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To interpret uncertainty estimates from differentiable probabilistic models, recent work has proposed generating Counterfactual Latent Uncertainty Explanations (CLUEs). However, for a single input, such approaches could output a variety of…
A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…
Neutrosophic Over-/Under-/Off-Set and -Logic were defined by the author in 1995 and published for the first time in 2007. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is over 1},…
Large language models (LLMs) are increasingly deployed for tabular question answering, yet calibration on structured data is largely unstudied. This paper presents the first systematic comparison of five confidence estimation methods across…
Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such…
Counterfactual explanations are a widely used approach in Explainable AI, offering actionable insights into decision-making by illustrating how small changes to input data can lead to different outcomes. Despite their importance, evaluating…
In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].
This unpublished note is an alternate, shorter (and hopefully more readable) proof of the decidability of all minimal models. The decidability follows from a proof of the existence of a cellular term in each observational equivalence class…
For estimating a positive normal mean, Zhang and Woodroofe (2003) as well as Roe and Woodroofe (2000) investigate 100($1-\alpha)%$ HPD credible sets associated with priors obtained as the truncation of noninformative priors onto the…
Recently, a concept of forward continuity and a concept of forward compactness are introduced in the senses that a function $f$ is forward continuous if $\lim_{n\to\infty} \Delta f(x_{n})=0$ whenever $\lim_{n\to\infty} \Delta x_{n}=0$,\;…
We classify all binary error correcting completely regular codes of length $n$ with minimum distance $\delta>n/2$.
In the last 20 years many proposals have been made to incorporate non-monotonic reasoning into description logics, ranging from approaches based on default logic and circumscription to those based on preferential semantics. In particular,…
In this note, we extend the notion of minimal gaps to the higher dimensional sequences. We bound the minimal gap for $(\{\boldsymbol{a}_n\boldsymbol{\alpha}\}),$ $(\{a_n\boldsymbol{\alpha}\})$ and…
This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in…
Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities,…
Vulnerability detection is crucial to protect software security. Nowadays, deep learning (DL) is the most promising technique to automate this detection task, leveraging its superior ability to extract patterns and representations within…
We call a CNF formula linear if any two clauses have at most one variable in common. Let m(k) be the largest integer m such that any linear k-CNF formula with <= m clauses is satisfiable. We show that 4^k / (4e^2k^3) <= m(k) < ln(2) k^4…
Many recent developments in causal inference, and functional estimation problems more generally, have been motivated by the fact that classical one-step (first-order) debiasing methods, or their more recent sample-split double…
This is the first of two articles dealing with the equation $(-\Delta)^{s} v= f(v)$ in $\mathbb{R}^{n}$, with $s\in (0,1)$, where $(-\Delta)^{s}$ stands for the fractional Laplacian ---the infinitesimal generator of a L\'evy process. This…