Related papers: Fully lifted \emph{blirp} interpolation -- a large…
Medical imaging involves high-dimensional data, yet their acquisition is obtained for limited samples. Multivariate predictive models have become popular in the last decades to fit some external variables from imaging data, and standard…
Large Language Models (LLM) and foundation models are popular as they offer new opportunities for individuals and businesses to improve natural language processing, interact with data, and retrieve information faster. However, training or…
Allocating extra computation at inference time has recently improved sample quality in large language models and diffusion-based image generation. In parallel, Flow Matching (FM) has gained traction in language, vision, and scientific…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
In the present paper, the notion of Lidstone Fractal Interpolation Function ($Lidstone \ FIF$) is introduced to interpolate and approximate data generating functions that arise from real life objects and outcomes of several scientific…
The iterated posterior linearization filter (IPLF) is an algorithm for Bayesian state estimation that performs the measurement update using iterative statistical regression. The main result behind IPLF is that the posterior approximation is…
Mixup is a data-dependent regularization technique that consists in linearly interpolating input samples and associated outputs. It has been shown to improve accuracy when used to train on standard machine learning datasets. However,…
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…
Federated Learning (FL) is a distributed learning paradigm that enables a large number of resource-limited nodes to collaboratively train a model without data sharing. The non-independent-and-identically-distributed (non-i.i.d.) data…
Retrieval-enhanced language models (LMs), which condition their predictions on text retrieved from large external datastores, have recently shown significant perplexity improvements compared to standard LMs. One such approach, the $k$NN-LM,…
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $\Omega$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation.…
To solve the problem of poor performance of deep neural network models due to insufficient data, a simple yet effective interpolation-based data augmentation method is proposed: MSMix (Manifold Swap Mixup). This method feeds two different…
We propose an exact slice sampler for Hierarchical Dirichlet process (HDP) and its associated mixture models (Teh et al., 2006). Although there are existing MCMC algorithms for sampling from the HDP, a slice sampler has been missing from…
The latest research on Large Language Models (LLMs) has demonstrated significant advancement in the field of Natural Language Processing (NLP). However, despite this progress, there is still a lack of reliability in these models. This is…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…
Federated Learning (FL) allows collaborative machine learning training without sharing private data. Numerous studies have shown that one significant factor affecting the performance of federated learning models is the heterogeneity of data…
Standard tabular benchmarks mainly focus on the evaluation of a model's capability to interpolate values inside a data manifold, where models good at performing local statistical smoothing are rewarded. However, there exists a very large…
Dramatic increases in the size and complexity of modern datasets have made traditional "centralized" statistical inference prohibitive. In addition to computational challenges associated with big data learning, the presence of numerous data…
To gain a comprehensive view of what the LHC tells us about physics beyond the Standard Model (BSM), it is crucial that different BSM-sensitive analyses can be combined. But in general, search analyses are not statistically orthogonal, so…
This paper introduces the Trimmed Functional Empirical Process (TFEP) as a robust framework for statistical inference when dealing with heavy-tailed or skewed distributions, where classical moments such as the mean or variance may be…