Related papers: Taylor-based Optimized Recursive Extended Exponent…

Short-term load forecasting (STLF) is challenging due to complex time series (TS) which express three seasonal patterns and a nonlinear trend. This paper proposes a novel hybrid hierarchical deep learning model that deals with multiple…

In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…

Time series modeling has entered an era of unprecedented growth in the size and complexity of data which require new modeling approaches. While many new general purpose machine learning approaches have emerged, they remain poorly understand…

The objective of this work is to improve the accuracy of building demand forecasting. This is a more challenging task than grid level forecasting. For the said purpose, we develop a new technique called recurrent transform learning (RTL).…

Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…

Time series forecasting is an active research topic in academia as well as industry. Although we see an increasing amount of adoptions of machine learning methods in solving some of those forecasting challenges, statistical methods remain…

This paper suggests parametrically transformed nested error regression models (TNERM), which transform the data flexibly to follow the normal linear mixed regression. We provide a procedure for estimating consistently the parameters of the…

Spatiotemporal forecasting is critical for real-world applications like traffic management, yet capturing reliable interactions remains challenging under noisy and non-stationary conditions. Existing methods primarily rely on historical…

We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…

Time series forecasting gets much attention due to its impact on many practical applications. Higher-order neural network with recurrent feedback is a powerful technique which used successfully for forecasting. It maintains fast learning…

The matrix exponential is a fundamental operator in scientific computing and system simulation, with applications ranging from control theory and quantum mechanics to modern generative machine learning. While Pad\'e approximants combined…

We propose \emph{Taylorized training} as an initiative towards better understanding neural network training at finite width. Taylorized training involves training the $k$-th order Taylor expansion of the neural network at initialization,…

Machine Learning (ML) is increasingly used to construct surrogate models for physical simulations. We take advantage of the ability to generate data using numerical simulations programs to train ML models better and achieve accuracy gain…

As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…

State-of-the-art forecasting methods using Recurrent Neural Net- works (RNN) based on Long-Short Term Memory (LSTM) cells have shown exceptional performance targeting short-horizon forecasts, e.g given a set of predictor features, forecast…

We address the problem of prediction for extreme observations by proposing an extremal linear prediction method. We construct an inner product space of nonnegative random variables derived from transformed-linear combinations of independent…

Recurrent Neural Networks (RNNs) have emerged as an interesting alternative to conventional material modeling approaches, particularly for nonlinear path dependent materials. Remarkable computational enhancements are obtained using RNNs…

Recurrent neural networks (RNNs) are more suitable for learning non-linear dependencies in dynamical systems from observed time series data. In practice all the external variables driving such systems are not known a priori, especially in…

Hierarchical forecasting methods have been widely used to support aligned decision-making by providing coherent forecasts at different aggregation levels. Traditional hierarchical forecasting approaches, such as the bottom-up and top-down…

Empirical risk minimization stands behind most optimization in supervised machine learning. Under this scheme, labeled data is used to approximate an expected cost (risk), and a learning algorithm updates model-defining parameters in search…