Montana ASA Chapter Meeting 2019

In regression problems, regularization via the L-1 norm (called the Lasso) is a common tool for feature selection.  By shrinking less important features all the way to zero, the Lasso is able to achieve sparsity in the set of available predictors.  However, L-1 penalization need not be constrained to supervised regression problems; rather, it can be utilized in many unsupervised methods, including clustering and dimension-reduction.  This talk overviews a method for implementing sparse clustering in k-means and hierarchical clustering settings by imposing an L-1 penalty on the dissimilarity matrix (for hierarchical clustering) or on the variables used (for k-means). Further, I will describe how we might impose sparsity on two other unsupervised statistical tools and some challenges in doing this for each method: t-distributed Stochastic Neighbor Embedding (a tool for dimension reduction) and monothetic clustering (a divisive clustering algorithm).

Topological Data Analysis (TDA) is a growing field with the ability to analyze a variety of data that is of nonstandard type. In this talk, I will describe the use of TDA in the context of image classification and some interesting statistical questions that arise. Specifically, a certain topological descriptor can be represented as a point process (called a persistence diagram), whose intensity measure can be used as a datum in a functional regression model. This talk is focused on the estimation of these intensity measures for a given
sampling plan and the inferences we can draw from them.

Spatial point process models are a natural way to model and map things that occur discretely in two-dimensional space, such as munitions debris observed through metal detector surveys or animals observed through distance sampling. However, for decades fitting these models has been computationally infeasible in all but the simplest examples. I provide an overview of recent computational developments that open the door to routine implementation of spatial point process models.

I will be discussing new tools available to obtain useful information about anything from Amazon deforestation rates to population trends in Zimbabwe. Let's create a world in which data is not a limiting factor to making decisions, and the only thing standing in our way is the ability to ask the right questions.

Particle swarm optimization (PSO) is a meta-heuristic optimization algorithm well suited for optimizing high dimensional non-convex functions.  Strengths of PSO include: minimal assumptions regarding the behavior of the objective function, robustness to getting entrapped in local optima, and simplicity as the core logic of the algorithm relies on two simple update equations. These strengths make PSO an attractive candidate for applications in statistics that involve high dimensional searches on multimodal objectives. In this presentation we will present the basic PSO algorithm, illustrate its application to the 2-D Rastrigin function, and show proof of concept for PSO in solving non-linear model parameter estimation, parameter estimation for mixture distributions, and optimal design of experiments.