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Related papers: Asymmetric scale functions for $t$-digests

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Recurrent neural networks have been widely used in sequence learning tasks. In previous studies, the performance of the model has always been improved by either wider or deeper structures. However, the former becomes more prone to…

Machine Learning · Computer Science 2019-11-20 Yu-Xuan Li , Jin-Yuan Liu , Liang Li , Xiang Guan

Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…

Machine Learning · Statistics 2019-02-20 Dimitris Berberidis , Athanasios N. Nikolakopoulos , Georgios B. Giannakis

The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…

General Topology · Mathematics 2020-01-30 Jialiang He , Hongliang Lai , Lili Shen

In this paper, a new and novel data structure is proposed to dynamically insert and delete segments. Unlike the standard segment trees[3], the proposed data structure permits insertion of a segment with interval range beyond the interval…

Computational Geometry · Computer Science 2015-01-15 K. S. Easwarakumar , T. Hema

Local general depth ($LGD$) functions are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of $LGD$ and establish several analytical and…

Statistics Theory · Mathematics 2022-11-04 Giacomo Francisci , Claudio Agostinelli , Alicia Nieto-Reyes , Anand N. Vidyashankar

Food diary applications represent a tantalizing market. Such applications, based on image food recognition, opened to new challenges for computer vision and pattern recognition algorithms. Recent works in the field are focusing either on…

Computer Vision and Pattern Recognition · Computer Science 2016-12-21 Niki Martinel , Gian Luca Foresti , Christian Micheloni

Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a…

Information Theory · Computer Science 2015-06-05 Sheng-Yuan Tu , Ali H. Sayed

We prove asymptotic convergence for a general class of $k$-means algorithms performed over streaming data from a distribution: the centers asymptotically converge to the set of stationary points of the $k$-means cost function. To do so, we…

Machine Learning · Computer Science 2022-02-23 Sanjoy Dasgupta , Gaurav Mahajan , Geelon So

There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling…

Computer Vision and Pattern Recognition · Computer Science 2020-04-07 Itai Lang , Asaf Manor , Shai Avidan

We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…

Optimization and Control · Mathematics 2016-01-05 Ali Makhdoumi , Asuman Ozdaglar

The similarity between objects is significant in a broad range of areas. While similarity can be measured using off-the-shelf distance functions, they may fail to capture the inherent meaning of similarity, which tends to depend on the…

Quantum Physics · Physics 2022-01-10 Santosh Kumar Radha , Casey Jao

A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning,…

Segmenting multiple objects (e.g., organs) in medical images often requires an understanding of their topology, which simultaneously quantifies the shape of the objects and their positions relative to each other. This understanding is…

Image and Video Processing · Electrical Eng. & Systems 2024-08-16 Mehmet Bahadir Erden , Sinan Unver , Ilke Ali Gurses , Rustu Turkay , Cigdem Gunduz-Demir

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…

Machine Learning · Statistics 2022-10-18 Sloan Nietert , Ritwik Sadhu , Ziv Goldfeld , Kengo Kato

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

Machine Learning · Computer Science 2023-11-01 Aaron Lou , Minkai Xu , Stefano Ermon

Distribution matching is the process of invertibly mapping a uniformly distributed input sequence onto sequences that approximate the output of a desired discrete memoryless source. The special case of a binary output alphabet and…

Information Theory · Computer Science 2017-12-19 Patrick Schulte , Bernhard C. Geiger

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…

Machine Learning · Statistics 2024-09-12 Yifan Chen , Daniel Zhengyu Huang , Jiaoyang Huang , Sebastian Reich , Andrew M. Stuart

High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…

Machine Learning · Statistics 2026-02-24 Xinyu Tian , Xiaotong Shen

Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a…

Methodology · Statistics 2024-02-16 Yoichi Miyata , Takayuki Shiohama , Toshihiro Abe

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…

Computer Vision and Pattern Recognition · Computer Science 2017-06-20 Zsuzsanna Püspöki , John Paul Ward , Daniel Sage , Michael Unser