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The scalar auxiliary variable (SAV) approach is a very popular and efficient method to simulate various phase field models. To save the computational cost, a new SAV approach is given by introducing a new variable $\theta$. The new SAV…
The Shapley value (SV) has emerged as a promising method for data valuation. However, computing or estimating the SV is often computationally expensive. To overcome this challenge, Jia et al. (2019) propose an advanced SV estimation…
We demonstrate SAGE-32B, a 32 billion parameter language model that focuses on agentic reasoning and long range planning tasks. Unlike chat models that aim for general conversation fluency, SAGE-32B is designed to operate in an agentic…
Algorithmic fairness has received considerable attention due to the failures of various predictive AI systems that have been found to be unfairly biased against subgroups of the population. Many approaches have been proposed to mitigate…
This paper deals with variable selection in the regression and binary classification frameworks. It proposes an automatic and exhaustive procedure which relies on the use of the CART algorithm and on model selection via penalization. This…
The Chisholm rational approximant is a natural generalization to two variables of the well-known single variable Pad\'e approximant, and has the advantage of reducing to the latter when one of the variables is set equals to 0. We present,…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Deep search agents, which aim to answer complex questions requiring reasoning across multiple documents, can significantly speed up the information-seeking process. Collecting human annotations for this application is prohibitively…
Model-based reinforcement learning algorithms are typically more sample efficient than their model-free counterparts, especially in sparse reward problems. Unfortunately, many interesting domains are too complex to specify the complete…
Interpretability is a pressing issue for decision systems. Many post hoc methods have been proposed to explain the predictions of a single machine learning model. However, business processes and decision systems are rarely centered around a…
We introduce Synthetic Alignment data Generation for Safety Evaluation and Red Teaming (SAGE-RT or SAGE) a novel pipeline for generating synthetic alignment and red-teaming data. Existing methods fall short in creating nuanced and diverse…
Variable aggregation has been largely studied as an important pre-solve algorithm for optimization of linear and mixed-integer programs. Although some nonlinear solvers and algebraic modeling languages implement variable aggregation as a…
This paper introduces the \proglang{R} package \pkg{meta4diag} for implementing Bayesian bivariate meta-analyses of diagnostic test studies. Our package \pkg{meta4diag} is a purpose-built front end of the \proglang{R} package \pkg{INLA}.…
Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…
In (S.B. Ekhad and D. Zeilberger, 2020) an exciting case study has been initiated in which experimental mathematics and symbolic computation are utilized to discover new properties concerning the so-called Absent-Minded Passengers Problem.…
The software package developed in the MS thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user-defined expected sequence factors of the input coefficients. We present a specialized…
Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of…
In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…
We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE which provides…