具有权重约束的逻辑回归(非自然，降序) [英] logistic regression with weights constraints(non-nagetive,desceding order)

问题描述

在一次采访中，我被问到是否有权重约束的逻辑回归，例如 1.weights均为非负和 2.weights保持降序全局最优，我知道没有约束它可以达到全局最优，在非消极约束下，我认为通过使用带kkt条件的lagrange乘数可以管理局部最优，但是有一种方法可以使用某种方法在递减的情况下获得局部最优重量?

I was asked in an interview if logistic regression with weights constraints such as 1.weights are all non-negative and 2.weights are keep descending order can get the global optima,I know that without constraints it can reach the global optima,under non-nagetive constraints I think by using lagrange multiplier with kkt condition can manage to local optima,but is there a way by using some method to get local optima under desceding weights?

推荐答案

对权重顺序的限制仅将搜索限制在权重空间的某个区域内，并且最大似然性位于该区域内或位于它的边界.这与非负权重的情况相同，只是区域不同.在两个维度上，w1 ＜0.w2是线w1 = w2下方的区域.我在将该图片推广到更高维度时遇到了麻烦，但是也许您可以做到.

The constraint on the order of the weights just limits the search to a region of the weight space, and the maximum of the likelihood is either within the region or on its boundary. This is the same situation as for nonnegative weights, just with a different region. In two dimensions, w1 < w2 is the region below the line w1 = w2. I'm having trouble generalizing that picture to higher dimensions but maybe you can do it.

请注意约束优化.发挥约束条件只能使约束条件最大化，即在允许区域边界上的解决方案.如果不受约束的全局最大值在该区域内，则约束已满足，您无需发挥约束的作用.因此，解决此问题的方法是首先找到无约束的最大值.如果它在区域内，那么您就完成了.否则，您需要解决约束问题.

Be careful about constrained optimization. Bringing the constraint into play only gives the maximum subject to the constraint, i.e. a solution on the boundary of the allowed region. If the unconstrained global maximum is within the region, then the constraint is satisfied and you don't need to bring the constraints into play. So the way to solve such a problem is to first find the unconstrained maximum. If it's within the region, then you're done. Otherwise, you need to solve the constrained problem.

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