Related papers: Tropical Geometric Tools for Machine Learning: the…
Weighted Finite State Transducers (WFSTs) are versatile data structures that can model a great number of problems, ranging from Automatic Speech Recognition to DNA sequencing. Traditional computer science algorithms are employed when…
Due to their flexibility and superior performance, machine learning models frequently complement and outperform traditional statistical survival models. However, their widespread adoption is hindered by a lack of user-friendly tools to…
OpenML is an online machine learning platform where researchers can easily share data, machine learning tasks and experiments as well as organize them online to work and collaborate more efficiently. In this paper, we present an R package…
Meta-analytical models are typically formulated as a mixed-effects model where the sampling variances of the effect sizes are treated as known. In principle, such models could be fitted with standard mixed-modelling software such as the…
Tropical geometry has recently found several applications in the analysis of neural networks with piecewise linear activation functions. This paper presents a new look at the problem of tropical polynomial division and its application to…
We introduce ToRL (Tool-Integrated Reinforcement Learning), a framework for training large language models (LLMs) to autonomously use computational tools via reinforcement learning. Unlike supervised fine-tuning, ToRL allows models to…
Exponential-family random graph models (ERGMs) are probabilistic network models that are parametrized by sufficient statistics based on structural (i.e., graph-theoretic) properties. The ergm package for the R statistical computing system…
Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…
The tropical convex hull of a finite set of points in tropical projective space has a natural structure of a cellular free resolution. Therefore, methods from computational commutative algebra can be used to compute tropical convex hulls.…
TMB is an open source R package that enables quick implementation of complex nonlinear random effect (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, admb-project.org). In addition, it offers…
Correlation among the observations in high-dimensional regression modeling can be a major source of confounding. We present a new open-source package, plmmr, to implement penalized linear mixed models in R. This R package estimates…
This work proposes a novel general-purpose estimator for supervised machine learning (ML) based on tensor trains (TT). The estimator uses TTs to parametrize discretized functions, which are then optimized using Riemannian gradient descent…
The rapid development of modern technology facilitates the appearance of numerous unprecedented complex data which do not satisfy the axioms of Euclidean geometry, while most of the statistical hypothesis tests are available in Euclidean or…
This note introduces the $\texttt{LikelihoodGeometry}$ package for the computer algebra system $\textit{Macaulay2}$. This package gives tools to construct the likelihood correspondence of a discrete algebraic statistical model, a variety…
We develop a number of general techniques for comparing analytifications and tropicalizations of algebraic varieties. Our basic results include a projection formula for tropical multiplicities and a generalization of the Sturmfels-Tevelev…
Supervised machine learning (ML) algorithms have recently been proposed as an alternative to traditional tractography methods in order to address some of their weaknesses. They can be path-based and local-model-free, and easily incorporate…
Significant advancements in Large Multimodal Models (LMMs) have enabled them to tackle complex problems involving visual-mathematical reasoning. However, their ability to identify geometric elements remains underexplored. To address this…
We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples…
In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a…
Even though in recent years the scale of statistical analysis problems has increased tremendously, many statistical software tools are still limited to single-node computations. However, statistical analyses are largely based on dense…