A Full Probabilistic Model for Yes/No Type Crowdsourcing in Multi-Class Classification

Crowdsourcing has become widely used in supervised scenarios where training sets are scarce and difficult to obtain. Most crowdsourcing models in the literature assume labelers can provide answers to full questions. In classification contexts, full questions require a labeler to discern among all possible classes. Unfortunately, discernment is not always easy in realistic scenarios. Labelers may not be experts in differentiating all classes. In this work, we provide a full probabilistic model for a shorter type of queries. Our shorter queries only require "yes" or "no" responses. Our model estimates a joint posterior distribution of matrices related to labelers' confusions and the posterior probability of the class of every object. We developed an approximate inference approach, using Monte Carlo Sampling and Black Box Variational Inference, which provides the derivation of the necessary gradients. We built two realistic crowdsourcing scenarios to test our model. The first scenario queries for irregular astronomical time-series. The second scenario relies on the image classification of animals. We achieved results that are comparable with those of full query crowdsourcing. Furthermore, we show that modeling labelers' failures plays an important role in estimating true classes. Finally, we provide the community with two real datasets obtained from our crowdsourcing experiments. All our code is publicly available.Comment: SIAM International Conference on Data Mining (SDM19), 9 official pages, 5 supplementary page

The expansion rate of the intermediate Universe in light of Planck

We use cosmology-independent measurements of the expansion history in the redshift range 0.1 < z <1.2 and compare them with the Cosmic Microwave Background-derived expansion history predictions. The motivation is to investigate if the tension between the local (cosmology independent) Hubble constant H0 value and the Planck-derived H0 is also present at other redshifts. We conclude that there is no tension between Planck and cosmology independent-measurements of the Hubble parameter H(z) at 0.1 < z < 1.2 for the LCDM model (odds of tension are only 1:15, statistically not significant). Considering extensions of the LCDM model does not improve these odds (actually makes them worse), thus favouring the simpler model over its extensions. On the other hand the H(z) data are also not in tension with the local H0 measurements but the combination of all three data-sets shows a highly significant tension (odds ~ 1:400). Thus the new data deepen the mystery of the mismatch between Planck and local H0 measurements, and cannot univocally determine wether it is an effect localised at a particular redshift. Having said this, we find that assuming the NGC4258 maser distance as the correct anchor for H0, brings the odds to comfortable values. Further, using only the expansion history measurements we constrain, within the LCDM model, H0 = 68.5 +- 3.5 and Omega_m = 0.32 +- 0.05 without relying on any CMB prior. We also address the question of how smooth the expansion history of the universe is given the cosmology independent data and conclude that there is no evidence for deviations from smoothness on the expansion history, neither variations with time in the value of the equation of state of dark energy.Comment: Submitted to Physics of the Dark Univers

Planck and the local Universe: quantifying the tension

We use the latest Planck constraints, and in particular constraints on the derived parameters (Hubble constant and age of the Universe) for the local universe and compare them with local measurements of the same quantities. We propose a way to quantify whether cosmological parameters constraints from two different experiments are in tension or not. Our statistic, T, is an evidence ratio and therefore can be interpreted with the widely used Jeffrey's scale. We find that in the framework of the LCDM model, the Planck inferred two dimensional, joint, posterior distribution for the Hubble constant and age of the Universe is in "strong" tension with the local measurements; the odds being ~ 1:50. We explore several possibilities for explaining this tension and examine the consequences both in terms of unknown errors and deviations from the LCDM model. In some one-parameter LCDM model extensions, tension is reduced whereas in other extensions, tension is instead increased. In particular, small total neutrino masses are favored and a total neutrino mass above 0.15 eV makes the tension "highly significant" (odds ~ 1:150). A consequence of accepting this interpretation of the tension is that the degenerate neutrino hierarchy is highly disfavoured by cosmological data and the direct hierarchy is slightly favored over the inverse.Comment: Submitted to Physics of the Dark Univers