炼丹魔法书-Convex Optimization for Machine Learning 这本书是由 Michael Nielsen 和 Isaac Schreiber 合著的，于2019年由MIT出版社出版。该书是机器学习领域中关于非凸优化问题的经典著作之一，主要介绍了一些非凸优化算法以及如何求解非凸优化问题。书中主要讲了两种非凸情况：一是目标函数是凸的，约束集合不是凸的...
定义1(Convex function):一个函数 f 被称为凸函数,如果对任意 x,y ,满足 (0.1)f(y)≥f(x)+⟨∇f(x),y−x⟩ 定义2(Strong convexity):一个函数 f 被称为 μ -强凸函数,如果对任意 x,y ,满足 (0.2)f(y)≥f(x)+⟨∇f(x),y−x⟩+μ2‖y−x‖2 (别小看后面多出...
In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-convex function. This is especially true of algorithms that operate in high-dimensional spaces or ...
The challenge that we address here, in turn, becomes proving that an objective function belongs to this class. We establish such results for the natural learning objectives of matrix completion and linear dynamical systems.;Finally, we make steps towards interpreting the non-linear models that ...
In this paper machine learning methods for automatic classification problems using computational geometry are considered. Classes are defined with convex hulls of points sets in a multidimensional feature space. Classification algorithms based on the estimation of the proximity of the test point to convex...
(andsomeadditionalregularityproperty).Suchfunctionscanbeoptimizedbylocalimprovementalgorithmsefficientlyfromarandomorarbitrarystartingpoint.Thechallengethatweaddresshere,inturn,becomesprovingthatanobjectivefunctionbelongstothisclass.Weestablishsuchresultsforthenaturallearningobjectivesofmatrixcompletionandlineardynamicalsystems...
A convex function However, if you cross the function line, then the function is non-convex. A non-convex function As you can see in the figure above, the red line crosses the function, which means it is non-convex. Note, however, that the function is convex on some intervals, for ins...
In online convex programming, the convex set is known in advance, but in each step of some repeated optimization problem, one must select a point in F before seeing the cost function for that step. This can be used to model factory production, farm production, and many other industrial ...
Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records... K Chaudhuri,C Monteleoni,D Sarwate - 《Journal of Machine Learning Research》 被引量: 625发表: 2011年 Differentially Private Empirical Risk ...
In machine learning and optimization, one often wants to minimize a convex objective function $F$ but can only evaluate a noisy approximation $\hat{F}$ to it. Even though $F$ is convex, the noise may render $\hat{F}$ nonconvex, making the task of minimizing $F$ intractable in general...