Topic: linear regression

Alex Gittens studies how many data points must be labelled to fit a linear regression model with nearly the predictive power of a fully labelled dataset. Existing coreset and iterative approaches handle constant-factor approximations, but tighter approximations that improve with dataset size need different methods. The talk presents a polynomial-time algorithm that reduces label complexity by an additive O(sqrt(n)), using a sharp analysis of regression error for a coreset formed by backward selection.

Linear regression and Pearson correlations are bedrock statistical analyses in neuroscience: correlations between neurons are a signature of collective information coding and computation, and linear regression quantifies the linear or nonlinear (e.g., polynomial) relationships among, e.g., neurons or brain regions. However, noise can bias the regression and correlation coefficient estimates towards zero, an effect known as regression dilution. While averaging over trials, time, or neurons--a widespread practice to mitigate noise in neuroscience--reduces the effects of noise, it does not genera

In this study, we aim to broaden our understanding of the mouse’s primary visual cortex by modeling data provided by the datasets from Stringer et al. (2019) and the Allen Institute. We investigated the roles of the different excitatory and inhibitory cell types in the visual cortex whose functions remain unclear. Using the Stringer dataset, we explored the correlation between the activity of excitatory cells in the mouse visual cortex and mouse running behavior without any visual input. Principle Component Analysis (PCA) was applied to reduce the dimension of our neuron activity data of 119

Stringer et al. used two-photon calcium imaging to record activity from tens of thousands of V1 cells in head-fixed mice during a visual orientation discrimination task, and showed that the neural response encodes stimulus discrimination thresholds nearly 100 times more precise than the corresponding behavioral thresholds. Animal arousal state was monitored by measuring the locomotion speed during task execution, but could not explain this large discrepancy in discrimination threshold. Here, we take advantage of the fact that the behavioral data was acquired in that experiment, and ask whethe