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By this way, we can obtain a sparse weight vector of base classifiers.
An SVM model can be represented by a sparse weight vector w →.
The outcome of such regression analysis is a sparse weight vector w n whose small number of non-zero elements specify which genes influence gene n.
Given a value of k, the number of possible choices of predictors that must be examined is N C k. Since there are many genes (N is large) and each choice of predictor variables requires solving an optimization problem, learning a sparse weight vector using an l0 norm-based approach is prohibitive, even for small k.
The LPM is known to produce a sparse weight vector w by solving the following minimization problem: (4) We thus apply a LPM to the training data in a 5 × 10 cross-validation procedure with the goal to obtain a ranking of the features according to | E(w i/|| w||)|.
Given a training set for gene n (2) D n = { (x n i, y n i ) | x n i ∈ R N ; y n i ∈ R ; i = 1,..., I } the sparse linear regression problem is the task of inferring a sparse weight vector, w n, under the assumption that gene-gene interactions obey a linear model, i.e., the abundance of a gene n, y ni = x n, is a weighted sum of the abundances of other genes, y n i = w n T x n i.
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The general idea is that we first randomly construct a set of basic MIML learners and then learn a sparse weights vector under the relevant vector machine (RVM) [ 23] framework to combine the basic learners together.
Each source network is stored on disk as a sparse weighted adjacency matrix, where weight corresponds to gene interaction strength.
Convolutional neural networks is a model that is optimized for vision while minimizing the complexity of the model based on three ideas: sparse weight, tied weight, and equivariant representation.
Sparsity of weights: We use regularization in our optimization function, which does not produce sparse weight vectors.
Aggregating the N sparse weight vectors produced by solving N independent sparse linear regression problems [ w1,..., w N ], yields the matrix W that parameterizes the graph.
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