Search

Your search keyword '"Kumar, Manish"' showing total 12,671 results
Start Over Author "Kumar, Manish"
12,671 results on '"Kumar, Manish"'

40. Mambular: A Sequential Model for Tabular Deep Learning

Author

Thielmann, Anton Frederik, Kumar, Manish, Weisser, Christoph, Reuter, Arik, Säfken, Benjamin, and Samiee, Soheila

Subjects
Computer Science - Machine Learning
Abstract

The analysis of tabular data has traditionally been dominated by gradient-boosted decision trees (GBDTs), known for their proficiency with mixed categorical and numerical features. However, recent deep learning innovations are challenging this dominance. We introduce Mambular, an adaptation of the Mamba architecture optimized for tabular data. We extensively benchmark Mambular against state-of-the-art models, including neural networks and tree-based methods, and demonstrate its competitive performance across diverse datasets. Additionally, we explore various adaptations of Mambular to understand its effectiveness for tabular data. We investigate different pooling strategies, feature interaction mechanisms, and bi-directional processing. Our analysis shows that interpreting features as a sequence and passing them through Mamba layers results in surprisingly performant models. The results highlight Mambulars potential as a versatile and powerful architecture for tabular data analysis, expanding the scope of deep learning applications in this domain. The source code is available at https://github.com/basf/mamba-tabular.

Published
2024

41. Constructing Multiresolution Analysis via Wavelet Packets on Sobolev Space in Local Fields

Author

Kumar, Manish

Subjects
Mathematics - Rings and Algebras, 42C40, 40A30, 11F87, 43A70, 46E35
Abstract

We define Sobolev spaces $H^{\mathfrak{s}}(K_q)$ over a local field $K_q$ of finite characteristic $p>0$, where $q=p^c$ for a prime $p$ and $c\in \mathbb{N}$. This paper introduces novel fractal functions, such as the Weierstrass type and 3-adic Cantor type, as intriguing examples within these spaces and a few others. Employing prime elements, we develop a Multi-Resolution Analysis (MRA) and examine wavelet expansions, focusing on the orthogonality of both basic and fractal wavelet packets at various scales. We utilize convolution theory to construct Haar wavelet packets and demonstrate the orthogonality of all discussed wavelet packets within $H^{\mathfrak{s}}(K_q)$, enhancing the analytical capabilities of these Sobolev spaces.

Published
2024

Catalog

Books, media, physical & digital resources
See catalog results