Related papers: Probabilistic function-on-function nonlinear autor…

Animals are known to make efficient probabilistic inferences based on uncertain and noisy information from the outside world. Although it is known that generic neural networks can perform near-optimal point estimation by probabilistic…

Continuous-time long-term event prediction plays an important role in many application scenarios. Most existing works rely on autoregressive frameworks to predict event sequences, which suffer from error accumulation, thus compromising…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

We consider the use of probabilistic neural networks for fluid flow {surrogate modeling} and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the…

Non-autoregressive (NAR) language models offer notable efficiency in text generation by circumventing the sequential bottleneck of autoregressive decoding. However, accurately modeling dependencies in discrete sequences remains challenging…

The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms…

We propose a statistical emulator for a climate-economy deterministic integrated assessment model ensemble, based on a functional regression framework. Inference on the unknown parameters is carried out through a mixed effects hierarchical…

An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…

Diffusion probabilistic models have demonstrated an outstanding capability to model natural images and raw audio waveforms through a paired diffusion and reverse processes. The unique property of the reverse process (namely, eliminating…

The present study applies a novel two-dimensional learning framework (2D-UPSO) based on particle swarms for structure selection of polynomial nonlinear auto-regressive with exogenous inputs (NARX) models. This learning approach explicitly…

The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

This paper addresses the problem of inferring a hybrid automaton from a set of input-output traces of a hybrid system exhibiting discrete mode switching between continuously evolving dynamics. Existing approaches mainly adopt a…

This paper investigates gradient-based adaptive prediction and control for nonlinear stochastic dynamical systems under a weak convexity condition on the prediction-based loss. This condition accommodates a broad range of nonlinear models…

Efficient machine translation models are commercially important as they can increase inference speeds, and reduce costs and carbon emissions. Recently, there has been much interest in non-autoregressive (NAR) models, which promise faster…

Neural networks and in particular the attention mechanism have brought significant advances to the field of Automated Essay Scoring. Many of these systems use a regression-based model which may be prone to underfitting when the model only…

We propose a conditional non-autoregressive neural sequence model based on iterative refinement. The proposed model is designed based on the principles of latent variable models and denoising autoencoders, and is generally applicable to any…

In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…

We study reasoning tasks through a framework that integrates auto-regressive (AR) and non-autoregressive (NAR) language models. AR models, which generate text sequentially, excel at producing coherent outputs but often suffer from slow…