We introduce an individual claims forecasting framework utilizing Bayesian mixture density networks that can be used for claims analytics tasks such as case reserving and triaging. The proposed approach enables incorporating claims information from both structured and unstructured data sources, producing multi-period cash flow forecasts, and generating different scenarios of future payment patterns. We implement and evaluate the modeling framework using publicly available data.
Combining Structural and Unstructured Data: A Topic-based Finite Mixture Model for Insurance Claim Prediction
School of Data Science, Fudan University（复旦大学数据科学学院）；Center for Applied Statistics and School of Statistics, Renmin University of China（中国人民大学应用统计中心与统计学院）
This paper sets out a forecasting method that employs a mixture of parametric functions to capture the pattern of fertility with respect to age. The overall level of cohort fertility is decomposed over the range of fertile ages using a mixture of parametric density functions. The level of fertility and the parameters describing the shape of the fertility curve are projected foward using time series methods. The model is estimated within a Bayesian framework, allowing predictive distributions of future fertility rates to be produced that naturally incorporate both time series and parametric unc…
Accurate forecasting of bus travel time and its uncertainty is critical to service quality and operation of transit systems; for example, it can help passengers make better decisions on departure time, route choice, and even transport mode choice and also support transit operators to make informed decisions on tasks such as crew/vehicle scheduling and timetabling. However, most existing approaches in bus travel time forecasting are based on deterministic models that provide only point estimation. To this end, we develop in this paper a Bayesian probabilistic forecasting model for bus travel ti…
XRMDN: An Extended Recurrent Mixture Density Network for Short-Term Probabilistic Rider Demand Forecasting with High Volatility
Concordia University（康考迪亚大学）；Concordia Institute for Information Systems Engineering (CIISE)（康考迪亚信息系统工程研究所）；Concordia John Molson School of Business (JMSB)（康考迪亚约翰莫尔森商学院）
针对 MoD 需求受内外因素影响且高波动、传统点预测难以刻画不确定性的问题，提出 XRMDN 深度概率预测框架，并在真实数据集上验证其优于基准模型。
Forecasting the outstanding claim liabilities to set adequate reserves is critical for a nonlife insurer's solvency. Chain-Ladder and Bornhuetter-Ferguson are two prominent actuarial approaches used for this task. The selection between the two approaches is often ad hoc due to different underlying assumptions. We introduce a Dirichlet model that provides a common statistical framework for the two approaches, with some appealing properties. Depending on the type of information available, the model inference naturally leads to either Chain-Ladder or Bornhuetter-Ferguson prediction. Using claims …
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 lat…
AdaMixT: Adaptive Weighted Mixture of Multi-Scale Expert Transformers for Time Series Forecasting
School of Computer Science, Peking University（北京大学计算机科学系）；Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）；Tsinghua University（清华大学）
Probabilistic Computing Project Massachusetts Institute of Technology（麻省理工学院概率计算项目）
This article proposes a Bayesian nonparametric method for forecasting, imputation, and clustering in sparsely observed, multivariate time series data. The method is appropriate for jointly modeling hundreds of time series with widely varying, non-stationary dynamics. Given a collection of $N$ time series, the Bayesian model first partitions them into independent clusters using a Chinese restaurant process prior. Within a cluster, all time series are modeled jointly using a novel "temporally-reweighted" extension of the Chinese restaurant process mixture. Markov chain Monte Carlo techniques are…
LeMoLE: LLM-Enhanced Mixture of Linear Experts for Time Series Forecasting
Hong Kong University of Science and Technology（香港科技大学）；Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；University of Cologne（科隆大学）
Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）；Respirer Living Sciences（Respirer生命科学公司）
The identification and control of human factors in climate change is a rapidly growing concern and robust, real-time air-quality monitoring and forecasting plays a critical role in allowing effective policy formulation and implementation. This paper presents DELFI, a novel deep learning-based mixture model to make effective long-term predictions of Particulate Matter (PM) 2.5 concentrations. A key novelty in DELFI is its multi-scale approach to the forecasting problem. The observation that point predictions are more suitable in the short-term and probabilistic predictions in the long-term allo…
In general insurance, risks from different categories are often modeled independently and their sum is regarded as the total risk the insurer takes on in exchange for a premium. The dependence from multiple risks is generally neglected even when correlation could exist, for example a single car accident may result in claims from multiple risk categories. It is desirable to take the covariance of different categories into consideration in modeling in order to better predict future claims and hence allow greater accuracy in ratemaking. In this work multivariate severity models are investigated u…
Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly desig…
