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We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown…

Statistics Theory · Mathematics 2013-12-02 Mikhail A. Langovoy , Olaf Wittich

In this paper, we describe how to get Janet decomposition for a finite set of terms and detect completeness of that set by means of the associated Bar Code. Moreover, we explain an algorithm to find a variable ordering (if it exists) s.t. a…

Combinatorics · Mathematics 2019-10-08 Michela Ceria

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…

Machine Learning · Computer Science 2024-11-08 Matthew A. Chan , Maria J. Molina , Christopher A. Metzler

Hypergraphs are increasingly utilized in both unimodal and multimodal data scenarios due to their superior ability to model and extract higher-order relationships among nodes, compared to traditional graphs. However, current hypergraph…

Machine Learning · Computer Science 2024-09-10 Ziming Zhao , Tiehua Zhang , Zijian Yi , Zhishu Shen

In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…

Analysis of PDEs · Mathematics 2015-12-10 Vo Anh Khoa , Le Trong Lan , Nguyen Huy Tuan , Tran The Hung

In medical domain, data features often contain missing values. This can create serious bias in the predictive modeling. Typical standard data mining methods often produce poor performance measures. In this paper, we propose a new method to…

Machine Learning · Statistics 2015-03-24 Talayeh Razzaghi , Oleg Roderick , Ilya Safro , Nick Marko

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources…

Methodology · Statistics 2010-08-30 Nicolas Dobigeon , Jean-Yves Tourneret

We introduce new lower bounds for the fractional Fisher information. Equipped with these bounds we study a hyperbolic-parabolic model of chemotaxis and prove the global existence of solutions in certain dissipation regimes.

Analysis of PDEs · Mathematics 2016-09-05 Rafael Granero-Belinchón

We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Luis Lehner

The sheer scale of high-resolution raw data generated by simulation has motivated non-conventional approaches for data exploration referred as `immersive' and `in situ' query processing of the raw simulation data. Another step towards…

Databases · Computer Science 2015-08-25 Bernardo Gonçalves , Fabio Porto

In the series of our earlier papers on the subject, we proposed a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed…

Computation · Statistics 2011-02-24 Mikhail A. Langovoy , Olaf Wittich

In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated…

Statistics Theory · Mathematics 2022-04-22 Susan Athey , Mohsen Bayati , Nikolay Doudchenko , Guido Imbens , Khashayar Khosravi

In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…

Numerical Analysis · Mathematics 2009-04-02 Juergen Geiser

In this uncertain world, data uncertainty is inherent in many applications and its importance is growing drastically due to the rapid development of modern technologies. Nowadays, researchers have paid more attention to mine patterns in…

Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing linear recurrence relations of a sequence with the Berlekamp-Massey…

Symbolic Computation · Computer Science 2021-07-07 Jérémy Berthomieu , Jean-Charles Faugère

We consider a dynamics generated by families of maps whose invariant density depends on a parameter a and where a itself obeys a stochastic or periodic dynamics. For slowly varying a the long-term behavior of iterates is described by a…

Chaotic Dynamics · Physics 2016-01-08 Chris Penrose , Christian Beck

This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab…

Information Theory · Computer Science 2015-10-28 Yannis Kopsinis , Konstantinos Slavakis , Sergios Theodoridis

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…

Optimization and Control · Mathematics 2018-12-18 Po-Wei Wang , J. Zico Kolter

With the rapid increase of compound databases available in medicinal and material science, there is a growing need for learning representations of molecules in a semi-supervised manner. In this paper, we propose an unsupervised hierarchical…

Machine Learning · Statistics 2017-11-30 Hai Nguyen , Shin-ichi Maeda , Kenta Oono

Current systems and formalisms for representing incomplete information generally suffer from at least one of two weaknesses. Either they are not strong enough for representing results of simple queries, or the handling and processing of the…

Databases · Computer Science 2008-02-14 Lyublena Antova , Christoph Koch , Dan Olteanu
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