Almost sure invariance principle for random piecewise expanding maps

We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on martingale techniques

Accuracy and interpretability trade-offs in machine learning applied to safer gambling

Responsible gambling is an area of research and industry which seeks to understand the pathways to harm from gambling and implement programmes to reduce or prevent harm that gambling might cause. There is a growing body of research that has used gambling behavioural data to model and predict harmful gambling, and the industry is showing increasing interest in technologies that can help gambling operators to better predict harm and prevent it through appropriate interventions. However, industry surveys and feedback clearly indicate that in order to enable wider adoption of such data-driven methods, industry and policy makers require a greater understanding of how machine learning methods make these predictions. In this paper, we make use of the TREPAN algorithm for extracting decision trees from Neural Networks and Random Forests. We present the first comparative evaluation of predictive performance and tree properties for extracted trees, which is also the first comparative evaluation of knowledge extraction for safer gambling. Results indicate that TREPAN extracts better performing trees than direct learning of decision trees from the data. Overall, trees extracted with TREPAN from different models offer a good compromise between prediction accuracy and interpretability. TREPAN can produce decision trees with extended tests rules of different forms, so that interpretability depends on multiple factors. We present detailed results and a discussion of the trade-offs with regard to performance and interpretability and use in the gambling industry

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

"Vegeu el resum a l'inici del document del fitxer adjunt.

The Need for Knowledge Extraction: Understanding Harmful Gambling Behavior with Neural Networks

Responsible gambling is a field of study that involves supporting gamblers so as to reduce the harm that their gambling activity might cause. Recently in the literature, machine learning algorithms have been introduced as a way to predict potentially harmful gambling based on patterns of gambling behavior, such as trends in amounts wagered and the time spent gambling. In this paper, neural network models are analyzed to help predict the outcome of a partial proxy for harmful gambling behavior: when a gambler “self-excludes”, requesting a gambling operator to prevent them from accessing gambling opportunities. Drawing on survey and interview insights from industry and public officials as to the importance of interpretability, a variant of the knowledge extraction algorithm TREPAN is proposed which can produce compact, human-readable logic rules efficiently, given a neural network trained on gambling data. To the best of our knowledge, this paper reports the first industrial-strength application of knowledge extraction from neural networks, which otherwise are black-boxes unable to provide the explanatory insights which are crucially required in this area of application. We show that through knowledge extraction one can explore and validate the kinds of behavioral and demographic profiles that best predict self-exclusion, while developing a machine learning approach with greater potential for adoption by industry and treatment providers. Experimental results reported in this paper indicate that the rules extracted can achieve high fidelity to the trained neural network while maintaining competitive accuracy and providing useful insight to domain experts in responsible gambling

Measurement of WZ and ZZ production in pp collisions at [Formula: see text] in final states with b-tagged jets.

Measurements are reported of the WZ and ZZ production cross sections in proton-proton collisions at [Formula: see text][Formula: see text] in final states where one Z boson decays to b-tagged jets. The other gauge boson, either W or Z, is detected through its leptonic decay (either [Formula: see text], [Formula: see text] or [Formula: see text], [Formula: see text], or [Formula: see text]). The results are based on data corresponding to an integrated luminosity of 18.9 fb[Formula: see text] collected with the CMS detector at the Large Hadron Collider. The measured cross sections, [Formula: see text] and [Formula: see text], are consistent with next-to-leading order quantum chromodynamics calculations

Measurement of differential cross sections for the production of a pair of isolated photons in pp collisions at [Formula: see text].

A measurement of differential cross sections for the production of a pair of isolated photons in proton-proton collisions at [Formula: see text] is presented. The data sample corresponds to an integrated luminosity of 5.0[Formula: see text] collected with the CMS detector. A data-driven isolation template method is used to extract the prompt diphoton yield. The measured cross section for two isolated photons, with transverse energy above 40 and 25[Formula: see text] respectively, in the pseudorapidity range [Formula: see text], [Formula: see text] and with an angular separation [Formula: see text], is [Formula: see text][Formula: see text]. Differential cross sections are measured as a function of the diphoton invariant mass, the diphoton transverse momentum, the azimuthal angle difference between the two photons, and the cosine of the polar angle in the Collins-Soper reference frame of the diphoton system. The results are compared to theoretical predictions at leading, next-to-leading, and next-to-next-to-leading order in quantum chromodynamics

Measurement of masses in the [Formula: see text] system by kinematic endpoints in pp collisions at [Formula: see text].

A simultaneous measurement of the top-quark, W-boson, and neutrino masses is reported for [Formula: see text] events selected in the dilepton final state from a data sample corresponding to an integrated luminosity of 5.0 fb-1 collected by the CMS experiment in pp collisions at [Formula: see text]. The analysis is based on endpoint determinations in kinematic distributions. When the neutrino and W-boson masses are constrained to their world-average values, a top-quark mass value of [Formula: see text] is obtained. When such constraints are not used, the three particle masses are obtained in a simultaneous fit. In this unconstrained mode the study serves as a test of mass determination methods that may be used in beyond standard model physics scenarios where several masses in a decay chain may be unknown and undetected particles lead to underconstrained kinematics

Measurement of jet multiplicity distributions in [Formula: see text] production in pp collisions at [Formula: see text].

The normalised differential top quark-antiquark production cross section is measured as a function of the jet multiplicity in proton-proton collisions at a centre-of-mass energy of 7[Formula: see text] at the LHC with the CMS detector. The measurement is performed in both the dilepton and lepton+jets decay channels using data corresponding to an integrated luminosity of 5.0[Formula: see text]. Using a procedure to associate jets to decay products of the top quarks, the differential cross section of the [Formula: see text] production is determined as a function of the additional jet multiplicity in the lepton+jets channel. Furthermore, the fraction of events with no additional jets is measured in the dilepton channel, as a function of the threshold on the jet transverse momentum. The measurements are compared with predictions from perturbative quantum chromodynamics and no significant deviations are observed

Distributions of topological observables in inclusive three- and four-jet events in pp collisions at [Formula: see text][Formula: see text].

This paper presents distributions of topological observables in inclusive three- and four-jet events produced in pp collisions at a centre-of-mass energy of 7[Formula: see text] with a data sample collected by the CMS experiment corresponding to a luminosity of 5.1[Formula: see text]. The distributions are corrected for detector effects, and compared with several event generators based on two- and multi-parton matrix elements at leading order. Among the considered calculations, MadGraph interfaced with pythia6 displays the overall best agreement with data