Related papers: Proving Conjectures Acquired by Composing Multiple…

I begin by summarizing key ideas of the paper under discussion. Then I will talk about a graphical modeling perspective, posterior contraction rates and alternative methods of aggregation. Moreover, I will also discuss possible applications…

A typical theme for many well-known decomposition problems is to show that some obvious necessary conditions for decomposing a graph $G$ into copies $H_1, \ldots, H_m$ are also sufficient. One such problem was posed in 1987, by Alavi,…

Cheating in examinations is acknowledged by an increasing number of organizations to be widespread. We examine two different approaches to assess their effectiveness at detecting anomalous results, suggestive of collusion, using data taken…

Confounding matters in almost all observational studies that focus on causality. In order to eliminate bias caused by connfounders, oftentimes a substantial number of features need to be collected in the analysis. In this case, large p…

This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…

The demand for Explainable AI (XAI) has triggered an explosion of methods, producing a landscape so fragmented that we now rely on surveys of surveys. Yet, fundamental challenges persist: conflicting metrics, failed sanity checks, and…

In a recent work, Andrews gave analytic proofs of two conjectures concerning some variations of two combinatorial identities between partitions of a positive integer into odd parts and partitions into distinct parts discovered by Beck.…

As the use of AI in society grows, addressing emerging biases is essential to prevent systematic discrimination. Several bias detection methods have been proposed, but, with few exceptions, these tend to ignore transparency. Instead,…

Despite peer-reviewing being an essential component of academia since the 1600s, it has repeatedly received criticisms for lack of transparency and consistency. We posit that recent work in machine learning and explainable AI provide tools…

Recent advancements in machine learning have emphasized the need for transparency in model predictions, particularly as interpretability diminishes when using increasingly complex architectures. In this paper, we propose leveraging…

We prove a few simple cases of a random graph statement that would imply the "second" Kahn--Kalai Conjecture. Even these cases turn out to be reasonably challenging, and it is hoped that the ideas introduced here may lead to further…

This note generalizes factorization for formulas with multiplicities and conjectures that the connection method along with this feature is computationally as powerful as resolution, also seen from a complexity point of view.

In this short note, it is shown that there is a gap in the proof of Theorem 11 in the paper of Meyer and Neutsch (J. of Algebra, 1993). We prove, nevertheless, that the statement of the theorem is true and fix the proof by using a certain…

In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…

We prove a conjecture of Kumbhakar, Roy, and Srinivasan (2024) on the classification of order one differential equations, and a conjecture of Kumbhakar and Srinivasan (2025) on higher order equations. Both conjectures are shown to be…

This paper shows that the common method used for making predictions under uncertainty in A1 and science is in error. This method is to use currently available data to select the best model from a given class of models-this process is called…

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

This article deals with plausible reasoning from incomplete knowledge about large-scale spatial properties. The availableinformation, consisting of a set of pointwise observations,is extrapolated to neighbour points. We make use of belief…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

We introduce a novel method to aggregate Bipolar Argumentation (BA) Frameworks expressing opinions by different parties in debates. We use Bipolar Assumption-based Argumentation (ABA) as an all-encompassing formalism for BA under different…