We present two algorithms to solve the Group Lasso problem (Yuan and Lin in, J R Stat Soc Ser B (Stat Methodol) 68(1):49–67, ). First, we propose a general version of the Block Coordinate Descent (BCD) algorith
本仓库归档弃用 移至https://github.com/AkexStar/Algorithms-group-LASSO-problem - AkexStar/Archived-group-lasso-optimization
Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to...
(2006a) for penal- ized ℓ 1 regression is motivated by the problem of choosing the tuning pa- rameter λ. Their algorithm follows the central path determined by the min- imum of f(θ) as a function of λ. This procedure reveals exactly when each estimated β j enters the linear ...
the term ‘omics integration’ encompasses a wide spectrum of methodological approaches. An important distinction is the level at which integration occurs. In some cases, each omics dataset is analyzed independently, with individual findings being combined for biological interpretation. Alternatively, all ...
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the host. The main function of the microbiota is to protect the intestine against colonization by harmful microorganisms like pathogens through mechanisms, such as competition for nutrients and modulation of host immune responses. Studying the interaction of the microbiota with pathogens and the host ...
proximity algorithm 的核心是 使用邻近算子(proximal operator)去迭代地求解子问题(sub-problem)。 proximity algorithm 被广泛地应用于求解非光滑(nonsmooth),约束凸优化问题(constrained convex optimization problems) [29]。 假设一个简单的约束优化问题 其中χ⊂Rn。
(NLP with non-negativity constraints) Forandwe recover non-linear programming problems with linear equality constraints and non-negativity constraints: Example 2 (Optimization over the second-order cone) Considerand, the second-order cone (SOC). In this case problem (Opt) becomes a non-linear sec...
Moreover, the strong ℓ 1 ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire ...