122,960 research outputs found
R package 'ROSE': Random Over-Sampling Examples
No full textThe package provides functions to deal with binary classification problems in the presence of imbalanced classes. Synthetic balanced samples are generated according to ROSE (Menardi and Torelli, 2013). Functions that implement more traditional remedies to the class imbalance are also provided, as well as different metrics to evaluate a learner accuracy. These are estimated by holdout, bootstrap or cross-validation methods
The cobordism group of homology cylinders
No full textGaroufalidis and Levine introduced the homology cobordism group of homology cylinders over a surface. This group can be regarded as an enlargement of the mapping class group. Using torsion invariants, we show that the abelianization of this group is infinitely generated provided that the first Betti number of the surface is positive. In particular, this shows that the group is not perfect. This answers questions of Garoufalidis and Levine, and Goda and Sakasai. Furthermore, we show that the abelianization of the group has infinite rank for the case that the surface has more than one boundary component. These results also hold for the homology cylinder analogue of the Torelli group
An obstruction to the strong relative hyperbolicity of a group
No full textWe give a simple combinatorial criterion for a group that,
when satisfied, implies the group cannot be strongly relatively
hyperbolic. Our criterion applies to several classes of groups, such
as surface mapping class groups, Torelli groups, and automorphism
and outer automorphism groups of free groups
Torelli, Pietro
No full textBiografia di Pietro Torelli, professore di Storia del diritto italiano nella Facoltà giuridica bolognese nella prima metà del XX secolo
ROSE: A Package for Binary Imbalanced Learning
No full textThe ROSE package provides functions to deal with binary classification problems in the presence of imbalanced classes. Artificial balanced samples are generated according to a smoothed
bootstrap approach and allow for aiding both the phases of estimation and accuracy evaluation of a binary classifier in the presence of a rare class. Functions that implement more traditional remedies for
the class imbalance and different metrics to evaluate accuracy are also provided. These are estimated by holdout, bootstrap or cross-validation methods
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The cohomology of Torelli groups is algebraic
No full textThe Torelli group of is the subgroup of the diffeomorphisms of fixing a disc which act trivially on . The rational cohomology groups of the Torelli group are representations of an arithmetic subgroup of or . In this paper we prove that for and , they are in fact algebraic representations. Combined with previous work, this determines the rational cohomology of the Torelli group in a stable range. We further prove that the classifying space of the Torelli group is nilpotent
Homological infiniteness of Torelli groups
No full textAbstractThe rational homology of the Torelli group of genus g relative to n distinguished points and r fixed embedded disks is proved to be infinite dimensional if g is sufficiently large relative to n+r. In particular, the rational homology of the (classical) Torelli group of genus g is infinite dimensional when g⩾7. In addition, the rational homology of the subgroup of the Torelli group of genus g generated by all the Dehn twists along separating simple closed curves is proved to be infinite dimensional when g⩾2
Comparing Goal-Based and Result-Based Approaches in Modelling Football Outcomes
No full textTwo main approaches are considered when building statistical models for football outcomes: (1) the goal-based approach, where the number of goals scored by two competing teams is modelled, and (2) the result-based approach, where a three-category outcome (win–draw–loss) is modelled. The debate about which approach is preferable is still ongoing, although the general agreement is that any direct comparison between the forecasting abilities of the two approaches should be based on the quality of the forecasts. Alternatively, a greater emphasis can be given to diagnostic measures in order to judge the quality of model specifications, as is more customary in statistical modelling. In this paper, we develop a broad comparison of four possible Bayesian models, focusing on model checking and calibration and then using Markov chain Monte Carlo replications to explore the predictive performance over future matches. Although inconclusive, we believe our set of comparison tools may be beneficial for future scholars in differentiating the two approaches
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