Events
Department of Mathematics and Statistics
Texas Tech University
When i.i.d. random variables are strongly correlated then the Gaussian or normal distribution does not appear in any limiting sense as the number of variables grows. Such a situation arises with the singular values of Wishart or double-Wishart matrices. The single and double Wishart matrices under the null hypothesis are also known as the Laguerre and Jacobi Orthogonal Ensembles within random matrix theory. This is an area where a number of very different disciplines have overlapped ranging from mathematical physics, combinatorics, number theory, analysis and not least of all, statistics.
A review of recent works investigating the current state of affairs beyond the the largest eigenvalue of a random real symmetric matrix, first identified in 1994. These new distributions are believed to be universal in a similar way to the normal distribution, in that they are the limiting form (as the matrix rank grows) of broad categories of population distributions.
However, since 1994, additional ones have been revealed such as in studies of the largest eigenvalue $ \lambda_1 $ of certain non-null sample covariance matrices, in particular the complex ones. Here one has large values of the sample size $ n $ and the number of variables $ p $. It has been shown that the resulting distribution of $ \lambda_1 $ as $ n, p \to \infty $ can swing from one behaviour to another depending on their ratio. Even for finite $ n, p $ this can mean that the eigenvector of the sample PCA (e.g. associated with eigenvalue $ \lambda_1 $) may exhibit a sharp loss of tracking suddenly losing its relation to the eigenvector of the population PCA. In statistical mechanics language the system exhibits a "phase transition" - the BBP transition after Baik, Ben Arous and P\'ech\'e (2005).
Null case, such as the above, will be given. A great deal of detailed information is known about these universal distributions exploiting the fact they are intimately connected with integrable systems, such as the class of Painlev\'e transcendants.
Please attend this week's hybrid Statistics seminar at 4 PM (UT-5) Monday the 12th in person in MA 111 or virtually via this Zoom link.
Meeting ID: 948 7629 6935
Passcode: 602422
(presentation for SMB 2022) Collective human behavior has a strong impact on global ecosystems, but humans’ overall behavior is driven by individual decision-making. These decisions are often shaped by complex interactions between people with differing ideas. They may also be informed by historical human behaviors and, either directly or indirectly, the current ecosystem-level effects of those behaviors. In order to understand changing impacts on ecosystem, it is necessary to incorporate this potential feedback loop between social decisions and ecosystem outcomes. To demonstrate this, we consider a preliminary problem describing human food choices. We model a toy system in which humans are sustained by an aquatic ecosystem and can allocate harvesting efforts on different species. The choice of an aquatic ecosystem is to facilitate the use of simple, generalizable models in which feeding strengths are constrained by allometric (size-based) relationships. To determine allocation of harvesting efforts, we model harvesting preference as diffusion along a social network. The speed of diffusion is determined by the current abundance of potential food sources. Over discrete intervals, prevailing sentiment on the social network informs harvesting rates; this simulates a delay between growing consensus and behavior change. We demonstrate that, even for this very simple scenario, incorporating feedback between humans and ecosystems allows us to describe a range of ecosystem outcomes. At the end of the presentation, we build towards future work with more complex models informed by social networks from the archaeological past.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
 | Wednesday
Sep. 14
|
| Algebra and Number Theory
No Seminar
|
Environmental, Social, and Governance (ESG) are non-financial factors that are garnering attention
from investors as they increasingly look to apply these as part of their analysis to identify material
risks and growth opportunities.
Some of this attention is also driven by clients who, now more aware than ever, are demanding for their
money to be managed and invested responsibly.
As the interest in ESG grows, so does the need for investors to have access to consumable ESG information.
Since most of it is in text form in reports, disclosures, press releases, and 10-Q filings,
we see a need for sophisticated natural language processing (NLP) techniques for classification tasks for ESG text.
We hypothesize that an ESG domain specific pre-trained model will help with such and study building of the same in this paper.
We explored doing this by fine-tuning BERT’s pre-trained weights using ESG specific text and then further
fine-tuning the model for a classification task.
We were able to achieve accuracy better than the original BERT and baseline models in environment-specific classification tasks.