Seminaria

Lasso and ridge regression are well established and successful models for variance reduction and, for the lasso, variable selection. However, they come with a disadvantage of an increased bias in the estimator. In this seminar, I will talk about our general method that learns individual weights for each term in the regularisation penalty (e.g. lasso or ridge) with the goal to reduce the bias. To bound the amount of freedom for the model to choose the weights, a new regularisation term, that imposes a cost for choosing small weights, is introduced. If the form of this term is chosen wisely, the apparent doubling of the number of parameters vanishes, by means of solving for the weights in terms of the parameter estimates. We show that these estimators potentially keep the original estimators’ fundamental properties and experimentally verify that this can indeed reduce bias.

Quasiconvex subgroups are basic building blocks of hyperbolic groups, and relatively quasiconvex subgroups play a similar role in relatively hyperbolic groups. If $Q$ and $R$ are relatively quasiconvex subgroups of a relatively hyperbolic group $G$ then the intersection $Q \cap R$ will also be relatively quasiconvex, but the join $\langle Q,R \rangle$ may not be. I will discuss criteria for the existence of finite index subgroups $Q’ \leqslant_f Q$ and $R’ \leqslant_f R$ such that the ``virtual join’’ $\langle Q’, R’ \rangle$ is relatively quasiconvex. This is closely related to separability properties of $G$ and I will present applications to limit groups, Kleinian groups and fundamental groups of graphs of free groups with cyclic edge groups. The talk will be based on joint work with Lawk Mineh.

=== 13:15 - 14:00 ===
prof. Anna K. Panorska (University of Nevada, Reno)
From Atmospheric Rivers to Flood Risk: A Multivariate Model for Extreme Precipitation

Water resources and flood risk in the western United States are commonly driven by large scale precipitation events lasting several consecutive days. Some of the largest precipitation events are driven by the Atmospheric Rivers, the “rivers in the sky”. We propose a multivariate model for the extreme precipitation events describing their duration, intensity, and maximum. We also link it to the atmospheric flow patterns, like those producing the Atmospheric Rivers. As the most important questions related to the impact of extreme precipitation are about the risk or probability of these extreme events, our ultimate goal is to employ the statistical model along with the meteorological and statistical methods leading to estimation of these probabilities. This talk is based on joint work with Alexander Weyant (SCRIPPS Institution of Oceanography, UC San Diego).

=== 13:15 - 14:00 ===
prof. Tomasz J. Kozubowski (University of Nevada, Reno)
Flexible Multivariate Skew Distributions via Coordinate-wise and Spectral Gaussian Mixtures

Gaussian mean - variance mixtures form a powerful and widely used framework in probability and statistics, with applications spanning hierarchical modeling, Bayesian computation, stochastic processes, and machine learning. In this talk, we consider two new families of multivariate skew distributions derived from novel extensions of the classical Gaussian mixture construction. The first extension employs coordinate-wise mixing, allowing different dimensions of the random vector to exhibit distinct skewness and tail behavior. The second is based on spectral (eigenvalue-driven) mixing, where the mixture structure is tied to the eigenvalues of the Gaussian covariance matrix, producing rich dependence patterns and highly adaptable distributional shapes. We present key analytical properties of these new distribution families, including moments, dependence structure, and infinite divisibility, and briefly discuss parameter estimation. A financial data example highlights the improved flexibility and fit provided by these models. This talk is based on joint work with Amos Natido.