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Simulation-based inference provides a powerful framework for Bayesian inference when the likelihood is analytically intractable or computationally prohibitive. By leveraging machine-learning techniques and neural density estimators, it…

This paper deals with the modeling of non-stationary signals, from the point of view of signal synthesis. A class of random, non-stationary signals, generated by synthesis from a random timescale representation, is introduced and studied.…

Extracting time-varying latent variables from computational cognitive models is a key step in model-based neural analysis, which aims to understand the neural correlates of cognitive processes. However, existing methods only allow…

A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…

Increased use of sensor signals from wearable devices as rich sources of physiological data has sparked growing interest in developing health monitoring systems to identify changes in an individual's health profile. Indeed, machine learning…

Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their…

Recently, multivariate time series forecasting tasks have garnered increasing attention due to their significant practical applications, leading to the emergence of various deep forecasting models. However, real-world time series exhibit…

The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…

Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of…

Time series data analysis is a critical component in various domains such as finance, healthcare, and meteorology. Despite the progress in deep learning for time series analysis, there remains a challenge in addressing the non-stationary…

A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…

Finding an appropriate representation of dynamic activities in the brain is crucial for many downstream applications. Due to its highly dynamic nature, temporally averaged fMRI (functional magnetic resonance imaging) can only provide a…

It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…

Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…

We present a fully non neural learning framework based on Graph Laplacian Wavelet Transforms (GLWT). Unlike traditional architectures that rely on convolutional, recurrent, or attention based neural networks, our model operates purely in…

Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…

In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…

A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent…

Modeling response surfaces with abrupt jumps and discontinuities remains a major challenge across scientific and engineering domains. Although Gaussian process models excel at capturing smooth nonlinear relationships, their stationarity…

Spectral singularities at non-zero frequencies play an important role in investigating cyclic or seasonal time series. The publication [2] introduced the generalized filtered method-of-moments approach to simultaneously estimate singularity…