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  1. Analytical model of the effect of tangent length between vertical curves on train derailments
بررسی تحلیل جداساز مربعی تنک و مدل بیز انجمنی
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بررسی تحلیل جداساز مربعی تنک و مدل بیز انجمنی

بایبوردی، آرزو Bybordi, Arezoo

Sparse Quadratic Discriminant Analysis and Community Bayes

Bybordi, Arezoo | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51707 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Haji Mirsadeghi, Miromid
  7. Abstract:
  8. In this thesis, various methods for solving the classification problem with algorithms for some of their estimations, will be discussed. First, linear discriminant analysis (LDA), which is the most basic likelihood based method of classification is studied. In the next section, regularized discriminant analysis, a version of LDA in which the covariance matrix of each class is shrank toward the identity matrix, is studied. Then the ridge fusion in which a penalty is added to the likelihood function so that in the joint estimation of covariance matrices of dierent classes, all arrays become equal as much as possible is discussed. In the joint graphical lasso,precision matrices of dierent classes, will be estimated jointly. In that section, using two penalty functions, fused graphical lasso and group graphical lasso are introduced. In the next section, a brief explanation about regression with grouped variables is given and as an example, the group lasso penalty in discussed. Further,for the classication problems with the number of classes equal two, the sparse quadratic discriminant analysis is discussed, which is built through thresholding on the means and covariance matrices of classes. At last, through sparse graphical models, a method is discussed which will cover classifiers from quadratic discriminant analysis to naive Bayes. A group lasso penalty is used to present shrinkage and reassure similar sparsity pattern on all precision matrices which will lead to sparse estimations of interactions and will produce interpretable models.Inspired from the connected component structure of estimated precision matrices,community Bayes model is illustrated which partitions the features to some conditionally independent communities and as a result, will break the classification problem into smaller classification problems. The idea of community Bayes model is general and can be used on nongaussian data and likelihood based classifiers
  9. Keywords:
  10. Classification ; Clustering ; Convex Optimization ; Group Lasso ; Sparse Quadratic Discriminant Analysis

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