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Since its introduction, the transformer has shifted the development trajectory away from traditional models (e.g., RNN, MLP) in time series forecasting, which is attributed to its ability to capture global dependencies within temporal…

We introduce a framework for expanding residual computational graphs using jets, operators that generalize truncated Taylor series. Our method provides a systematic approach to disentangle contributions of different computational paths to…

We introduce a neural network conformal prediction method for time series that enhances adaptivity in non-stationary environments. Our approach acts as a neural controller designed to achieve desired target coverage, leveraging auxiliary…

The explosion of Time Series (TS) data, driven by advancements in technology, necessitates sophisticated analytical methods. Modern management systems increasingly rely on analyzing this data, highlighting the importance of effcient…

In this work we explore a straightforward variational Bayes scheme for Recurrent Neural Networks. Firstly, we show that a simple adaptation of truncated backpropagation through time can yield good quality uncertainty estimates and superior…

Recurrent Neural Networks (RNNs) produce state-of-art performance on many machine learning tasks but their demand on resources in terms of memory and computational power are often high. Therefore, there is a great interest in optimizing the…

Deep learning-based tropical cyclone (TC) forecasting methods have demonstrated significant potential and application advantages, as they feature much lower computational cost and faster operation speed than numerical weather prediction…

The innovations algorithm is a classical recursive forecasting algorithm used in time series analysis. We develop the innovations algorithm for a class of nonnegative regularly varying time series models constructed via transformed-linear…

Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at forecasting tasks and quantifying the associated uncertainty with those forecasts (prediction intervals). One example is Exponential Smoothing…

We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…

Missing data scenarios are very common in ML applications in general and time-series/sequence applications are no exceptions. This paper pertains to a novel Recurrent Neural Network (RNN) based solution for sequence prediction under missing…

This paper proposes new linear regression models to deal with overdispersed binomial datasets. These new models, called tilted beta binomial regression models, are defined from the tilted beta binomial distribution, proposed assuming that…

The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step…

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

Three methods of temporal data upscaling, which may collectively be called the generalized k-nearest neighbor (GkNN) method, are considered. The accuracy of the GkNN simulation of month by month yield is considered (where the term yield…

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…

The standard method for the propagation of errors, based on a Taylor series expansion, is approximate and frequently inadequate for realistic problems. A simple and generic technique is described in which the likelihood is constructed…

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…

By removing parameters from deep neural networks, unstructured pruning methods aim at cutting down memory footprint and computational cost, while maintaining prediction accuracy. In order to tackle this otherwise intractable problem, many…

This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…