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 of the challenges faced by widely-used classical approaches to the problem. We show through extensive empirical evaluation on several real-world forecasting data sets accuracy improvements of around 15% compared to state-of-the-art methods.

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We propose an unbounded-depth, hierarchical, Bayesian nonparametric model for discrete sequence data. This model can be estimated from a single training sequence, yet shares statistical strength between subsequent symbol predictive distributions in such a way that predictive performance generalizes well. The model builds on a specific parameterization of an unbounded-depth hierarchical Pitman-Yor process. We introduce analytic marginalization steps (using coagulation operators) to reduce this model to one that can be represented in time and space linear in the length of the training sequence. We show how to perform inference in such a model without truncation approximation and introduce fragmentation operators necessary to do predictive inference. We demonstrate the sequence memoizer by using it as a language model, achieving state-of-the-art results.

We present a platform built on large-scale, data-centric machine learning (ML) approaches, whose particular focus is demand forecasting in retail. At its core, this platform enables the training and application of probabilistic demand forecasting models, and provides convenient abstractions and support functionality for forecasting problems. The platform comprises of a complex end-to-end machine learning system built on Apache Spark, which includes data preprocessing, feature engineering, distributed learning, as well as evaluation, experimentation and ensembling. Furthermore, it meets the demands of a production system and scales to large catalogues containing millions of items. We describe the challenges of building such a platform and discuss our design decisions. We detail aspects on several levels of the system, such as a set of general distributed learning schemes, our machinery for ensembling predictions, and a high-level dataflow abstraction for modeling complex ML pipelines. To the best of our knowledge, we are not aware of prior work on real-world demand forecasting systems which rivals our approach in terms of scalability.

Probabilistic models of sequences play a central role in most machine translation, automated speech recognition, lossless compression, spell-checking, and gene identification applications to name but a few. Unfortunately, real-world sequence data often exhibit long range dependencies which can only be captured by computationally challenging, complex models. Sequence data arising from natural processes also often exhibits power-law properties, yet common sequence models do not capture such properties. The sequence memoizer is a new hierarchical Bayesian model for discrete sequence data that captures long range dependencies and power-law characteristics, while remaining computationally attractive. Its utility as a language model and general purpose lossless compressor is demonstrated.

Time series forecasting is a key ingredient in the automation and optimization of business processes: in retail, deciding which products to order and where to store them depends on the forecasts of future demand in different regions; in cloud computing, the estimated future usage of services and infrastructure components guides capacity planning; and workforce scheduling in warehouses, call centers, factories requires forecasts of the future workload. Recent years have witnessed a paradigm shift in forecasting techniques and applications, from computer-assisted model-and assumptionbased to data-driven and fully-automated. This shift can be attributed to the availability of large, rich, and diverse time series data sources, posing unprecedented challenges to traditional time series forecasting methods. As such, how can we build statistical models to efficiently and effectively learn to forecast from large and diverse data sources? How can we leverage the statistical power of "similar" time series to improve forecasts in the case of limited observations? What are the implications for building forecasting systems that can handle large data volumes? The objective of this tutorial is to provide a concise and intuitive overview of the most important methods and tools available for solving large-scale forecasting problems. We review the state of the art in three related fields: (1) classical modeling of time series, (2) scalable tensor methods, and (3) deep learning for forecasting. Further, we share lessons learned from building scalable forecasting systems. While our focus is on providing an intuitive overview of the methods and practical issues, we also present technical details underlying these powerful tools.

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Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several realworld datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.