Anomaly Detection at Scale: The Case for Deep Distributional Time Series Models

This paper introduces a new methodology for detecting anomalies in time series data, with a primary application to monitoring the health of (micro-) services and cloud resources. The main novelty in our approach is that instead of modeling time series consisting of real values or vectors of real values, we model time series of probability distributions over real values (or vectors). This extension to time series of probability distributions allows the technique to be applied to the common scenario where the data is generated by requests coming in to a service, which is then aggregated at a fixed temporal frequency. Our method is amenable to streaming anomaly detection and scales to monitoring for anomalies on millions of time series. We show the superior accuracy of our method on synthetic and public real-world data. On the Yahoo Webscope data set, we outperform the state of the art in 3 out of 4 data sets and we show that we outperform popular open-source anomaly detection tools by up to 17% average improvement for a real-world data set.

The Effectiveness of Discretization in Forecasting: An Empirical Study on Neural Time Series Models

Time series modeling techniques based on deep learning have seen many advancements in recent years, especially in data-abundant settings and with the central aim of learning global models that can extract patterns across multiple time series. While the crucial importance of appropriate data pre-processing and scaling has often been noted in prior work, most studies focus on improving model architectures. In this paper we empirically investigate the effect of data input and output transformations on the predictive performance of several neural forecasting architectures. In particular, we investigate the effectiveness of several forms of data binning, i.e. converting real-valued time series into categorical ones, when combined with feed-forward, recurrent neural networks, and convolution-based sequence models. In many non-forecasting applications where these models have been very successful, the model inputs and outputs are categorical (e.g. words from a fixed vocabulary in natural language processing applications or quantized pixel color intensities in computer vision). For forecasting applications, where the time series are typically real-valued, various ad-hoc data transformations have been proposed, but have not been systematically compared. To remedy this, we evaluate the forecasting accuracy of instances of the aforementioned model classes when combined with different types of data scaling and binning. We find that binning almost always improves performance (compared to using normalized real-valued inputs), but that the particular type of binning chosen is of lesser importance.

Neural forecasting: Introduction and literature overview

Neural network based forecasting methods have become ubiquitous in large-scale industrial forecasting applications over the last years. As the prevalence of neural network based solutions among the best entries in the recent M4 competition shows, the recent popularity of neural forecasting methods is not limited to industry and has also reached academia. This article aims at providing an introduction and an overview of some of the advances that have permitted the resurgence of neural networks in machine learning. Building on these foundations, the article then gives an overview of the recent literature on neural networks for forecasting and applications.

Intermittent Demand Forecasting with Deep Renewal Processes

Intermittent demand, where demand occurrences appear sporadically in time, is a common and challenging problem in forecasting. In this paper, we first make the connections between renewal processes, and a collection of current models used for intermittent demand forecasting. We then develop a set of models that benefit from recurrent neural networks to parameterize conditional interdemand time and size distributions, building on the latest paradigm in "deep" temporal point processes. We present favorable empirical findings on discrete and continuous time intermittent demand data, validating the practical value of our approach.

GluonTS: Probabilistic Time Series Models in Python

We introduce Gluon Time Series (GluonTS, available at https://gluon-ts.mxnet.io), a library for deep-learning-based time series modeling. GluonTS simplifies the development of and experimentation with time series models for common tasks such as forecasting or anomaly detection. It provides all necessary components and tools that scientists need for quickly building new models, for efficiently running and analyzing experiments and for evaluating model accuracy.

Deep Factors for Forecasting

Producing probabilistic forecasts for large collections of similar and/or dependent time series is a practically relevant and challenging task. Classical time series models fail to capture complex patterns in the data, and multivariate techniques struggle to scale to large problem sizes. Their reliance on strong structural assumptions makes them data-efficient, and allows them to provide uncertainty estimates. The converse is true for models based on deep neural networks, which can learn complex patterns and dependencies given enough data. In this paper, we propose a hybrid model that incorporates the benefits of both approaches. Our new method is data-driven and scalable via a latent, global, deep component. It also handles uncertainty through a local classical model. We provide both theoretical and empirical evidence for the soundness of our approach through a necessary and sufficient decomposition of exchangeable time series into a global and a local part. Our experiments demonstrate the advantages of our model both in term of data efficiency, accuracy and computational complexity.

Approximate Bayesian Inference in Linear State Space Models for Intermittent Demand Forecasting at Scale

We present a scalable and robust Bayesian inference method for linear state space models. The method is applied to demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target statistics. Inference is approximated by the Newton-Raphson algorithm, reduced to linear-time Kalman smoothing, which allows us to operate on several orders of magnitude larger problems than previous related work. In a study on large real-world sales datasets, our method outperforms competing approaches on fast and medium moving items.