Related papers: Dynamic Gaussian Mixture based Deep Generative Mod…

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific…

We develop a mixture model for transition density approximation, together with soft model selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our model builds on the Gaussian mixture transition distribution (MTD) model…

Inference-time scaling (ITS) in latent reasoning models typically relies on heuristic perturbations, such as dropout or fixed Gaussian noise, to generate diverse candidate trajectories. However, we show that stronger perturbations do not…

Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that…

Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…

This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack…

Long-term action anticipation has become an important task for many applications such as autonomous driving and human-robot interaction. Unlike short-term anticipation, predicting more actions into the future imposes a real challenge with…

While generative modeling on time series facilitates more capable and flexible probabilistic forecasting, existing generative time series models do not address the multi-dimensional properties of time series data well. The prevalent…

Time series forecasting (TSF) remains a challenging problem due to the intricate entanglement of intraperiod-fluctuations and interperiod-trends. While recent advances have attempted to reshape 1D sequences into 2D period-phase…

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as…

These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…

Generative Adversarial Networks (GANs) have gained significant attention in recent years, with impressive applications highlighted in computer vision in particular. Compared to such examples, however, there have been more limited…

Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

Reliable 4D aircraft trajectory prediction, whether in a real-time setting or for analysis of counterfactuals, is important to the efficiency of the aviation system. Toward this end, we first propose a highly generalizable efficient…

Remarkable advances in recent 2D image and 3D shape generation have induced a significant focus on dynamic 4D content generation. However, previous 4D generation methods commonly struggle to maintain spatial-temporal consistency and adapt…

Tremendous efforts have been put forth on predicting pedestrian trajectory with generative models to accommodate uncertainty and multi-modality in human behaviors. An individual's inherent uncertainty, e.g., change of destination, can be…