Related papers: Probabilistic Functional Neural Networks
Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges…
Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue…
Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs…
This paper is concerned with forecasting probability density functions. Density functions are nonnegative and have a constrained integral; thus, they do not constitute a vector space. Implementing unconstrained functional time-series…
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…
We study the modeling and forecasting of high-dimensional functional time series, which can be temporally dependent and cross-sectionally correlated. We implement a functional analysis of variance (FANOVA) to decompose high-dimensional…
Spatial prediction problems often use Gaussian process models, which can be computationally burdensome in high dimensions. Specification of an appropriate covariance function for the model can be challenging when complex non-stationarities…
Despite the eminent successes of deep neural networks, many architectures are often hard to transfer to irregularly-sampled and asynchronous time series that commonly occur in real-world datasets, especially in healthcare applications. This…
Probabilistic time series forecasting is crucial in many application domains such as retail, ecommerce, finance, or biology. With the increasing availability of large volumes of data, a number of neural architectures have been proposed for…
In this paper, we present SSDNet, a novel deep learning approach for time series forecasting. SSDNet combines the Transformer architecture with state space models to provide probabilistic and interpretable forecasts, including trend and…
Time series forecasting plays a central role in many real-world applications and has been extensively studied. Most existing approaches rely on deterministic models. However, real-world environments exhibit inherently uncertain and complex…
In the fast-fashion industry, overproduction and unsold inventory create significant environmental problems. Precise sales forecasts for unreleased items could drastically improve the efficiency and profits of industries. However,…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
A classification technique incorporating a novel feature derivation method is proposed for predicting failure of a system or device with multivariate time series sensor data. We treat the multivariate time series sensor data as images for…
Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables $p$ diverges as the number of serially dependent observations $n$ increases. In this paper, we…
Identifying the obstacle space is crucial for path planning. However, generating an accurate obstacle space remains a significant challenge due to various sources of uncertainty, including motion, behavior, and perception limitations. Even…
The fast and accurate prediction of unsteady flow becomes a serious challenge in fluid dynamics, due to the high-dimensional and nonlinear characteristics. A novel hybrid deep neural network (DNN) architecture was designed to capture the…
Hyperspectral image classification (HSIC) has been significantly advanced by deep learning methods that exploit rich spatial-spectral correlations. However, existing approaches still face fundamental limitations: transformer-based models…
The architecture of a neural network and the selection of its activation function are both fundamental to its performance. Equally vital is ensuring these two elements are well-matched, as their alignment is key to achieving effective…
Deep neural networks has been increasingly applied in fault diagnostics, where it uses historical data to capture systems behavior, bypassing the need for high-fidelity physical models. However, despite their competence in prediction tasks,…