Related papers: Marginalization Consistent Probabilistic Forecasti…

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel,…

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have underlying hierarchical relations. Most methods focus on point…

Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have underlying hierarchical relations. Most methods focus on point…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…

Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…

The non-stationary nature of real-world Multivariate Time Series (MTS) data presents forecasting models with a formidable challenge of the time-variant distribution of time series, referred to as distribution shift. Existing studies on the…

Deep learning-based multivariate and multistep-ahead traffic forecasting models are typically trained with the mean squared error (MSE) or mean absolute error (MAE) as the loss function in a sequence-to-sequence setting, simply assuming…

Machine learning methods are widely and successfully used for probabilistic wind power forecasting, yet the pervasive issue of missing values (e.g., due to sensor faults or communication outages) has received limited attention. The…

Hierarchical models in Bayesian inverse problems are characterized by an assumed prior probability distribution for the unknown state and measurement error precision, and hyper-priors for the prior parameters. Combining these probability…

Unbinned likelihood fits aim at maximizing the information one can extract from experimental data, yet their application in realistic statistical analyses is often hindered by the computational cost of profiling systematic uncertainties.…

Accurate univariate forecasting remains a pressing need in real-world systems, such as energy markets, hydrology, retail demand, and IoT monitoring, where signals are often intermittent and horizons span both short- and long-term. While…

Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by…

Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…

Current density modeling approaches suffer from at least one of the following shortcomings: expensive training, slow inference, approximate likelihood, mode collapse or architectural constraints like bijective mappings. We propose a simple…

In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…