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This paper proposes an extension to conventional regression Neural Networks (NNs) for replacing the point predictions they produce with prediction intervals that satisfy a required level of confidence. Our approach follows a novel machine…

We consider the general problem of modeling temporal data with long-range dependencies, wherein new observations are fully or partially predictable based on temporally-distant, past observations. A sufficiently powerful temporal model…

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network…

Neural Controlled Differential Equations (NCDEs) are a state-of-the-art tool for supervised learning with irregularly sampled time series (Kidger, 2020). However, no theoretical analysis of their performance has been provided yet, and it…

The analysis of temporal networks heavily depends on the analysis of time-respecting paths. However, before being able to model and analyze the time-respecting paths, we have to infer the timescales at which the temporal edges influence…

This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…

Background: Fault tree analysis (FTA) is a well established method for qualitative as well as probabilistic reliability and safety analysis. As a Boolean model it does not support modelling of dynamic effects like sequence dependencies…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

Temporal networks are effective in capturing the evolving interactions of networks over time, such as social networks and e-commerce networks. In recent years, researchers have primarily concentrated on developing specific model…

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…

Short fixed-length inputs are the main bottleneck of deep learning methods in long time-series forecasting tasks. Prolonging input length causes overfitting, rapidly deteriorating accuracy. Our research indicates that the overfitting is a…

We provide non-asymptotic bounds for the well-known temporal difference learning algorithm TD(0) with linear function approximators. These include high-probability bounds as well as bounds in expectation. Our analysis suggests that a…

The evolution of sequence modeling architectures, from recurrent neural networks and convolutional models to Transformers and structured state-space models, reflects ongoing efforts to address the diverse temporal dependencies inherent in…

In many environmental applications, recurrent neural networks (RNNs) are often used to model physical variables with long temporal dependencies. However, due to mini-batch training, temporal relationships between training segments within…

Traditional statistical learning theory relies on the assumption that data are identically and independently distributed (i.i.d.). However, this assumption often does not hold in many real-life applications. In this survey, we explore…

Wide neural networks have proven to be a rich class of architectures for both theory and practice. Motivated by the observation that finite width convolutional networks appear to outperform infinite width networks, we study scaling laws for…

Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only…

Multivariate time series (MTS) forecasting plays an important role in the automation and optimization of intelligent applications. It is a challenging task, as we need to consider both complex intra-variable dependencies and inter-variable…

Convolutional neural networks (CNNs) and transformer architectures offer strengths for modeling temporal data: CNNs excel at capturing local patterns and translational invariances, while transformers effectively model long-range…

Deep time series metric learning is challenging due to the difficult trade-off between temporal invariance to nonlinear distortion and discriminative power in identifying non-matching sequences. This paper proposes a novel neural…