From the results shown inTable A5, we can see that the C-DGP slightly outperforms the DLFM on Scenario A, likely because the C-DGP explicitly includes constraints specific to this system.

Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary ``pure-state'' periods as well as transition periods between adjacent segments, such as a gradual slowdown between running and walking. However, most prior work assumes instantaneous transitions between pure discrete states. We propose a dynamical Wasserstein barycentric (DWB) model that estimates the system state over time as well as the data-generating distributions of pure states in an unsupervised manner. Our model assumes each pure state generates data from a multivariate normal distribution, and characterizes transitions between states via displacement-interpolation specified by the Wasserstein barycenter. The system state is represented by a barycentric weight vector which evolves over time via a random walk on the simplex. Parameter learning leverages the natural Riemannian geometry of Gaussian distributions under the Wasserstein distance, which leads to improved convergence speeds. Experiments on several human activity datasets show that our proposed DWB model accurately learns the generating distribution of pure states while improving state estimation for transition periods compared to the commonly used linear interpolation mixture models.

Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary pure-state'' periods as well as transition periods between adjacent segments, such as a gradual slowdown between running and walking. However, most prior work assumes instantaneous transitions between pure discrete states. We propose a dynamical Wasserstein barycentric (DWB) model that estimates the system state over time as well as the data-generating distributions of pure states in an unsupervised manner. Our model assumes each pure state generates data from a multivariate normal distribution, and characterizes transitions between states via displacement-interpolation specified by the Wasserstein barycenter.

Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary pure-state'' periods as well as transition periods between adjacent segments, such as a gradual slowdown between running and walking. However, most prior work assumes instantaneous transitions between pure discrete states. We propose a dynamical Wasserstein barycentric (DWB) model that estimates the system state over time as well as the data-generating distributions of pure states in an unsupervised manner. Our model assumes each pure state generates data from a multivariate normal distribution, and characterizes transitions between states via displacement-interpolation specified by the Wasserstein barycenter.

This paper proposes safe active learning algorithm for learning time-series models with piecewise trajectory sections. The basic model for the trajectory section is Gaussian Process, and the safety criterion is modeled as probability of certain safe value, which is modeled as a continuous function of inputs, being in the right region is greater than some threshold. The active learner explores the input space by generating trajectories that maximizes certain criterion in system identification. The paper also provides theoretical analysis in the safety perspective, as well as in the predictive variance reduction perspective. In the evaluation, besides simulated examples on predefined continuous functions and low dimensional models, this paper provides a specific use case for learning surrogate model of the high-pressure fluid system.

Learning time-series models is useful for many applications, such as simulation and forecasting. In this study, we consider the problem of actively learning time-series models while taking given safety constraints into account. For time-series modeling we employ a Gaussian process with a nonlinear exogenous input structure. The proposed approach generates data appropriate for time series model learning, i.e. input and output trajectories, by dynamically exploring the input space. The approach parametrizes the input trajectory as consecutive trajectory sections, which are determined stepwise given safety requirements and past observations.

We present a new convolutional neural network-based time-series model. Typical convolutional neural network (CNN) architectures rely on the use of max-pooling operators in between layers, which leads to reduced resolution at the top layers. Instead, in this work we consider a fully convolutional network (FCN) architecture that uses causal filtering operations, and allows for the rate of the output signal to be the same as that of the input signal. We furthermore propose an undecimated version of the FCN, which we refer to as the undecimated fully convolutional neural network (UFCNN), and is motivated by the undecimated wavelet transform. Our experimental results verify that using the undecimated version of the FCN is necessary in order to allow for effective time-series modeling. The UFCNN has several advantages compared to other time-series models such as the recurrent neural network (RNN) and long short-term memory (LSTM), since it does not suffer from either the vanishing or exploding gradients problems, and is therefore easier to train. Convolution operations can also be implemented more efficiently compared to the recursion that is involved in RNN-based models. We evaluate the performance of our model in a synthetic target tracking task using bearing only measurements generated from a state-space model, a probabilistic modeling of polyphonic music sequences problem, and a high frequency trading task using a time-series of ask/bid quotes and their corresponding volumes. Our experimental results using synthetic and real datasets verify the significant advantages of the UFCNN compared to the RNN and LSTM baselines.