Related papers: Fractal interpolation in the context of prediction…
In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One…
Starting from the observation that the correlation coefficient defined by the scattered field data tested by two adjacent antennas decreases with the noise, it turns out that the imaging performance can be improved by adding non-redundant…
Recent advances in uncertainty quantification increasingly emphasise the distinction between aleatory and epistemic uncertainty in machine learning, motivating the need for more unified frameworks. However, despite much progress in…
In many environmental applications, time series are either incomplete or irregularly spaced. We investigate the application of the Spartan random process to missing data prediction. We employ a novel modified method of moments (MMoM) for…
We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we…
An adaptive interpolation scheme is proposed to accurately calculate the wideband responses in electromagnetic simulations. In the proposed scheme, the sampling points are first carefully divided into several groups based on their responses…
Meteorological satellite imagery is critical for meteorologists. The data have played an important role in monitoring and analyzing weather and climate changes. However, satellite imagery is a kind of observation data and exists a…
Inference-time scaling has emerged as a powerful technique for enhancing the reasoning performance of Large Language Models (LLMs). However, existing approaches often rely on heuristic strategies for parallel sampling, lacking a principled…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and…
Careful curation of data sources can significantly improve the performance of LLM pre-training, but predominant approaches rely heavily on intuition or costly trial-and-error, making them difficult to generalize across different data…
In the linear minimum mean square error (LMMSE) estimation for orthogonal frequency division multiplexing (OFDM) systems, the problem about the determination of the algorithm's parameters, especially those related with channel frequency…
This paper gives a general interpretation of Linear Prediction (LP) by interpolation framework different from the perspective of statistics. This interpretation is proved to be useful by several following results, such as: The mechanism of…
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible…
Continual learning poses a fundamental challenge for modern machine learning systems, requiring models to adapt to new tasks while retaining knowledge from previous ones. Addressing this challenge necessitates the development of efficient…
The standard paradigm for training deep learning models on sensor data assumes that more data is always better. However, raw sensor streams are often imbalanced and contain significant redundancy, meaning that not all data points contribute…
Multi-fidelity simulation is a widely used strategy to reduce the computational cost of many-query numerical simulation tasks such as uncertainty quantification, design space exploration, and design optimization. The reduced basis approach…
In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in [9] for adaptive interpolation by radial basis functions (RBFs). More precisely, we introduce in the context of sub-sampling methods a maximum profile…
There is proposed a method for improving the convergence of Fourier series by function systems, orthogonal at the segment, the application of which allows for smooth functions to receive uniformly convergent series. There is also proposed…
Dataset Condensation aims to condense a large dataset into a smaller one while maintaining its ability to train a well-performing model, thus reducing the storage cost and training effort in deep learning applications. However, conventional…