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Level Set Estimation (LSE) is an important problem with applications in various fields such as material design, biotechnology, machine operational testing, etc. Existing techniques suffer from the scalability issue, that is, these methods…

Machine Learning · Statistics 2020-12-21 Huong Ha , Sunil Gupta , Santu Rana , Svetha Venkatesh

Level set estimation (LSE), the problem of identifying the set of input points where a function takes value above (or below) a given threshold, is important in practical applications. When the function is expensive-to-evaluate and…

Machine Learning · Statistics 2024-12-02 Yu Inatsu , Shion Takeno , Kentaro Kutsukake , Ichiro Takeuchi

Testing under what conditions the product satisfies the desired properties is a fundamental problem in manufacturing industry. If the condition and the property are respectively regarded as the input and the output of a black-box function,…

Machine Learning · Statistics 2025-07-30 Yu Inatsu , Masayuki Karasuyama , Keiichi Inoue , Ichiro Takeuchi

A common problem encountered in many real-world applications is level set estimation where the goal is to determine the region in the function domain where the function is above or below a given threshold. When the function is black-box and…

Machine Learning · Computer Science 2024-02-27 Giang Ngo , Dang Nguyen , Dat Phan-Trong , Sunil Gupta

Level set estimation (LSE) is the problem of identifying regions where an unknown function takes values above or below a specified threshold. Active sampling strategies for efficient LSE have primarily been studied in continuous-valued…

Machine Learning · Statistics 2022-03-21 Benjamin Letham , Phillip Guan , Chase Tymms , Eytan Bakshy , Michael Shvartsman

We consider the problem of active learning in the context of spatial sampling for level set estimation (LSE), where the goal is to localize all regions where a function of interest lies above/below a given threshold as quickly as possible.…

Machine Learning · Computer Science 2025-07-24 Phillip Kearns , Bruno Jedynak , John Lipor

The level set estimation problem seeks to identify regions within a set of candidate points where an unknown and costly to evaluate function's value exceeds a specified threshold, providing an efficient alternative to exhaustive evaluations…

Machine Learning · Statistics 2025-03-27 Hideaki Ishibashi , Kota Matsui , Kentaro Kutsukake , Hideitsu Hino

In image classification tasks, deep learning models are vulnerable to image distortion. For successful deployment, it is important to identify distortion levels under which the model is usable i.e. its accuracy stays above a stipulated…

Computer Vision and Pattern Recognition · Computer Science 2024-12-31 Dang Nguyen , Sunil Gupta

High-order (non-linear) functionals have become very popular in segmentation, stereo and other computer vision problems. Level sets is a well established general gradient descent framework, which is directly applicable to optimization of…

Computer Vision and Pattern Recognition · Computer Science 2013-11-12 Lena Gorelick , Ismail BenAyed , Frank R. Schmidt , Yuri Boykov

We present a novel hierarchical triplet loss (HTL) capable of automatically collecting informative training samples (triplets) via a defined hierarchical tree that encodes global context information. This allows us to cope with the main…

Computer Vision and Pattern Recognition · Computer Science 2018-10-17 Weifeng Ge , Weilin Huang , Dengke Dong , Matthew R. Scott

The level set estimation problem seeks to find all points in a domain ${\cal X}$ where the value of an unknown function $f:{\cal X}\rightarrow \mathbb{R}$ exceeds a threshold $\alpha$. The estimation is based on noisy function evaluations…

Machine Learning · Statistics 2021-11-03 Blake Mason , Romain Camilleri , Subhojyoti Mukherjee , Kevin Jamieson , Robert Nowak , Lalit Jain

A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit…

Machine Learning · Statistics 2021-08-10 Anthony Gruber , Max Gunzburger , Lili Ju , Yuankai Teng , Zhu Wang

Estimation of the level set of a function (i.e., regions where the function exceeds some value) is an important problem with applications in digital elevation mapping, medical imaging, astronomy, etc. In many applications, the function of…

Applications · Statistics 2018-03-06 Kalyani Krishnamurthy , Waheed U. Bajwa , Rebecca Willett

In the manufacturing industry, it is often necessary to repeat expensive operational testing of machine in order to identify the range of input conditions under which the machine operates properly. Since it is often difficult to accurately…

Machine Learning · Statistics 2019-10-29 Shogo Iwazaki , Yu Inatsu , Ichiro Takeuchi

In this paper we investigate the problem of learning an unknown bounded function. We be emphasize special cases where it is possible to provide very simple (in terms of computation) estimates enjoying in addition the property of being…

Statistics Theory · Mathematics 2007-06-13 Gerard Kerkyacharian , Dominique Picard

Selectivity estimation aims at estimating the number of database objects that satisfy a selection criterion. Answering this problem accurately and efficiently is essential to many applications, such as density estimation, outlier detection,…

Databases · Computer Science 2021-05-28 Yaoshu Wang , Chuan Xiao , Jianbin Qin , Rui Mao , Onizuka Makoto , Wei Wang , Rui Zhang , Yoshiharu Ishikawa

Deep reinforcement learning (DRL) is capable of learning high-performing policies on a variety of complex high-dimensional tasks, ranging from video games to robotic manipulation. However, standard DRL methods often suffer from poor sample…

Machine Learning · Computer Science 2020-03-04 Caleb Chuck , Supawit Chockchowwat , Scott Niekum

High dimensional data analysis for exploration and discovery includes three fundamental tasks: dimensionality reduction, clustering, and visualization. When the three associated tasks are done separately, as is often the case thus far,…

Machine Learning · Computer Science 2020-12-02 Stan Z. Li , Lirong Wu , Zelin Zang

In a given classification task, the accuracy of the learner is often hampered by finiteness of the training set, high-dimensionality of the feature space and severe overlap between classes. In the context of interpretable learners, with…

Machine Learning · Computer Science 2025-04-03 Marco Canducci , Lida Abdi , Alessandro Prete , Roland J. Veen , Michael Biehl , Wiebke Arlt , Peter Tino

Due to the curse of dimensionality and the limitation on training data, approximating high-dimensional functions is a very challenging task even for powerful deep neural networks. Inspired by the Nonlinear Level set Learning (NLL) method…

Machine Learning · Computer Science 2021-12-03 Yuankai Teng , Zhu Wang , Lili Ju , Anthony Gruber , Guannan Zhang
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