A method for detecting outliers in linear-circular non-parametric regression

This study proposes a robust outlier detection method based on the circular median for non-parametric linear-circular regression in case the response variable includes outlier(s) and the residuals are Wrapped-Cauchy distributed. Nadaraya-Watson and local linear regression methods were employed to obtain non-parametric regression fits. The proposed method's performance was investigated by using a real dataset and a comprehensive simulation study with different sample sizes, contamination, and heterogeneity degrees. The method performs quite well in medium and higher contamination degrees, and its performance increases as the sample size and the homogeneity of data increase. In addition, when the response variable of linear-circular regression contains outliers, the Local Linear Estimation method fits the data set better than the Nadaraya Watson method.

Variable selection in linear-circular regression models

Applications of circular regression models are ubiquitous in many disciplines, particularly in meteorology, biology and geology. In circular regression models, variable selection problem continues to be a remarkable open question. In this paper, we address variable selection in linear-circular regression models where uni-variate linear dependent and a mixed set of circular and linear independent variables constitute the data set. We consider Bayesian lasso which is a popular choice for variable selection in classical linear regression models. We show that Bayesian lasso in linear-circular regression models is not able to produce robust inference as the coefficient estimates are sensitive to the choice of hyper-prior setting for the tuning parameter. To eradicate the problem, we propose a robustified Bayesian lasso that is based on an empirical Bayes (EB) type methodology to construct a hyper-prior for the tuning parameter while using Gibbs Sampling. This hyper-prior construction is computationally more feasible than the hyper-priors that are based on correlation measures. We show in a comprehensive simulation study that Bayesian lasso with EB-GS hyper-prior leads to a more robust inference. Overall, the method offers an efficient Bayesian lasso for variable selection in linear-circular regression while reducing model complexity.

Dynamic and reversible remapping of network representations in an unchanging environment

Neurons in the medial entorhinal cortex alter their firing properties in response to environmental changes. This flexibility in neural coding is hypothesized to support navigation and memory by dividing sensory experience into unique episodes. However, it is unknown how the entorhinal circuit as a whole transitions between different representations when sensory information is not delineated into discrete contexts. Here we describe rapid and reversible transitions between multiple spatial maps of an unchanging task and environment. These remapping events were synchronized across hundreds of neurons, differentially affected navigational cell types, and correlated with changes in running speed. Despite widespread changes in spatial coding, remapping comprised a translation along a single dimension in population-level activity space, enabling simple decoding strategies. These findings provoke reconsideration of how the medial entorhinal cortex dynamically represents space and suggest a remarkable capacity of cortical circuits to rapidly and substantially reorganize their neural representations.