arXiv subjects

S. Akansha

Publications and source records attributed to S. Akansha.

5 recordsLinked to original sources

arXiv2026

Affirmative Results on a Conjecture on the Column Space of the Adjacency Matrix

The Akbari-Cameron-Khosrovshahi (ACK) conjecture, which appears to be unresolved, states that for any simple graph $G$ with at least one edge, there exists a nonzero {$\{0,1\}$}-vector in the row space of its adjacency matrix that is not a row of the matrix itself. In this talk, we present a unified framework that includes several families and operations of graphs that satisfy the ACK conjecture. Using these fundamental results, we introduce new graph constructions and demonstrate, through graph structural and linear algebraic arguments, that these constructions adhere to the conjecture. Further, we show that certain graph operations preserve the ACK property. These results collectively expand the known classes of graphs satisfying the conjecture and provide insight into its structural invariance under composition and extension.

math.CO↗

arXiv2024

RoCP-GNN: Robust Conformal Prediction for Graph Neural Networks in Node-Classification

Graph Neural Networks (GNNs) have emerged as powerful tools for predicting outcomes in graph-structured data. However, a notable limitation of GNNs is their inability to provide robust uncertainty estimates, which undermines their reliability in contexts where errors are costly. One way to address this issue is by providing prediction sets that contain the true label with a predefined probability margin. Our approach builds upon conformal prediction (CP), a framework that promises to construct statistically robust prediction sets or intervals. There are two primary challenges: first, given dependent data like graphs, it is unclear whether the critical assumption in CP - exchangeability - still holds when applied to node classification. Second, even if the exchangeability assumption is valid for conformalized link prediction, we need to ensure high efficiency, i.e., the resulting prediction set or the interval length is small enough to provide useful information. In this article, we propose a novel approach termed Robust Conformal Prediction for GNNs (RoCP-GNN), which integrates conformal prediction (CP) directly into the GNN training process. This method generates prediction sets, instead of just point predictions, that are valid at a user-defined confidence level, assuming only exchangeability. Our approach robustly predicts outcomes with any predictive GNN model while quantifying the uncertainty in predictions within the realm of graph-based semi-supervised learning (SSL). Experimental results demonstrate that GNN models with size loss provide a statistically significant increase in performance. We validate our approach on standard graph benchmark datasets by coupling it with various state-of-the-art GNNs in node classification. The code will be made available after publication.

cs.LG↗

arXiv2024

Conditional Shift-Robust Conformal Prediction for Graph Neural Network

Graph Neural Networks (GNNs) have emerged as potent tools for predicting outcomes in graph-structured data. Despite their efficacy, a significant drawback of GNNs lies in their limited ability to provide robust uncertainty estimates, posing challenges to their reliability in contexts where errors carry significant consequences. Moreover, GNNs typically excel in in-distribution settings, assuming that training and test data follow identical distributions a condition often unmet in real world graph data scenarios. In this article, we leverage conformal prediction, a widely recognized statistical technique for quantifying uncertainty by transforming predictive model outputs into prediction sets, to address uncertainty quantification in GNN predictions amidst conditional shift\footnote{Representing the change in conditional probability distribution $P(label|input)$ from source domain to target domain.} in graph-based semi-supervised learning (SSL). Additionally, we propose a novel loss function aimed at refining model predictions by minimizing conditional shift in latent stages. Termed Conditional Shift Robust (CondSR) conformal prediction for GNNs, our approach CondSR is model-agnostic and adaptable to various classification models. We validate the effectiveness of our method on standard graph benchmark datasets, integrating it with state-of-the-art GNNs in node classification tasks. Comprehensive evaluations demonstrate that our approach consistently achieves any predefined target marginal coverage, enhances the accuracy of state of the art GNN models by up to 12\% under conditional shift, and reduces the prediction set size by up to 48\%. The code implementation is publicly available for further exploration and experimentation.

cs.LG↗

arXiv2021

Adaptive Padé-Chebyshev Type Approximation of Piecewise Smooth Functions

A piecewise Padé-Chebyshev type (PiPCT) approximation method is proposed to minimize the Gibbs phenomenon in approximating piecewise smooth functions. A theorem on $L^1$-error estimate is proved for sufficiently smooth functions using a decay property of the Chebyshev coefficients. Numerical experiments are performed to show that the PiPCT method accurately captures isolated singularities of a function without using the positions and the types of singularities. Further, an adaptive partition approach to the PiPCT method is developed (referred to as the APiPCT method) to achieve the required accuracy with a lesser computational cost. Numerical experiments are performed to show some advantages of using the PiPCT and APiPCT methods compared to some well-known methods in the literature.

math.NA↗

arXiv2019

Adaptive Padé-Chebyshev Type Approximation to Piecewise Smooth Functions

The aim of this article is to study the role of piecewise implementation of Padé-Chebyshev type approximation in minimising Gibbs phenomena in approximating piecewise smooth functions. A piecewise Padé-Chebyshev type (PiPCT) algorithm is proposed and an $L^1$-error estimate for at most continuous functions is obtained using a decay property of the Chebyshev coefficients. An advantage of the PiPCT approximation is that we do not need to have an {\it a prior} knowledge of the positions and the types of singularities present in the function. Further, an adaptive piecewise Padé-Chebyshev type (APiPCT) algorithm is proposed in order to get the essential accuracy with a relatively lower computational cost. Numerical experiments are performed to validate the algorithms. The numerical results are also found to be well in agreement with the theoretical results. Comparison results of the PiPCT approximation with the singular Padé-Chebyshev and the robust Padé-Chebyshev methods are also presented.

math.NA↗