The UW Center for Evaluation and Research for STEM Equity (CERSE) conducted a climate survey and focus groups in the Statistics Department over the past calendar year that involved students, faculty, and staff. In this seminar, several of CERSE's Research Scientists will share the results of the climate study. The results fall under the following themes: Inclusion; Community; Communication; Career & Advising Support. CERSE will conclude with some recommendations moving forward to foster an increasingly equitable departmental climate.
I will discuss the problem of statistical estimation with contaminated data. In the first part of the talk, I will discuss depth-based approaches that achieve minimax rates in various problems. In general, the minimax rate of a given problem with contamination consists of two terms: the statistical complexity without contamination, and the contamination effect in the form of modulus of continuity. In the second part of the talk, I will discuss computational challenges of these depth-based estimators.
Classical multidimensional scaling is an important tool for data reduction in many applications. It takes in a distance matrix and outputs low-dimensional embedded samples such that the pairwise distances between the original data points can be preserved, when treating them as deterministic points. However, data are often noisy in practice. In such case, the quality of embedded samples produced by classical multidimensional scaling starts to break down, when either the ambient dimensionality or the noise variance gets larger.
Data exhibiting complicated spatial structures are common in many areas of science (e.g. cosmology, biology), but can be difficult to analyze. Persistent homology is a popular approach within the area of Topological Data Analysis (TDA) that offers a way to represent, visualize, and interpret complex data by extracting topological features, which can be used to infer properties of the underlying structures. For example, TDA may be useful for analyzing the large-scale structure (LSS) of the Universe, which is an intricate and spatially complex web of matter.
Many traditional statistical prediction methods mainly deal with the problem of overfitting to the given data set. On the other hand, there is a vast literature on the estimation of causal parameters for prediction under interventions. However, both types of estimators can perform poorly when used for prediction on heterogeneous data. We show that the change in loss under certain perturbations (interventions) can be written as a convex penalty. This motivates anchor regression, a “causal” regularization scheme that encourages the estimator to generalize well to perturbed data.
Scientific research is often concerned with questions of cause and effect. For example, does eating processed meat cause certain types of cancer? Ideally, such questions are answered by randomized controlled experiments. However, these experiments can be costly, time-consuming, unethical or impossible to conduct. Hence, often the only available data to answer causal questions is observational.
We discuss several problems related to the challenge of making accurate inferences about a complex phenomenon, given relatively little data. We show that for several fundamental and practically relevant settings, including estimating the intrinsic dimensionality of a high-dimensional distribution, and learning a population of distributions given few data points from each distribution, it is possible to ``denoise'' the empirical distribution significantly.
Fundamental to the study of the inheritance is the partitioning of the total phenotypic variation into genetic and environmental components. Using twin studies, the phenotypic variance-covariance matrix can be parameterized to include an additive genetic effect, shared and non-shared environmental effects. The ratio of the genetic variance component to the total phenotypic variance is the proportion of genetically controlled variation and is termed as the ‘narrow-sense heritability’.
Functional data analysis has been increasingly used in biomedical studies, where the basic unit of measurement is a function, curve, or image. For example, in mobile health (mHealth) studies, wearable sensors collect high-resolution trajectories of physiological and behavioral signals over time. Functional linear regression models are useful tools for quantifying the association between functional covariates and scalar/functional responses, where a popular approach is via functional principal component analysis.