This article, in a first step, considers two Bayes estimators for the relativity premium of a given Bonus--Malus system. It then develops a linear relativity premium that closes, in the sense of weighted mean square error loss, to such Bayes estimators. In a second step, it supposes that the claim size distribution for a given Bonus--Malus system can be formulated as a finite mixture distribution. It then evaluates the base premium under a Bayesian framework for such a finite mixture distribution. The Loimaranta efficiency of such a linear relativity premium, for several Bonus--Malus systems, …
There has been growing interest on forecasting mortality. In this article, we propose a novel dynamic Bayesian approach for modeling and forecasting the age-at-death distribution, focusing on a three-components mixture of a Dirac mass, a Gaussian distribution and a Skew-Normal distribution. According to the specified model, the age-at-death distribution is characterized via seven parameters corresponding to the main aspects of infant, adult and old-age mortality. The proposed approach focuses on coherent modeling of multiple countries, and following a Bayesian approach to inference we allow to…
University of Oxford（牛津大学）；Oxford-Man Institute of Quantitative Finance（牛津-曼量化金融研究所）
Generative Adversarial Networks (GANs) have gained significant attention in recent years, with impressive applications highlighted in computer vision in particular. Compared to such examples, however, there have been more limited applications of GANs to time series modelling, including forecasting. In this work, we present the Mixture Density Conditional Generative Adversarial Model (MD-CGAN), with a focus on time series forecasting. We show that our model is capable of estimating a probabilistic posterior distribution over forecasts and that, in comparison to a set of benchmark methods, the M…
Massive informations about individual (household, small and medium enterprise) consumption are now provided with new metering technologies and the smart grid. Two major exploitations of these data are load profiling and forecasting at different scales on the grid. Customer segmentation based on load classification is a natural approach for these purposes. We propose here a new methodology based on mixture of high-dimensional regression models. The novelty of our approach is that we focus on uncovering classes or clusters corresponding to different regression models. As a consequence, these cla…
MoFE: A Novel Mixture-of-Experts Framework with Fourier Neural Operators for Cryptocurrency Forecasting
School of Art and Science University of Rochester（罗切斯特大学艺术与科学学院）；AGI Lab Beijing Institute of Mathematical Sciences and Applications（北京数学科学与应用研究院AGI实验室）
Virginia Tech（弗吉尼亚理工大学）；Mississippi State University（密西西比州立大学）
Modeling the spatiotemporal nature of the spread of infectious diseases can provide useful intuition in understanding the time-varying aspect of the disease spread and the underlying complex spatial dependency observed in people's mobility patterns. Besides, the county level multiple related time series information can be leveraged to make a forecast on an individual time series. Adding to this challenge is the fact that real-time data often deviates from the unimodal Gaussian distribution assumption and may show some complex mixed patterns. Motivated by this, we develop a deep learning-based …
TimeSynth: A Framework for Uncovering Systematic Biases in Time Series Forecasting
Scientific Computing and Imaging Institute, University of Utah（科学计算与成像研究所，犹他大学）；Kahlert School of Computing, University of Utah（Kahlert计算学院，犹他大学）；Mountain Biometrics Inc.（山景生物医学公司）；Department of Psychiatry, University of Utah（精神病学系，犹他大学）
Recent studies concerning the point electricity price forecasting have shown evidence that the hourly German Intraday Continuous Market is weak-form efficient. Therefore, we take a novel, advanced approach to the problem. A probabilistic forecasting of the hourly intraday electricity prices is performed by simulating trajectories in every trading window to receive a realistic ensemble to allow for more efficient intraday trading and redispatch. A generalized additive model is fitted to the price differences with the assumption that they follow a zero-inflated distribution, precisely a mixture …
This article introduces a k-Inflated Negative Binomial mixture distribution/regression model as a more flexible alternative to zero-inflated Poisson distribution/regression model. An EM algorithm has been employed to estimate the model's parameters. Then, such new model along with a Pareto mixture model have been employed to design an optimal rate--making system. Namely, this article employs number/size of reported claims of Iranian third party insurance dataset. Then, it employs the k-Inflated Negative Binomial mixture distribution/regression model as well as other well developed counting mod…
National University of Singapore（新加坡国立大学）；Shenzhen University（深圳大学）；The Hong Kong Polytechnic University（香港理工大学）；ETRI（韩国电子通信研究院）；UST（韩国科学技术联合大学院大学）；National Yang Ming Chiao Tung University（阳明交通大学）
This companion paper supports the replication of the fashion trend forecasting experiments with the KERN (Knowledge Enhanced Recurrent Network) method that we presented in the ICMR 2020. We provide an artifact that allows the replication of the experiments using a Python implementation. The artifact is easy to deploy with simple installation, training and evaluation. We reproduce the experiments conducted in the original paper and obtain similar performance as previously reported. The replication results of the experiments support the main claims in the original paper.
