311 research outputs found
Generalized Stationary Points and an Interior Point Method for MPEC
Mathematical program with equilibrium constraints (MPEC)has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC.A primal-dual interior point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or linear independence constraint qualification. Under very general assumptions, the algorithm can always find some point with strong or weak stationarity. In particular, it is shown that every limiting point of the generated sequence is a piece-wise stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a certain point with weak stationarity can be obtained. Preliminary numerical results are satisfactory, which include a case analyzed by Leyffer for which the penalty interior point algorithm failed to find a stationary solution.Singapore-MIT Alliance (SMA
Knockoffs-SPR: Clean Sample Selection in Learning with Noisy Labels
A noisy training set usually leads to the degradation of the generalization
and robustness of neural networks. In this paper, we propose a novel
theoretically guaranteed clean sample selection framework for learning with
noisy labels. Specifically, we first present a Scalable Penalized Regression
(SPR) method, to model the linear relation between network features and one-hot
labels. In SPR, the clean data are identified by the zero mean-shift parameters
solved in the regression model. We theoretically show that SPR can recover
clean data under some conditions. Under general scenarios, the conditions may
be no longer satisfied; and some noisy data are falsely selected as clean data.
To solve this problem, we propose a data-adaptive method for Scalable Penalized
Regression with Knockoff filters (Knockoffs-SPR), which is provable to control
the False-Selection-Rate (FSR) in the selected clean data. To improve the
efficiency, we further present a split algorithm that divides the whole
training set into small pieces that can be solved in parallel to make the
framework scalable to large datasets. While Knockoffs-SPR can be regarded as a
sample selection module for a standard supervised training pipeline, we further
combine it with a semi-supervised algorithm to exploit the support of noisy
data as unlabeled data. Experimental results on several benchmark datasets and
real-world noisy datasets show the effectiveness of our framework and validate
the theoretical results of Knockoffs-SPR. Our code and pre-trained models are
available at https://github.com/Yikai-Wang/Knockoffs-SPR.Comment: update: refined theory and analysis, release cod
New uniqueness results for boundary value problem of fractional differential equation
In this paper, uniqueness results for boundary value problem of fractional differential equation are obtained. Both the Banach's contraction mapping principle and the theory of linear operator are used, and a comparison between the obtained results is provided
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