Related papers: Fractal interpolation in the context of prediction…

There is growing importance to detecting faults and implementing the best methods in industrial and real-world systems. We are searching for the most trustworthy and practical data-based fault detection methods proposed by artificial…

Data augmentation in time series forecasting plays a crucial role in enhancing model performance by introducing variability while maintaining the underlying temporal patterns. However, time series data offers fewer augmentation strategies…

Diffusion probabilistic models (DPMs), while effective in generating high-quality samples, often suffer from high computational costs due to their iterative sampling process. To address this, we propose an enhanced ODE-based sampling method…

From a machine learning point of view, identifying a subset of relevant features from a real data set can be useful to improve the results achieved by classification methods and to reduce their time and space complexity. To achieve this…

In this paper, we apply conformal prediction to time series data. Conformal prediction isa method that produces predictive regions given a confidence level. The regions outputs arealways valid under the exchangeability assumption. However,…

In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be…

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of…

This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…

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…

For short-term solar irradiance forecasting, the traditional point forecasting methods are rendered less useful due to the non-stationary characteristic of solar power. The amount of operating reserves required to maintain reliable…

Sophisticated trajectory prediction models that effectively mimic team dynamics have many potential uses for sports coaches, broadcasters and spectators. However, through experiments on soccer data we found that it can be surprisingly…

Multivariate time series forecasting is widely used in various fields. Reasonable prediction results can assist people in planning and decision-making, generate benefits and avoid risks. Normally, there are two characteristics of time…

In order to improve the vessel's capacity and ensure maritime traffic safety, vessel intelligent trajectory prediction plays an essential role in the vessel's smart navigation and intelligent collision avoidance system. However, current…

Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and…

Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here,…

Multivariate time-series forecasting is vital in various domains, e.g., economic planning and weather prediction. Deep train-from-scratch models have exhibited effective performance yet require large amounts of data, which limits real-world…

Recent state-of-the-art forecasting methods are trained on collections of time series. These methods, often referred to as global models, can capture common patterns in different time series to improve their generalization performance.…

We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…

The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper we present a self-contained and comprehensive introduction to the fractal dimension. We…