instruction:
In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
question:
In this paper, we address the problem of embedded feature selection for ranking on top of the list problems. We pose this problem as a regularized empirical risk minimization with p-norm push loss function (p = ∞) and sparsity inducing regularizers. We leverage the issues related to this challenging optimization problem by considering an alternating direction method of multipliers algorithm which is built upon proximal operators of the loss function and the regularizer. Our main technical contribution is thus to provide a numerical scheme for computing the infinite push loss function proximal operator. Experimental results on toy, DNA microarray and BCI problems show how our novel algorithm compares favorably to competitors for ranking on top while using fewer variables in the scoring function.
answer:
Sparse Support Vector Infinite Push


question:
A two–step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the second step, build outcome variable Christoffel function, but use the bag’s Christoffel function value at given point as the weight for the bag’s outcome. The approach allows the result to be obtained in closed form and then to be evaluated numerically. While most of existing approaches minimize some kind an error between outcome and prediction, the proposed approach is conceptually different, because it uses Christoffel function for knowledge representation, what is conceptually equivalent working with probabilities only. To receive possible outcomes and their probabilities Gauss quadrature for second–step measure can be built, then the nodes give possible outcomes and normalized weights – outcome probabilities. A library providing numerically stable polynomial basis for these calculations is available, what make the proposed approach practical.
answer:
Multiple–Instance Learning: Christoffel Function Approach to Distribution Regression Problem


question:
We address the problem of learning a ranking by using adaptively chosen pairwise comparisons. Our goal is to recover the ranking accurately but to sample the comparisons sparingly. If all comparison outcomes are consistent with the ranking, the optimal solution is to use an efficient sorting algorithm, such as Quicksort. But how do sorting algorithms behave if some comparison outcomes are inconsistent with the ranking? We give favorable guarantees for Quicksort for the popular Bradley–Terry model, under natural assumptions on the parameters. Furthermore, we empirically demonstrate that sorting algorithms lead to a very simple and effective active learning strategy: repeatedly sort the items. This strategy performs as well as state-of-the-art methods (and much better than random sampling) at a minuscule fraction of the computational cost.
answer:

Just Sort It! A Simple and Effective Approach to Active Preference Learning