Sykacek, Peter, Roberts, Stephen J.

This paper proposes an approach to classification of adjacent segments of a time series as being either of classes. We use a hierarchical model that consists of a feature extraction stage and a generative classifier which is built on top of these features. Such two stage approaches are often used in signal and image processing. The novel part of our work is that we link these stages probabilistically by using a latent feature space. To use one joint model is a Bayesian requirement, which has the advantage to fuse information according to its certainty.

Sykacek, Peter, Roberts, Stephen J.

The autoregression integrated moving average model or ARIMA model can seem intimidating to beginners. A good way to pull back the curtain in the method is to to use a trained model to make predictions manually. This demonstrates that ARIMA is a linear regression model at its core. Making manual predictions with a fit ARIMA models may also be a requirement in your project, meaning that you can save the coefficients from the fit model and use them as configuration in your own code to make predictions without the need for heavy Python libraries in a production environment. In this tutorial, you will discover how to make manual predictions with a trained ARIMA model in Python.

Chen, Xi, Wang, Hongzhi, Wei, Yanjie, Li, Jianzhong, Gao, Hong

Time series prediction with missing values is an important problem of time series analysis since complete data is usually hard to obtain in many real-world applications. To model the generation of time series, autoregressive (AR) model is a basic and widely used one, which assumes that each observation in the time series is a noisy linear combination of some previous observations along with a constant shift. To tackle the problem of prediction with missing values, a number of methods were proposed based on various data models. For real application scenarios, how do these methods perform over different types of time series with different levels of data missing remains to be investigated. In this paper, we focus on online methods for AR-model-based time series prediction with missing values. We adapted five mainstream methods to fit in such a scenario. We make detailed discussion on each of them by introducing their core ideas about how to estimate the AR coefficients and their different strategies to deal with missing values. We also present algorithmic implementations for better understanding. In order to comprehensively evaluate these methods and do the comparison, we conduct experiments with various configurations of relative parameters over both synthetic and real data. From the experimental results, we derived several noteworthy conclusions and shows that imputation is a simple but reliable strategy to handle missing values in online prediction tasks.

Ghalebi, Elahe, Mirzasoleiman, Baharan, Grosu, Radu, Leskovec, Jure

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes (e.g., information diffusion, virus propagation) occurring over the unobserved network. While there have been efforts to infer networks based on such data, providing a generative probabilistic model that is able to identify the underlying time-varying network remains an open question. Here we consider the problem of inferring generative dynamic network models based on network cascade diffusion data. We propose a novel framework for providing a non-parametric dynamic network model---based on a mixture of coupled hierarchical Dirichlet processes---based on data capturing cascade node infection times.