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

Abstract

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.

Forecasting: theory and practice

“…In forecasting, a prominent example is the DeepAR model (Salinas et al, 2019b), which uses a recurrent neural network architecture and assumes the probability distribution to be from a standard probability density function (e.g., negative binomial or Student's t). Variations are possible, with either non-standard output distributions in forecasting such as the multinomial distribution (Rabanser et al, 2020) or via representing the probability density as cumulative distribution function (Salinas et al, 2019a) or the quantile function (Gasthaus et al, 2019).…”

Identifying the Factors Affecting Sensory Evaluation of Drinking Water and Assessing Its Social Impact Based on Drinking Water Consumption

“…To reduce the impact of noise and uncertainty on the results, and facilitate the identification of patterns and trends in the data, measured water quality was discretized (as shown in Table S2) before conducting Spearman correlation analysis, as discretization has been proven to be an effective data preprocessing technique. 30,31 The latent variables included in the SEM analysis will be determined based on the results of the reliability and validity tests. Reliability measurements were conducted using Cronbach's alpha coefficient, while the validity of the data was assessed through exploratory factor analysis (EFA) and confirmatory factor analysis (CFA).…”

“…Spearman correlations were employed to explore the associations between two variables. To reduce the impact of noise and uncertainty on the results, and facilitate the identification of patterns and trends in the data, measured water quality was discretized (as shown in Table S2) before conducting Spearman correlation analysis, as discretization has been proven to be an effective data preprocessing technique. , …”

Spliced Binned-Pareto Distribution for Robust Modeling of Heavy-tailed Time Series

“…We model the base of the predictive distribution with a discrete binned distribution to make it robust to extreme values and adaptable to the variety of real work distributions. As described by Rabanser et al (2020), we discretise the real axis between two points into n bins. A NN is trained to predict the probability of the next point falling in each of these bins, as shown in Figure 1a.…”

“…While some methods have been proposed for tail estimation, they assume little to no time-varying components Siffer et al (2017). To obtain a forecast robust to extreme values and adjustable to many shapes of distributions, discrete binned distributions can be used Rabanser et al (2020), these are parametrised by a Neural Network (NN), which have been shown capable of capturing complex long-term time dependencies in forecasting (Benidis et al, 2020). We address these two challenges by combining a binned distribution with Generalised Pareto distributions for the tails, all three distributions parameterised by a single NN, allowing us to jointly model time dependencies in the base distribution and in the tails.…”