity prices and to electricity generation. To address this challenge, the energy exchanges have been developing further trading possibilities, especially the intraday and balancing markets. For an energy trader participating in both markets, the forecasting of imbalance prices is of particular interest. Therefore, in this manuscript we conduct a very short-term probabilistic forecasting of imbalance prices, contributing to the scarce literature in this novel subject. The forecasting is performed 30 minut…
Dalian University of Technology（大连理工大学）；Shenyang Blower Works Group Corporation（沈阳鼓风机集团股份有限公司）
The demand of probabilistic time series forecasting has been recently raised in various dynamic system scenarios, for example, system identification and prognostic and health management of machines. To this end, we combine the advances in both deep generative models and state space model (SSM) to come up with a novel, data-driven deep probabilistic sequence model. Specifically, we follow the popular encoder-decoder generative structure to build the recurrent neural networks (RNN) assisted variational sequence model on an augmented recurrent input space, which could induce rich stochastic seque…
We propose a new framework of XGBoost that predicts the entire conditional distribution of a univariate response variable. In particular, XGBoostLSS models all moments of a parametric distribution (i.e., mean, location, scale and shape [LSS]) instead of the conditional mean only. Choosing from a wide range of continuous, discrete and mixed discrete-continuous distribution, modelling and predicting the entire conditional distribution greatly enhances the flexibility of XGBoost, as it allows to gain additional insight into the data generating process, as well as to create probabilistic forecasts…
We present new Bayesian methodology for consumer sales forecasting. With a focus on multi-step ahead forecasting of daily sales of many supermarket items, we adapt dynamic count mixture models to forecast individual customer transactions, and introduce novel dynamic binary cascade models for predicting counts of items per transaction. These transactions-sales models can incorporate time-varying trend, seasonal, price, promotion, random effects and other outlet-specific predictors for individual items. Sequential Bayesian analysis involves fast, parallel filtering on sets of decoupled items and…
Benchmarking Probabilistic Time Series Forecasting Models on Neural Activity
Department of Applied Mathematics, University of Washington（应用数学系，华盛顿大学）；Department of Neurobiology and Biophysics, University of Washington（神经生物学与生物物理学系，华盛顿大学）；Allen Institute for Brain Science（脑科学研究所）；Department of Electrical and Computer Engineering, University of Washington（电气与计算机工程系，华盛顿大学）
We propose a new framework of CatBoost that predicts the entire conditional distribution of a univariate response variable. In particular, CatBoostLSS models all moments of a parametric distribution (i.e., mean, location, scale and shape [LSS]) instead of the conditional mean only. Choosing from a wide range of continuous, discrete and mixed discrete-continuous distributions, modelling and predicting the entire conditional distribution greatly enhances the flexibility of CatBoost, as it allows to gain insight into the data generating process, as well as to create probabilistic forecasts from w…
Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（工业与系统工程系，佐治亚理工学院）；AI Institute for Advances in Optimization（优化前沿人工智能研究所）
Greater direct electrification of end-use sectors with a higher share of renewables is one of the pillars to power a carbon-neutral society by 2050. However, in contrast to conventional power plants, renewable energy is subject to uncertainty raising challenges for their interaction with power systems. Scenario-based probabilistic forecasting models have become a vital tool to equip decision-makers. This paper presents to the power systems forecasting practitioners a recent deep learning technique, the normalizing flows, to produce accurate scenario-based probabilistic forecasts that are cruci…
The M5 competition uncertainty track aims for probabilistic forecasting of sales of thousands of Walmart retail goods. We show that the M5 competition data faces strong overdispersion and sporadic demand, especially zero demand. We discuss resulting modeling issues concerning adequate probabilistic forecasting of such count data processes. Unfortunately, the majority of popular prediction methods used in the M5 competition (e.g. lightgbm and xgboost GBMs) fails to address the data characteristics due to the considered objective functions. The distributional forecasting provides a suitable mode…
We propose a fully probabilistic prediction model for spatially aggregated solar photovoltaic (PV) power production at an hourly time scale with lead times up to several days using weather forecasts from numerical weather prediction systems as covariates. After an appropriate logarithmic transformation of the power production, we develop a multivariate Gaussian prediction model under a Bayesian inference framework. The model incorporates the temporal error correlation yielding physically consistent forecast trajectories. Several formulations of the correlation structure are proposed and invest…
