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We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some methods of this approximation for functions in a class induced by the convolution with a given function,…

The output of predictive models is routinely recalibrated by reconciling low-level predictions with known derived quantities defined at higher levels of aggregation. For example, models predicting turnout probabilities at the individual…

We study the log-alignment ratio (LAR), a measure of parameter-activation alignment, introduced in parameterization theory. We reformulate it as the overlap between a weight spectrum $p$ of the normalized squared singular values of a matrix…

Given a list of N numbers, the maximum can be computed in N iterations. During these N iterations, the maximum gets updated on average as many times as the Nth harmonic number. We first use this fact to approximate the Nth harmonic number…

The $p$-adic logarithm appears in many places in number theory. Hence having a good description of the image of the $p$-adic logarithm could be useful, and in particular, to figure out the image of $1 + \mathfrak{m}_K$, where $K$ is an…

Capturing the similarities between human language units is crucial for explaining how humans associate different objects, and therefore its computation has received extensive attention, research, and applications. With the ever-increasing…

The Lasso regression is a popular regularization method for feature selection in statistics. Prior to computing the Lasso estimator in both linear and generalized linear models, it is common to conduct a preliminary rescaling of the feature…

We give improved algorithms for the $\ell_{p}$-regression problem, $\min_{x} \|x\|_{p}$ such that $A x=b,$ for all $p \in (1,2) \cup (2,\infty).$ Our algorithms obtain a high accuracy solution in $\tilde{O}_{p}(m^{\frac{|p-2|}{2p + |p-2|}})…

Humans are believed to perceive numbers on a logarithmic mental number line, where smaller values are represented with greater resolution than larger ones. This cognitive bias, supported by neuroscience and behavioral studies, suggests that…

Pruning is an effective method to reduce the memory footprint and computational cost associated with large natural language processing models. However, current pruning algorithms either only focus on one pruning category, e.g., structured…

It is shown that any linear estimator that satisfies the moment conditions up to order $p$ is equivalent to a local polynomial regression of order $p$ with some non-negative weight function if and only if the kernel has at most $p$ sign…

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…

In this paper, we introduce and investigate the fractional logarithmic $p$-Laplacian $(-\Delta)_{p}^{s+\log}$, defined as the first-order derivative with respect to the parameter $t$ of the fractional $p$-Laplacian $(-\Delta)_{p}^{t}$…

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…

Generalized linear models play an essential role in a wide variety of statistical applications. This paper discusses an approximation of the likelihood in these models that can greatly facilitate computation. The basic idea is to replace a…

Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such…

Machine learning models with both good predictability and high interpretability are crucial for decision support systems. Linear regression is one of the most interpretable prediction models. However, the linearity in a simple linear…

We put forward a novel calibration of p values, the "Adaptive Robust Lower Bound" (ARLB) which maps p values into approximations of posterior probabilities taking into account the effect of sample sizes. We build on the Robust Lower Bound…