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:
The paper addresses the problem of learning a regression model parameterized by a fixedrank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixed-rank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks.
answer:
Regression on fixed-rank positive semidefinite matrices: a Riemannian approach

question:
We study the helpful product reviews identification problem in this paper. We observe that the evidence-conclusion discourse relations, also known as arguments, often appear in product reviews, and we hypothesise that some argumentbased features, e.g. the percentage of argumentative sentences, the evidencesconclusions ratios, are good indicators of helpful reviews. To validate this hypothesis, we manually annotate arguments in 110 hotel reviews, and investigate the effectiveness of several combinations of argument-based features. Experiments suggest that, when being used together with the argument-based features, the state-of-the-art baseline features can enjoy a performance boost (in terms of F1) of 11.01% in average.
answer:
Using Argument-based Features to Predict and Analyse Review Helpfulness

question:
We consider the estimation of an i.i.d. (possibly non-Gaussian) vector x R from measurements y R obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise (possibly nonlinear) measurement channel. A novel method, called adaptive generalized approximate message passing (Adaptive GAMP), that enables joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector x is presented. The proposed algorithm is a generalization of a recently-developed EM-GAMP that uses expectationmaximization (EM) iterations where the posteriors in the E-steps are computed via approximate message passing. The methodology can be applied to a large class of learning problems including the learning of sparse priors in compressed sensing or identification of linear-nonlinear cascade models in dynamical systems and neural spiking processes. We prove that for large i.i.d. Gaussian transform matrices the asymptotic componentwise behavior of the adaptive GAMP algorithm is predicted by a simple set of scalar state evolution equations. In addition, we show that when a certain maximum-likelihood estimation can be performed in each step, the adaptive GAMP method can yield asymptotically consistent parameter estimates, which implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values. Remarkably, this result applies to essentially arbitrary parametrizations of the unknown distributions, including ones that are nonlinear and non-Gaussian. The adaptive GAMP methodology thus provides a systematic, general and computationally efficient method applicable to a large range of complex linear-nonlinear models with provable guarantees.
answer:
Approximate Message Passing with Consistent Parameter Estimation and Applications to Sparse Learning