Seoul National University（首尔大学）；Korea Aerospace University（韩国航空大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）
Multiple seasonal patterns play a key role in time series forecasting, especially for business time series where seasonal effects are often dramatic. Previous approaches including Fourier decomposition, exponential smoothing, and seasonal autoregressive integrated moving average (SARIMA) models do not reflect the distinct characteristics of each period in seasonal patterns. We propose a mixed hierarchical seasonality (MHS) model. Intermediate parameters for each seasonal period are first estimated, and a mixture of intermediate parameters is taken. This results in a model that automatically le…
A novel predictor for traffic flow forecasting, namely spatio-temporal Bayesian network predictor, is proposed. Unlike existing methods, our approach incorporates all the spatial and temporal information available in a transportation network to carry our traffic flow forecasting of the current site. The Pearson correlation coefficient is adopted to rank the input variables (traffic flows) for prediction, and the best-first strategy is employed to select a subset as the cause nodes of a Bayesian network. Given the derived cause nodes and the corresponding effect node in the spatio-temporal Baye…
Deep probabilistic time series forecasting models have become an integral part of machine learning. While several powerful generative models have been proposed, we provide evidence that their associated inference models are oftentimes too limited and cause the generative model to predict mode-averaged dynamics. Modeaveraging is problematic since many real-world sequences are highly multi-modal, and their averaged dynamics are unphysical (e.g., predicted taxi trajectories might run through buildings on the street map). To better capture multi-modality, we develop variational dynamic mixtures (V…
Our article considers the class of recently developed stochastic models that combine claims payments and incurred losses information into a coherent reserving methodology. In particular, we develop a family of Heirarchical Bayesian Paid-Incurred-Claims models, combining the claims reserving models of Hertig et al. (1985) and Gogol et al. (1993). In the process we extend the independent log-normal model of Merz et al. (2010) by incorporating different dependence structures using a Data-Augmented mixture Copula Paid-Incurred claims model. The utility and influence of incorporating both payment a…
EPFL（洛桑联邦理工学院）；Cyber-Defence Campus, armasuisse Science and Technology（瑞士联邦国防采购局科技网络防御园区）；University of Geneva（日内瓦大学）；University of Applied Sciences of Western Switzerland（瑞士西部应用科学大学）
Because of the considerable heterogeneity and complexity of the technological landscape, building accurate models to forecast is a challenging endeavor. Due to their high prevalence in many complex systems, S-curves are a popular forecasting approach in previous work. However, their forecasting performance has not been directly compared to other technology forecasting approaches. Additionally, recent developments in time series forecasting that claim to improve forecasting accuracy are yet to be applied to technological development data. This work addresses both research gaps by comparing the …
A well-designed framework for risk classification and ratemaking in automobile insurance is key to insurers' profitability and risk management, while also ensuring that policyholders are charged a fair premium according to their risk profile. In this paper, we propose to adapt a flexible regression model, called the Mixed LRMoE, to the problem of a posteriori risk classification and ratemaking, where policyholder-level random effects are incorporated to better infer their risk profile reflected by the claim history. We also develop a stochastic variational Expectation-Conditional-Maximization …
Online Time Series Forecasting with Theoretical Guarantees
Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Guangdong University of Technology（广东技术大学）；Johns Hopkins University（约翰霍普金斯大学）；University of California San Diego（加州大学圣地亚哥分校）
Bayesian model averaging (BMA) is a statistical method for post-processing forecast ensembles of atmospheric variables, obtained from multiple runs of numerical weather prediction models, in order to create calibrated predictive probability density functions (PDFs). The BMA predictive PDF of the future weather quantity is the mixture of the individual PDFs corresponding to the ensemble members and the weights and model parameters are estimated using ensemble members and validating observation from a given training period. In the present paper we introduce a BMA model for calibrating wind speed…
