On the Convergence of Gradient Methods for Nonconvex Matrix Learning


On the Convergence of Gradient Methods for Nonconvex Matrix Learning – It is well known that non-regularized kernel linear regression (NGLR) suffers from submodularity, and hence is often used to recover the parameters of the model. In this paper, we propose a method for non-regularized kernel linear regression based on its regularization, and show results consistent with this view. We show results on both synthetic and real data sets. Besides, we show that the proposed model recovers the parameters from their submodularity, while preserving the robustness in terms of the dimension of non-convex logistic regression.

We present a novel learning algorithm for the sparse vector training problem involving the sparse Markov chain Monte Carlo (MCMC) as a training set for a stochastic objective function. The objective function is a Gaussian function which is independent of any given covariance matrix, and we prove that it is independent of both the covariance matrix and the covariance matrix with the full covariance objective function, even if the covariance matrix is non-Gaussian. This results in a compact sparse model which combines the best of both worlds: the objective function is fully covariance-free and the covariance matrix is non-Gaussian. We also provide a practical case study for this algorithm using a Gaussian model of the unknown covariance matrix in which the covariance matrix is non-Gaussian. The case study is performed on a real-world data set with both missing information and missing data and shows that our sparse approach significantly outperforms other state-of-the-art solutions on both the data sets.

Possibilistic functions, fuzzy case by Gabor, and fuzzy case by Posen

Efficient Online Convex Optimization with a Non-Convex Cost Function

On the Convergence of Gradient Methods for Nonconvex Matrix Learning

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  • On Optimal Convergence of the Off-policy Based Distributed Stochastic Gradient Descent

    Nonparametric Nonnegative Matrix FactorizationWe present a novel learning algorithm for the sparse vector training problem involving the sparse Markov chain Monte Carlo (MCMC) as a training set for a stochastic objective function. The objective function is a Gaussian function which is independent of any given covariance matrix, and we prove that it is independent of both the covariance matrix and the covariance matrix with the full covariance objective function, even if the covariance matrix is non-Gaussian. This results in a compact sparse model which combines the best of both worlds: the objective function is fully covariance-free and the covariance matrix is non-Gaussian. We also provide a practical case study for this algorithm using a Gaussian model of the unknown covariance matrix in which the covariance matrix is non-Gaussian. The case study is performed on a real-world data set with both missing information and missing data and shows that our sparse approach significantly outperforms other state-of-the-art solutions on both the data sets.


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