We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional spaces is sufficiently well studied in the literature. We generalize this problem to that in a Hilbert space and propose an algorithm for learning a polyhedron which correctly classifies at least $1- \varepsilon$ of the distribution, with a probability of at least $1 - \delta,$ where $\varepsilon$ and $\delta$ are given parameters. Also, as a corollary, we improve some previous bounds for polyhedral classification in finite-dimensional spaces.

翻译：我们研究二元分类问题，从在希尔伯特空间中学习凸多面体的视角展开，任何二元分类问题均可归约为此问题。有限维空间中凸多面体学习问题在文献中已得到充分研究。本文将这一问题推广至希尔伯特空间，并提出一种学习多面体的算法，该算法能以至少$1- \delta$的概率正确分类分布中至少$1- \varepsilon$的样本，其中$\varepsilon$和$\delta$为给定参数。此外，作为推论，我们改进了有限维空间中多面体分类的若干上界结果。