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Recent advances in large language models (LLMs) have yielded impressive performance on various tasks, yet they often depend on high-quality feedback that can be costly. Self-refinement methods attempt to leverage LLMs' internal evaluation…
Mixture models are flexible tools in density estimation and classification problems. Bayesian estimation of such models typically relies on sampling from the posterior distribution using Markov chain Monte Carlo. Label switching arises…
In this work, we focus on the challenging problem of Label Enhancement (LE), which aims to exactly recover label distributions from logical labels, and present a novel Label Information Bottleneck (LIB) method for LE. For the recovery…
Multi-label classification is crucial for comprehensive image understanding, yet acquiring accurate annotations is challenging and costly. To address this, a recent study suggests exploiting unsupervised multi-label classification…
Partial-label learning is a popular weakly supervised learning setting that allows each training example to be annotated with a set of candidate labels. Previous studies on partial-label learning only focused on the classification setting…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
We study fast Monte-Carlo methods for testing irreducibility and detecting arithmetic imprimitivity of polynomials over $\mathbb{Q}$. Building on the subset-sum criterion of Pemantle-Peres-Rivin, we develop a probabilistic irreducibility…
A weakly-supervised learning framework named as complementary-label learning has been proposed recently, where each sample is equipped with a single complementary label that denotes one of the classes the sample does not belong to. However,…
In multi-label learning, the issue of missing labels brings a major challenge. Many methods attempt to recovery missing labels by exploiting low-rank structure of label matrix. However, these methods just utilize global low-rank label…
Bar Codes are combinatorial objects encoding many properties of monomial ideals. In this paper we employ these objects to study Janet-like divisions. Given a finite set of terms U, from its Bar Code we can compute the Janet-like…
The "Curse of dimensionality" is prevalent across various data patterns, which increases the risk of model overfitting and leads to a decline in model classification performance. However, few studies have focused on this issue in Partial…
Proofs of two results about a monomial ideal -- describing membership in auxiliary ideals associated to the monomial ideal -- are given which do not invoke resolution of singularities. The AM--GM inequality is used as a substitute for…
Due to abundance of data from multiple modalities, cross-modal retrieval tasks with image-text, audio-image, etc. are gaining increasing importance. Of the different approaches proposed, supervised methods usually give significant…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal. The pruned resolution is not simplicial in…
The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal…
In recent years, deep neural network is widely used in machine learning. The multi-class classification problem is a class of important problem in machine learning. However, in order to solve those types of multi-class classification…
This article has been withdrawn by arXiv administrators due to plagiarized content from arXiv:1010.2469.
In supervised learning for medical image analysis, sample selection methodologies are fundamental to attain optimum system performance promptly and with minimal expert interactions (e.g. label querying in an active learning setup). In this…
The main focus of this paper is on the problem of relating an ideal $I$ in the polynomial ring $\mathbb Q[x_1, \dots, x_n]$ to a corresponding ideal in $\mathbb F_p[x_1,\dots, x_n]$ where $p$ is a prime number; in other words, the…