Waring-like decompositions of polynomials - 1

Let $F$ be a homogeneous form of degree $d$ in $n$ variables. A Waring decomposition of $F$ is a way to express $F$ as a sum of $d^{th}$ powers of linear forms. In this paper we consider the decompositions of a form as a sum of expressions, each of which is a fixed monomial evaluated at linear forms.Comment: 12 pages; Section 5 added in this versio

Random Forests model selection

Random Forests (RF) of tree classifiers are a popular ensemble method for classification. RF have shown to be effective in many different real world classification problems and nowadays are considered as one of the best learning algorithms in this context. In this paper we discuss the effect of the hyperparameters of the RF over the accuracy of the final model, with particular reference to different theoretically grounded weighing strategies of the tree in the forest. In this way we go against the common misconception which considers RF as an hyperparameter-free learning algorithm. Results on a series of benchmark datasets show that performing an accurate Model Selection procedure can greatly improve the accuracy of the final RF classifier

Waring decompositions of special ternary forms with different Hilbert functions

We prove the existence of ternary forms admitting apolar sets of points of cardinality equal to the Waring rank, but having different Hilbert function and different regularity. This is done exploiting liaison theory and Cayley-Bacharach properties for sets of points in the projective planeComment: 12 pages. Comments are welcome

Tuning the distribution dependent prior in the PAC-Bayes framework based on empirical data

In this paper we further develop the idea that the PAC-Bayes prior can be defined based on the data-generating distribution. In particular, following Catoni [1], we refine some recent generalisation bounds on the risk of the Gibbs Classifier, when the prior is defined in terms of the data generating distribution, and the posterior is defined in terms of the observed one. Moreover we show that the prior and the posterior distributions can be tuned based on the observed samples without worsening the convergence rate of the bounds and with a marginal impact on their constants

Human activity recognition on smartphones using a multiclass hardware-friendly support vector machine

Activity-Based Computing aims to capture the state of the user and its environment by exploiting heterogeneous sensors in order to provide adaptation to exogenous computing resources. When these sensors are attached to the subject’s body, they permit continuous monitoring of numerous physiological signals. This has appealing use in healthcare applications, e.g. the exploitation of Ambient Intelligence (AmI) in daily activity monitoring for elderly people. In this paper, we present a system for human physical Activity Recognition (AR) using smartphone inertial sensors. As these mobile phones are limited in terms of energy and computing power, we propose a novel hardware-friendly approach for multiclass classification. This method adapts the standard Support Vector Machine (SVM) and exploits fixed-point arithmetic for computational cost reduction. A comparison with the traditional SVM shows a significant improvement in terms of computational costs while maintaining similar accuracy, which can contribute to develop more sustainable systems for AmI.Peer ReviewedPostprint (author's final draft