A central question for active learning (AL) is: what is the optimal selection? Defining optimality by classifier loss produces a new characterisation of optimal AL behaviour, by treating expected loss reduction as a statistical target for estimation.
This target forms the basis of model retraining improvement (MRI), a novel approach providing a statistical estimation framework for AL. This framework is constructed to address the central question of AL optimality, and to motivate the design of estimation algorithms. MRI allows the exploration of optimal AL behaviour, and the examination of AL heuristics, showing precisely how they make sub-optimal selections. The abstract formulation of MRI is used to provide a new guarantee for AL, that an unbiased MRI estimator should outperform random selection. This MRI framework reveals intricate estimation issues that in turn motivate the construction of new statistical AL algorithms. One new algorithm in particular performs strongly in a large-scale experimental study, compared to standard AL methods. This competitive performance suggests that practical efforts to minimise estimation bias may be important for AL applications.
In many classification problems unlabelled data is abundant and a subset can be chosen for labelling. This defines the context of active learning (AL), where methods systematically select that subset, to improve a classifier by retraining. Given a cl
assification problem, and a classifier trained on a small number of labelled examples, consider the selection of a single further example. This example will be labelled by the oracle and then used to retrain the classifier. This example selection raises a central question: given a fully specified stochastic description of the classification problem, which example is the optimal selection? If optimality is defined in terms of loss, this definition directly produces expected loss reduction (ELR), a central quantity whose maximum yields the optimal example selection. This work presents a new theoretical approach to AL, example quality, which defines optimal AL behaviour in terms of ELR. Once optimal AL behaviour is defined mathematically, reasoning about this abstraction provides insights into AL. In a theoretical context the optimal selection is compared to existing AL methods, showing that heuristics can make sub-optimal selections. Algorithms are constructed to estimate example quality directly. A large-scale experimental study shows these algorithms to be competitive with standard AL methods.
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial selection for
function has recently become a powerful tool for understanding how evolution can innovate within its genetic rule space. However, conventional cellular automata lack the kind of state feedback that is surely present in natural evolving systems. Each new generation of a population leaves an indelible mark on its environment and thus affects the selective pressures that shape future generations of that population. To model this phenomenon, we have augmented traditional cellular automata with state-dependent feedback. Rather than generating automata executions from an initial condition and a static rule, we introduce mappings which generate iteration rules from the cellular automaton itself. We show that these new automata contain disconnected regions which locally act like conventional automata, thus encapsulating multiple functions into one structure. Consequently, we have provided a new model for processes like cell differentiation. Finally, by studying the size of these regions, we provide additional evidence that the dynamics of self-reference may be critical to understanding the evolution of natural language. In particular, the rules of elementary cellular automata appear to be distributed in the same way as words in the corpus of a natural language.
The observed Galactic rate of stellar mergers or the initiation of common envelope phases brighter than M_V=-3 (M_I=-4) is of order 0.5 (0.3)/year with 90% confidence statistical uncertainties of 0.24-1.1 (0.14-0.65) and factor of 2 systematic uncert
ainties. The (peak) luminosity function is roughly dN/dL L^(-1.4+/-0.3), so the rates for events more luminous than V1309 Sco (M_V=-7 mag) or V838Mon (M_V=-10 mag) are lower at r~0.1/year and 0.03/year, respectively. The peak luminosity is a steep function of progenitor mass, L M^(2-3). This very roughly parallels the scaling of luminosity with mass on the main sequence, but the transients are ~2000-4000 times more luminous at peak. Combining these, the mass function of the progenitors, dN/dM M^(-2.0+/-0.8), is consistent with the initial mass function, albeit with broad uncertainties. These observational results are also broadly consistent with the estimates of binary population synthesis models. While extragalactic variability surveys can better define the rates and properties of the high luminosity events, systematic, moderate depth (I>16 mag) surveys of the Galactic plane are needed to characterize the low luminosity events. The existing Galactic samples are only ~20% complete and Galactic surveys are (at best) reaching a typical magnitude limit of <13 mag.
We model the distance, extinction, and magnitude probability distributions of a successful Galactic core-collapse supernova (ccSN), its shock breakout radiation, and its massive star progenitor. We find, at very high probability (~100%), that the nex
t Galactic SN will easily be detectable in the near-IR and that near-IR photometry of the progenitor star very likely (~92%) already exists in the 2MASS survey. Most ccSNe (~98%) will be easily observed in the optical, but a significant fraction (~43%) will lack observations of the progenitor due to a combination of survey sensitivity and confusion. If neutrino detection experiments can quickly disseminate a likely position (~3 deg), we show that a modestly priced IR camera system can probably detect the shock breakout radiation pulse even in daytime (~64% for the cheapest design). Neutrino experiments should seriously consider adding such systems, both for their scientific return and as an added and internal layer of protection against false triggers. We find that shock breakouts from failed ccSNe of red supergiants may be more observable than those of successful SNe. We review the process by which neutrinos from a Galactic ccSN would be detected and announced. We provide new information on the EGADS system and its potential for providing instant neutrino alerts. We also discuss the distance, extinction, and magnitude probability distributions for the next Galactic Type Ia SN. Based on our modeled observability, we find a Galactic ccSN rate of 3.2 (+7.3/-2.6) per century and a Galactic Type Ia SN rate of 1.4 (+1.4/-0.8) per century for a total Galactic SN rate of 4.6 (+7.4/-2.7) per century is needed to account for the SNe observed over the last millennium.
In a sample of 54 galaxy clusters (0.04<z<0.15) containing 3551 early-type galaxies suitable for study, we identify those with tidal features both interactively and automatically. We find that ~3% have tidal features that can be detected with data th
at reaches a 3-sigma sensitivity limit of 26.5 mag arcsec^-2. Regardless of the method used to classify tidal features, or the fidelity imposed on such classifications, we find a deficit of tidally disturbed galaxies with decreasing clustercentric radius that is most pronounced inside of ~0.5R_200. We cannot distinguish whether the trend arises from an increasing likelihood of recent mergers with increasing clustercentric radius or a decrease in the lifetime of tidal features with decreasing clustercentric radius. We find no evidence for a relationship between local density and the incidence of tidal features, but our local density measure has large uncertainties. We find interesting behavior in the rate of tidal features among cluster early-types as a function of clustercentric radius and expect such results to provide constraints on the effect of the cluster environment on the structure of galaxy halos, the build-up of the red sequence of galaxies, and the origin of the intracluster stellar population.
