Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash 97 tok/s
Gemini 2.5 Pro 53 tok/s Pro
GPT-5 Medium 36 tok/s
GPT-5 High 34 tok/s Pro
GPT-4o 91 tok/s
GPT OSS 120B 462 tok/s Pro
Kimi K2 217 tok/s Pro
2000 character limit reached

Manually Selecting The Data Function for Supervised Learning of small datasets (2303.03894v1)

Published 7 Mar 2023 in stat.ML and cs.LG

Abstract: Supervised learning problems may become ill-posed when there is a lack of information, resulting in unstable and non-unique solutions. However, instead of solely relying on regularization, initializing an informative ill-posed operator is akin to posing better questions to achieve more accurate answers. The Fredholm integral equation of the first kind (FIFK) is a reliable ill-posed operator that can integrate distributions and prior knowledge as input information. By incorporating input distributions and prior knowledge, the FIFK operator can address the limitations of using high-dimensional input distributions by semi-supervised assumptions, leading to more precise approximations of the integral operator. Additionally, the FIFK's incorporation of probabilistic principles can further enhance the accuracy and effectiveness of solutions. In cases of noisy operator equations and limited data, the FIFK's flexibility in defining problems using prior information or cross-validation with various kernel designs is especially advantageous. This capability allows for detailed problem definitions and facilitates achieving high levels of accuracy and stability in solutions. In our study, we examined the FIFK through two different approaches. Firstly, we implemented a semi-supervised assumption by using the same Fredholm operator kernel and data function kernel and incorporating unlabeled information. Secondly, we used the MSDF method, which involves selecting different kernels on both sides of the equation to define when the mapping kernel is different from the data function kernel. To assess the effectiveness of the FIFK and the proposed methods in solving ill-posed problems, we conducted experiments on a real-world dataset. Our goal was to compare the performance of these methods against the widely used least-squares method and other comparable methods.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

Summary

We haven't generated a summary for this paper yet.

Ai Generate Text Spark Streamline Icon: https://streamlinehq.com

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

Don't miss out on important new AI/ML research

See which papers are being discussed right now on X, Reddit, and more:

“Emergent Mind helps me see which AI papers have caught fire online.”

Philip

Philip

Creator, AI Explained on YouTube