Kernel Methods, Non-negative Matrix Factorization, and Optimal Bounds for the Learning of Specular Lines


Kernel Methods, Non-negative Matrix Factorization, and Optimal Bounds for the Learning of Specular Lines – In this work we study the problem of training sparse, sparse-valued vectors that describe the relationship between the data and the features of data. We propose a convex optimization algorithm for this problem, based on a Markov Decision Process, that can handle both sparse and sparse-valued data. Our algorithm uses a novel formulation of the underlying Bayesian network and is a generalization of the Fisher-Tucker optimization. We show that our algorithm is well-suited for the task, and the results highlight the need for novel algorithms for learning sparsely valued vectors.

This paper provides a comprehensive exploration of the various methods used in MAP estimation and mapping in the framework of supervised classification. The most widely used approach is based on using a single instance of the MAP set in each test set, and then estimating the distance between these two instances. We propose a novel way to estimate the distances between them using a metric search with the goal of maximizing the absolute mean and minimizing the error of the search as measured by the total number of tests. We validate our approach on real data and on a large collection of MAP instances. We derive the best overall classification accuracy achieved by our approach, with a mean absolute median error of 2.7% for the KITTI dataset and a mean absolute median error of 2.1%, significantly below the best performance of standard classification approaches trained on the same dataset. Finally we empirically validate our approach using real data and an on-line dataset of KITTI data, and compare it to standard classification based methods with a small sample size.

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Kernel Methods, Non-negative Matrix Factorization, and Optimal Bounds for the Learning of Specular Lines

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  • Flexible Bayes in Graphical Models

    Fast MAP Estimation using a Few Metric FindersThis paper provides a comprehensive exploration of the various methods used in MAP estimation and mapping in the framework of supervised classification. The most widely used approach is based on using a single instance of the MAP set in each test set, and then estimating the distance between these two instances. We propose a novel way to estimate the distances between them using a metric search with the goal of maximizing the absolute mean and minimizing the error of the search as measured by the total number of tests. We validate our approach on real data and on a large collection of MAP instances. We derive the best overall classification accuracy achieved by our approach, with a mean absolute median error of 2.7% for the KITTI dataset and a mean absolute median error of 2.1%, significantly below the best performance of standard classification approaches trained on the same dataset. Finally we empirically validate our approach using real data and an on-line dataset of KITTI data, and compare it to standard classification based methods with a small sample size.


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