Linear regression is one of the simplest and most widely used tools to learn patterns from data: it fits a set of coefficients so that a linear combination of predictors best matches observed responses. The quality of the fit is measured by the residual sum of squares, the total squared mismatch between predictions and data, whose minimum defines the training loss. For Gaussian data, the...
The noisy voter model is a widely used framework for stochastic opinion dynamics in finite populations, where changes in individual opinions are driven by two competing mechanisms: spontaneous opinion changes and social imitation. Although the model is originally formulated in terms of discrete states and transition rates, its continuum approximation can be related to Fokker-Planck-type...
We consider a discrete-time random walk with resets on a connected undirected network. The resets, in which the walker is relocated to randomly chosen nodes, are governed by an independent discrete-time renewal process (we consider both light- and fat-tailed inter-reset distributions). Some nodes of the network are target nodes, and we focus on the statistics of first hitting of these nodes....
