PAC Classification based on PAC Estimates of Label Class Distributions

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect, the better our estimates of the label class distributions, the better the resulting classifier will be. In this paper we make this observation precise by identifying risk bounds of a classifier in terms of the quality of the estimates of the label class distributions. We show how PAC learnability relates to estimates of the distributions that have a PAC guarantee on their $L_1$ distance from the true distribution, and we bound the increase in negative log likelihood risk in terms of PAC bounds on the KL-divergence. We give an inefficient but general-purpose smoothing method for converting an estimated distribution that is good under the $L_1$ metric into a distribution that is good under the KL-divergence.Comment: 14 page

A Lorentz-Violating Alternative to Higgs Mechanism?

We consider a four-dimensional field-theory model with two massless fermions, coupled to an Abelian vector field without flavour mixing, and to another Abelian vector field with flavour mixing. Both Abelian vectors have a Lorentz-violating kinetic term, introducing a Lorentz-violation mass scale $M$, from which fermions and the flavour-mixing vector get their dynamical masses, whereas the vector coupled without flavour mixing remains massless. When the two coupling constants have similar values in order of magnitude, a mass hierarchy pattern emerges, in which one fermion is very light compared to the other, whilst the vector mass is larger than the mass of the heavy fermion. The work presented here may be considered as a Lorentz-symmetry-Violating alternative to the Higgs mechanism, in the sense that no scalar particle (fundamental or composite) is necessary for the generation of the vector-meson mass. However, the model is not realistic given that, as a result of Lorentz Violation, the maximal (light-cone) speed seen by the fermions is smaller than that of the massless gauge boson (which equals the speed of light in vacuo) by an amount which is unacceptably large to be compatible with the current tests of Lorentz Invariance, unless the gauge couplings assume unnaturally small values. Possible ways out of this phenomenological drawback are briefly discussed, postponing a detailed construction of more realistic models for future work.Comment: 16 pages revtex, three eps figures incorporate

The Stability of the orbits of Earth-mass planets in and near the habitable zones of known exoplanetary systems

We have shown that Earth-mass planets could survive in variously restricted regions of the habitable zones (HZs) of most of a sample of nine of the 93 main-sequence exoplanetary systems confirmed by May 2003. In a preliminary extrapolation of our results to the other systems, we estimate that roughly a third of the 93 systems might be able to have Earth-mass planets in stable, confined orbits somewhere in their HZs. Clearly, these systems should be high on the target list for exploration for terrestrial planets. We have reached this conclusion by launching putative Earth-mass planets in various orbits and following their fate with a mixed-variable symplectic integrator

Predicting Urban Dispersal Events: A Two-Stage Framework through Deep Survival Analysis on Mobility Data

Urban dispersal events are processes where an unusually large number of people leave the same area in a short period. Early prediction of dispersal events is important in mitigating congestion and safety risks and making better dispatching decisions for taxi and ride-sharing fleets. Existing work mostly focuses on predicting taxi demand in the near future by learning patterns from historical data. However, they fail in case of abnormality because dispersal events with abnormally high demand are non-repetitive and violate common assumptions such as smoothness in demand change over time. Instead, in this paper we argue that dispersal events follow a complex pattern of trips and other related features in the past, which can be used to predict such events. Therefore, we formulate the dispersal event prediction problem as a survival analysis problem. We propose a two-stage framework (DILSA), where a deep learning model combined with survival analysis is developed to predict the probability of a dispersal event and its demand volume. We conduct extensive case studies and experiments on the NYC Yellow taxi dataset from 2014-2016. Results show that DILSA can predict events in the next 5 hours with F1-score of 0.7 and with average time error of 18 minutes. It is orders of magnitude better than the state-ofthe-art deep learning approaches for taxi demand prediction.Comment: To appear in AAAI-19 proceedings. The reason for the replacement was the misspelled author name in the meta-data field. Author name was corrected from "Ynahua Li" to "Yanhua Li". The author list in the paper was correct and remained unchange