We propose Random Projection Filter Bank (RPFB) as a generic and simple approach to extract features from time series data. RPFB is a set of randomly generated stable autoregressive filters that are convolved with the input time series to generate the features. These features can be used by any conventional machine learning algorithm for solving tasks such as time series prediction, classification with time series data, etc. Different filters in RPFB extract different aspects of the time series, and together they provide a reasonably good summary of the time series. RPFB is easy to implement, fast to compute, and parallelizable. We provide an error upper bound indicating that RPFB provides a reasonable approximation to a class of dynamical systems. The empirical results in a series of synthetic and real-world problems show that RPFB is an effective method to extract features from time series.

The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters $U_1,\dots,U_k$ are mutually independent. Since mutual independence is the target, pairwise similarity measurements are of no use, and thus traditional clustering algorithms are inapplicable. The distribution of the random variables in $S$ is, in general, unknown, but a sample is available. Thus, the problem is cast in terms of time series. Two forms of sampling are considered: i.i.d.\ and stationary time series, with the main emphasis being on the latter, more general, case. A consistent, computationally tractable algorithm for each of the settings is proposed, and a number of fascinating open directions for further research are outlined.

We develop a Bayesian model for decision-making under time pressure with endogenous information acquisition. In our model, the decision-maker decides when to observe (costly) information by sampling an underlying continuous-time stochastic process (time series) that conveys information about the potential occurrence/non-occurrence of an adverse event which will terminate the decision-making process. In her attempt to predict the occurrence of the adverse event, the decision-maker follows a policy that determines when to acquire information from the time series (continuation), and when to stop acquiring information and make a final prediction (stopping). We show that the optimal policy has a rendezvous structure, i.e. a structure in which whenever a new information sample is gathered from the time series, the optimal date for acquiring the next sample becomes computable. The optimal interval between two information samples balances a trade-off between the decision maker's surprise, i.e. the drift in her posterior belief after observing new information, and suspense, i.e. the probability that the adverse event occurs in the time interval between two information samples. Moreover, we characterize the continuation and stopping regions in the decision-maker's state-space, and show that they depend not only on the decision-maker's beliefs, but also on the context, i.e. the current realization of the time series.

We present a general framework for classification of sparse and irregularly-sampled time series. The properties of such time series can result in substantial uncertainty about the values of the underlying temporal processes, while making the data difficult to deal with using standard classification methods that assume fixed-dimensional feature spaces. To address these challenges, we propose an uncertainty-aware classification framework based on a special computational layer we refer to as the Gaussian process adapter that can connect irregularly sampled time series data to any black-box classifier learnable using gradient descent. We show how to scale up the required computations based on combining the structured kernel interpolation framework and the Lanczos approximation method, and how to discriminatively train the Gaussian process adapter in combination with a number of classifiers end-to-end using backpropagation.

Multivariate time series usually contain a large number of missing values, which hinders the application of advanced analysis methods on multivariate time series data. Conventional approaches to addressing the challenge of missing values, including mean/zero imputation, case deletion, and matrix factorization-based imputation, are all incapable of modeling the temporal dependencies and the nature of complex distribution in multivariate time series. In this paper, we treat the problem of missing value imputation as data generation. Inspired by the success of Generative Adversarial Networks (GAN) in image generation, we propose to learn the overall distribution of a multivariate time series dataset with GAN, which is further used to generate the missing values for each sample. Different from the image data, the time series data are usually incomplete due to the nature of data recording process. A modified Gate Recurrent Unit is employed in GAN to model the temporal irregularity of the incomplete time series. Experiments on two multivariate time series datasets show that the proposed model outperformed the baselines in terms of accuracy of imputation. Experimental results also showed that a simple model on the imputed data can achieve state-of-the-art results on the prediction tasks, demonstrating the benefits of our model in downstream applications.

Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data.

We propose a novel Bayesian approach to modelling nonlinear alignments of time series based on latent shared information. We apply the method to the real-world problem of finding common structure in the sensor data of wind turbines introduced by the underlying latent and turbulent wind field. The proposed model allows for both arbitrary alignments of the inputs and non-parametric output warpings to transform the observations. This gives rise to multiple deep Gaussian process models connected via latent generating processes. We present an efficient variational approximation based on nested variational compression and show how the model can be used to extract shared information between dependent time series, recovering an interpretable functional decomposition of the learning problem. We show results for an artificial data set and real-world data of two wind turbines.

Time series with non-uniform intervals occur in many applications, and are difficulttomodel usingstandard recurrent neural networks(RNNs).

The dense connections between layers change the definition of what from one layer to the next.