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THÔNG BÁO Triệu tập thí sinh tham dự thi vấn đáp tại vòng 2
THÔNG BÁO Tuyển viên chức năm 2024
Kế hoạch tuyển viên chức năm 2024
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18/09/24, Hội nghị, hội thảo:
THE 3RD VIETNAM - KOREA JOINT WORKSHOP ON SELECTED TOPICS IN MATHEMATICS
02/01/25, Hội nghị, hội thảo:
Hội nghị toàn quốc lần thứ VII “Xác suất - Thống kê: Nghiên cứu, ứng dụng và giảng dạy”
18/12/24, Hội nghị, hội thảo:
International conference on commutative algebra to the memory of Jürgen Herzog
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Phạm Hữu Sách, Lê Anh Tuấn, Nguyễn Thế Vinh, Vector Quasi-Equilibria for the Sum of Two Multivalued Trifunctions, Journal of Optimization Theory and Applications, Volume 204, article number 44, (2025) (SCI-E, Scopus) .
Nguyễn Đình Công, Lưu Hoàng Đức, Phan Thanh Hồng, umerical Attractors via Discrete Rough Paths, Journal of Dynamics and Differential Equations, Volume 37, pages 727–748, (2025) (SCI-E, Scopus) .
Tan H. Cao, Nilson Chapagain, Haejoon Lee, Thi Phung, Nguyễn Năng Thiều, Optimal Control of Several Motion Models, Journal of Optimization Theory and Applications, Volume 205, article number 3, (2025) (SCI-E, Scopus) .

The Moment-SOS hierarchy for classification based on volume computation

Người báo cáo: Mai Ngọc Hoàng Anh


Thời gian: 9h30 thứ Tư ngày 18/10/2023

Địa điểm: Phòng seminar tầng 5 nhà A6, Viện Toán học

Tóm tắt: We rely on the volume computation developed by Dabbene and Henrion to build up a probabilistic Moment-SOS hierarchy for classification. More precisely, we minimize the integral of an unknown polynomial q on a given semialgebraic set Ω, subject to a positivity certificate of q on Ω and the positivity of q−1 on a set of uniformly random samples (X(j))j=1t in a subset A⊂Omega. Under mild conditions, the sequence of values returned by this hierarchy converges to the volume of A. We also prove that with probability near one, the sequence of polynomials returned by our SOS hierarchy converges to the indicator function χA when the sample size t is sufficiently large. Consequently, with probability near one and a sufficiently large number of uniformly random samples in each class Ar⊂Ω, for almost all points a in Ω, we can determine which class Ar the point a belongs to under mild conditions. This result is proved using Friedrichs' mollifiers, Weierstrass' theorem, Putinar's Positivstellensatz, and Korda's ϵ net. This is based on joint work with Jean-Bernard Lasserre, Victor Magron, and Srecko Durasinovic.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
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MessagesTimelineExceptionsViews7RouteQueries36Models149MailsGateSessionRequest
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