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Relative surprise regions are shown to minimize, among Bayesian credible regions, the prior probability of covering a false value from the prior. Such regions are also shown to be unbiased in the sense that the prior probability of covering…

Statistics Theory · Mathematics 2008-12-22 M. Evans , M. Shakhatreh

Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. In this paper, we introduce probabilistic sufficient…

Machine Learning · Computer Science 2021-05-24 Eric Wang , Pasha Khosravi , Guy Van den Broeck

We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…

Optimization and Control · Mathematics 2022-01-20 Haixiang Zhang , Zeyu Zheng , Javad Lavaei

We propose EBLIME to explain black-box machine learning models and obtain the distribution of feature importance using Bayesian ridge regression models. We provide mathematical expressions of the Bayesian framework and theoretical outcomes…

Machine Learning · Statistics 2023-05-02 Yuhao Zhong , Anirban Bhattacharya , Satish Bukkapatnam

We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are…

Data Structures and Algorithms · Computer Science 2019-06-06 Michael Matheny , Dong Xie , Jeff M. Phillips

We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It…

Optimization and Control · Mathematics 2018-11-21 Hung D. Nguyen , Krishnamurthy Dvijotham , Konstantin Turitsyn

Given noisy data, function estimation is considered when the unknown function is known apriori to consist of a small number of regions where the function is either convex or concave. When the regions are known apriori, the estimate is…

Methodology · Statistics 2020-02-18 Kurt S. Riedel

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…

Methodology · Statistics 2017-12-18 Karl Mosler , Pavel Bazovkin

Time series forecasting has seen considerable improvement during the last years, with transformer models and large language models driving advancements of the state of the art. Modern forecasting models are generally opaque and do not…

Machine Learning · Computer Science 2025-11-18 Tim Kreuzer , Jelena Zdravkovic , Panagiotis Papapetrou

Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…

Metric Geometry · Mathematics 2026-03-10 Steven Hoehner

Explaining opaque Machine Learning (ML) models is an increasingly relevant problem. Current explanation in AI (XAI) methods suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of…

Artificial Intelligence · Computer Science 2023-09-04 Laura State , Salvatore Ruggieri , Franco Turini

Complex black-box predictive models may have high performance, but lack of interpretability causes problems like lack of trust, lack of stability, sensitivity to concept drift. On the other hand, achieving satisfactory accuracy of…

Machine Learning · Computer Science 2020-02-12 Alicja Gosiewska , Przemyslaw Biecek

The goal of this work is to accelerate the identification of an unknown ARX system from trajectory data through online input design. Specifically, we present an active learning algorithm that sequentially selects the input to excite the…

Systems and Control · Electrical Eng. & Systems 2025-09-04 Nicolas Chatzikiriakos , Bowen Song , Philipp Rank , Andrea Iannelli

Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the…

Optimization and Control · Mathematics 2025-11-18 Anh Tuan Nguyen , Viet Anh Nguyen

Although neural networks can achieve very high predictive performance on various different tasks such as image recognition or natural language processing, they are often considered as opaque "black boxes". The difficulty of interpreting the…

Machine Learning · Statistics 2020-01-22 Enguerrand Horel , Virgile Mison , Tao Xiong , Kay Giesecke , Lidia Mangu

Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative…

Methodology · Statistics 2023-10-17 Yash Patel , Sahana Rayan , Ambuj Tewari

Sparse methods are the standard approach to obtain interpretable models with high prediction accuracy. Alternatively, algorithmic ensemble methods can achieve higher prediction accuracy at the cost of loss of interpretability. However, the…

Methodology · Statistics 2022-01-11 Anthony Christidis , Stefan Van Aelst , Ruben Zamar

Concept Bottleneck Models (CBMs) first map raw input(s) to a vector of human-defined concepts, before using this vector to predict a final classification. We might therefore expect CBMs capable of predicting concepts based on distinct…

Artificial Intelligence · Computer Science 2023-02-08 Jack Furby , Daniel Cunnington , Dave Braines , Alun Preece

Trajectory analysis is not only about obtaining movement data, but it is also of paramount importance in understanding the pattern in which an object moves through space and time, as well as in predicting its next move. Due to the…

Machine Learning · Computer Science 2025-06-26 Chanuka Don Samarasinghage , Dhruv Gulabani

From self-driving vehicles and back-flipping robots to virtual assistants who book our next appointment at the hair salon or at that restaurant for dinner - machine learning systems are becoming increasingly ubiquitous. The main reason for…

Machine Learning · Computer Science 2018-08-16 Milo Honegger