arXiv subjects
Publications and source records attributed to Valeriya Kirova.
We introduce a novel Mutual Information (MI) estimator that fundamentally reframes the discriminative approach. Instead of training a classifier to discriminate between joint and marginal distributions, we learn a normalizing flow that transforms one into the other. This technique produces a computationally efficient and precise MI estimate that scales well to high dimensions and across a wide range of ground-truth MI values.
We analyze functional magnetic resonance imaging (fMRI) data from the Human Connectome Project (HCP) to match brain activities during a range of cognitive tasks. Our findings demonstrate that even basic linear machine learning models can effectively classify brain states and achieve state-of-the-art accuracy, particularly for tasks related to motor functions and language processing. Feature importance ranking allows to identify distinct sets of brain regions whose activation patterns are uniquely associated with specific cognitive functions. These discriminative features provide strong support for the hypothesis of functional specialization across cortical and subcortical areas of the human brain. Additionally, we investigate the temporal dynamics of the identified brain regions, demonstrating that the time-dependent structure of fMRI signals are essential for shaping functional connectivity between regions: uncorrelated areas are least important for classification. This temporal perspective provides deeper insights into the formation and modulation of brain neural networks involved in cognitive processing.
Given a natural $n$, we construct a two-coloring of $\mathbb{R}^n$ with the maximum metric satisfying the following. For any finite set of reals $S$ with diameter greater than $5^{n}$ such that the distance between any two consecutive points of $S$ does not exceed one, no isometric copy of $S$ is monochromatic. As a corollary, we prove that any normed space can be two-colored such that all sufficiently long unit arithmetic progressions contain points of both colors.