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Large spatial datasets are becoming ubiquitous in environmental sciences with the explosion in the amount of data produced by sensors that monitor and measure the Earth system. Consequently, the geostatistical analysis of these data…
In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and…
Grokking describes a delayed generalization phenomenon in which a neural network achieves perfect training accuracy long before validation accuracy improves, followed by an abrupt transition to strong generalization. Existing detection…
We recently introduced the Alchemical Integral Transform (AIT) enabling the prediction of energy differences, and guessed an Ansatz to parametrize space $\pmb{r}$ in some alchemical change $\lambda$. Here, we present a rigorous derivation…
In this paper, we further investigate the problem of selecting a set of design points for universal kriging, which is a widely used technique for spatial data analysis. Our goal is to select the design points in order to make simultaneous…
We propose an architecture and process for using the Iterated Learning Model ("ILM") for artificial neural networks. We show that ILM does not lead to the same clear compositionality as observed using DCGs, but does lead to a modest…
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of…
Logarithmic transformation of the data has been recommended by the literature in the case of highly skewed distributions such as those commonly found in information science. The purpose of the transformation is to make the data conform to…
Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric…
Graph transformers have demonstrated remarkable capability on complex spatio-temporal tasks, yet their depth is often limited by oversmoothing and weak long-range dependency modeling. To address these challenges, we introduce GRIT-LP, a…
Isotonic distributional regression (IDR) is a powerful nonparametric technique for the estimation of conditional distributions under order restrictions. In a nutshell, IDR learns conditional distributions that are calibrated, and…
In stepwise derivations of programs from specifications, data type refinements are common. Many data type refinements involve isomorphic mappings between the more abstract and more concrete data representations. Examples include refinement…
We propose symmetric power transformation to enhance the capacity of Implicit Neural Representation~(INR) from the perspective of data transformation. Unlike prior work utilizing random permutation or index rearrangement, our method…
Kernel logistic regression (KLR) is a widely used supervised learning method for binary and multi-class classification, which provides estimates of the conditional probabilities of class membership for the data points. Unlike other kernel…
Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is…
Spatial prediction requires expensive computation to invert the spatial covariance matrix it depends on and also has considerable storage needs. This work concentrates on computationally efficient algorithms for prediction using very large…
The performance of Large Language Models (LLMs) is increasingly governed by data efficiency rather than raw scaling volume. However, existing selection methods often decouple global distribution balancing from local instance selection,…
Evaluating large language models (LLMs) on comprehensive benchmarks is a cornerstone of their development, yet it's often computationally and financially prohibitive. While Item Response Theory (IRT) offers a promising path toward…
The Interaction-Transformation (IT) is a new representation for Symbolic Regression that restricts the search space into simpler, but expressive, function forms. This representation has the advantage of creating a smoother search space…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…