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Register a new userIntermittent Demand Forecasting with Renewal Processes
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Intermittency is a common and challenging problem in demand forecasting. We introduce a new, unified framework for building intermittent demand forecasting models, which incorporates and allows to generalize existing methods in several directions. Our framework is based on extensions of well-established model-based methods to discrete-time renewal processes, which can parsimoniously account for patterns such as aging, clustering and quasi-periodicity in demand arrivals. The connection to discrete-time renewal processes allows not only for a principled extension of Croston-type models, but also for an natural inclusion of neural network based models---by replacing exponential smoothing with a recurrent neural network. We also demonstrate that modeling continuous-time demand arrivals, i.e., with a temporal point process, is possible via a trivial extension of our framework. This leads to more flexible modeling in scenarios where data of individual purchase orders are directly available with granular timestamps. Complementing this theoretical advancement, we demonstrate the efficacy of our framework for forecasting practice via an extensive empirical study on standard intermittent demand data sets, in which we report predictive accuracy in a variety of scenarios that compares favorably to the state of the art.
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Platelet products are both expensive and have very short shelf lives. As usage rates for platelets are highly variable, the effective management of platelet demand and supply is very important yet challenging. The primary goal of this paper is to present an efficient forecasting model for platelet demand at Canadian Blood Services (CBS). To accomplish this goal, four different demand forecasting methods, ARIMA (Auto Regressive Moving Average), Prophet, lasso regression (least absolute shrinkage and selection operator) and LSTM (Long Short-Term Memory) networks are utilized and evaluated. We use a large clinical dataset for a centralized blood distribution centre for four hospitals in Hamilton, Ontario, spanning from 2010 to 2018 and consisting of daily platelet transfusions along with information such as the product specifications, the recipients characteristics, and the recipients laboratory test results. This study is the first to utilize different methods from statistical time series models to data-driven regression and a machine learning technique for platelet transfusion using clinical predictors and with different amounts of data. We find that the multivariate approaches have the highest accuracy in general, however, if sufficient data are available, a simpler time series approach such as ARIMA appears to be sufficient. We also comment on the approach to choose clinical indicators (inputs) for the multivariate models.
We consider the problem of optimizing a vector-valued objective function $boldsymbol{f}$ sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space $({cal X},d)$ of designs. We assume that $boldsymbol{f}$ is not known beforehand and that evaluating $boldsymbol{f}$ at design $x$ results in a noisy observation of $boldsymbol{f}(x)$. Since identifying the Pareto optimal designs via exhaustive search is infeasible when the cardinality of ${cal X}$ is large, we propose an algorithm, called Adaptive $boldsymbol{epsilon}$-PAL, that exploits the smoothness of the GP-sampled function and the structure of $({cal X},d)$ to learn fast. In essence, Adaptive $boldsymbol{epsilon}$-PAL employs a tree-based adaptive discretization technique to identify an $boldsymbol{epsilon}$-accurate Pareto set of designs in as few evaluations as possible. We provide both information-type and metric dimension-type bounds on the sample complexity of $boldsymbol{epsilon}$-accurate Pareto set identification. We also experimentally show that our algorithm outperforms other Pareto set identification methods on several benchmark datasets.
Neural processes (NPs) constitute a family of variational approximate models for stochastic processes with promising properties in computational efficiency and uncertainty quantification. These processes use neural networks with latent variable inputs to induce predictive distributions. However, the expressiveness of vanilla NPs is limited as they only use a global latent variable, while target specific local variation may be crucial sometimes. To address this challenge, we investigate NPs systematically and present a new variant of NP model that we call Doubly Stochastic Variational Neural Process (DSVNP). This model combines the global latent variable and local latent variables for prediction. We evaluate this model in several experiments, and our results demonstrate competitive prediction performance in multi-output regression and uncertainty estimation in classification.
Demand forecasting is a central component of the replenishment process for retailers, as it provides crucial input for subsequent decision making like ordering processes. In contrast to point estimates, such as the conditional mean of the underlying probability distribution, or confidence intervals, forecasting complete probability density functions allows to investigate the impact on operational metrics, which are important to define the business strategy, over the full range of the expected demand. Whereas metrics evaluating point estimates are widely used, methods for assessing the accuracy of predicted distributions are rare, and this work proposes new techniques for both qualitative and quantitative evaluation methods. Using the supervised machine learning method Cyclic Boosting, complete individual probability density functions can be predicted such that each prediction is fully explainable. This is of particular importance for practitioners, as it allows to avoid black-box models and understand the contributing factors for each individual prediction. Another crucial aspect in terms of both explainability and generalizability of demand forecasting methods is the limitation of the influence of temporal confounding, which is prevalent in most state of the art approaches.
Earth observation (EO) by airborne and satellite remote sensing and in-situ observations play a fundamental role in monitoring our planet. In the last decade, machine learning and Gaussian processes (GPs) in particular has attained outstanding results in the estimation of bio-geo-physical variables from the acquired images at local and global scales in a time-resolved manner. GPs provide not only accurate estimates but also principled uncertainty estimates for the predictions, can easily accommodate multimodal data coming from different sensors and from multitemporal acquisitions, allow the introduction of physical knowledge, and a formal treatment of uncertainty quantification and error propagation. Despite great advances in forward and inverse modelling, GP models still have to face important challenges that are revised in this perspective paper. GP models should evolve towards data-driven physics-aware models that respect signal characteristics, be consistent with elementary laws of physics, and move from pure regression to observational causal inference.
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