相关论文: Rigorous Analytic Combinatorics in Several Variabl…

We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of…

Access to multiple predictive models trained for the same task, whether in regression or classification, is increasingly common in many applications. Aggregating their predictive uncertainties to produce reliable and efficient uncertainty…

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…

As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any…

In the present paper by using Mathematica system a symbolic programming method for generation of the expressions of the expansion terms of atomic stationary perturbation theory (PT) is presented. For this purpose, the package named as…

Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…

Reinforcement Learning with Verifiable Rewards (RLVR) has been successfully applied to significantly boost the capabilities of pretrained large language models, especially in the math and logic problem domains. However, current research and…

We provide a general mathematical framework for selective inference with supervised model selection procedures characterized by quadratic forms in the outcome variable. Forward stepwise with groups of variables is an important special case…

The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment, thereby enabling the R user…

Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…

Bagging is a useful method for large-scale statistical analysis, especially when the computing resources are very limited. We study here the asymptotic properties of bagging estimators for $M$-estimation problems but with massive datasets.…

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial…

In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zheng on the single variable case. As an application, for…

In this paper we present the SageMath package FlexRiLoG (short for flexible and rigid labelings of graphs). Based on recent results the software generates motions of graphs using special edge colorings. The package computes and illustrates…

In this article, we propose the Coopetititve Soft Gating Ensemble or CSGE for general machine learning tasks and interwoven systems. The goal of machine learning is to create models that generalize well for unknown datasets. Often, however,…

This article introduces the pammtools package, which facilitates data transformation, estimation and interpretation of Piece-wise exponential Additive Mixed Models. A special focus is on time-varying effects and cumulative effects of…

This paper sets a proposal of a new method and two new algorithms for Correspondence Analysis when we have Symbolic Multi--Valued Variables (SymCA). In our method, there are two multi--valued variables $X$ and $Y$, that is to say, the…

This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…