Related papers: Optimization Workshop Notes for Mathematical Progr…
We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…
Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the…
A mathematical framework for modelling constrained mixed-variable optimization problems is presented in a blackbox optimization context. The framework introduces a new notation and allows solution strategies. The notation framework allows…
Model interpretability has become an important problem in machine learning (ML) due to the increased effect that algorithmic decisions have on humans. Counterfactual explanations can help users understand not only why ML models make certain…
Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…
Pre-trained language models (PLMs) have gained increasing popularity due to their compelling prediction performance in diverse natural language processing (NLP) tasks. When formulating a PLM-based prediction pipeline for NLP tasks, it is…
A modelling language is described which is suitable for the correlation of information when the underlying functional model of the system is incomplete or uncertain and the temporal dependencies are imprecise. An efficient and incremental…
This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
Large language models (LLMs) demonstrate considerable potential in various natural language tasks but face significant challenges in mathematical reasoning, particularly in executing precise, multi-step logic. However, current evaluation…
In this paper, we evaluate the capability of transformer-based language models in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained Language Models (PLMs) and generative Large…
This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its…
Recent years have witnessed increasing interest in optimization proxies, i.e., machine learning models that approximate the input-output mapping of parametric optimization problems and return near-optimal feasible solutions. Following…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…
Peak estimation of hybrid systems aims to upper bound extreme values of a state function along trajectories, where this state function could be different in each subsystem. This finite-dimensional but nonconvex problem may be lifted into an…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
In the deployment of large language models (LLMs), accurate confidence estimation is critical for assessing the credibility of model predictions. However, existing methods often fail to overcome the issue of overconfidence on incorrect…
We develop first-order logic and some extensions for incomplete information scenarios and consider related complexity issues.
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
This paper shows how to harness existing theorem provers for first-order logic to automatically verify safety properties of imperative programs that perform dynamic storage allocation and destructive updating of pointer-valued structure…