Bayesian-Boosted MetaLoc: Efficient Training and Guaranteed Generalization for Indoor Localization

Existing localization approaches utilizing environment-specific channel state information (CSI) excel under specific environment but struggle to generalize across varied environments. This challenge becomes even more pronounced when confronted with limited training data. To address these issues, we present the Bayes-Optimal Meta-Learning for Localization (BOML-Loc) framework, inspired by the PAC-Optimal Hyper-Posterior (PACOH) algorithm. Improving on our earlier MetaLoc~\cite{MetaLoc}, BOML-Loc employs a Bayesian approach, reducing the need for extensive training, lowering overfitting risk, and offering per-test-point uncertainty estimation. Even with very limited training tasks, BOML-Loc guarantees robust localization and impressive generalization. In both LOS and NLOS environments with site-surveyed data, BOML-Loc surpasses existing models, demonstrating enhanced localization accuracy, generalization abilities, and reduced overfitting in new and previously unseen environments

The Age-Redshift Relationship of Old Passive Galaxies

We use 32 age measurements of passively evolving galaxies as a function of redshift to test and compare the standard model ($\Lambda$CDM) with the $R_{\rm h}=ct$ Universe. We show that the latter fits the data with a reduced $\chi^2_{\rm dof}=0.435$ for a Hubble constant $H_{0}= 67.2_{-4.0}^{+4.5}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$. By comparison, the optimal flat $\Lambda$CDM model, with two free parameters (including $\Omega_{\rm m}=0.12_{-0.11}^{+0.54}$ and $H_{0}=94.3_{-35.8}^{+32.7}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$), fits the age-\emph{z} data with a reduced $\chi^2_{\rm dof}=0.428$. Based solely on their $\chi^2_{\rm dof}$ values, both models appear to account for the data very well, though the optimized $\Lambda$CDM parameters are only marginally consistent with those of the concordance model ($\Omega_{\rm m}=0.27$ and $H_{0}= 70$ km $\rm s^{-1}$ $\rm Mpc^{-1}$). Fitting the age-$z$ data with the latter results in a reduced $\chi^2_{\rm dof}=0.523$. However, because of the different number of free parameters in these models, selection tools, such as the Akaike, Kullback and Bayes Information Criteria, favour $R_{\rm h}=ct$ over $\Lambda$CDM with a likelihood of $\sim 66.5\%-80.5\%$ versus $\sim 19.5\%-33.5\%$. These results are suggestive, though not yet compelling, given the current limited galaxy age-$z$ sample. We carry out Monte Carlo simulations based on these current age measurements to estimate how large the sample would have to be in order to rule out either model at a $\sim 99.7\%$ confidence level. We find that if the real cosmology is $\Lambda$CDM, a sample of $\sim 45$ galaxy ages would be sufficient to rule out $R_{\rm h}=ct$ at this level of accuracy, while $\sim 350$ galaxy ages would be required to rule out $\Lambda$CDM if the real Universe were instead $R_{\rm h}=ct$.Comment: 36 pages, 13 figures, 1 table; accepted for publication in The Astronomical Journal. arXiv admin note: text overlap with arXiv:1405.238