Seminars and Colloquia by Series

Spectrum Reconstruction Technique and Improved Naive Bayes Models for Text Classification Problems

Series
Dissertation Defense
Time
Thursday, April 16, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Bluejeans Meeting 866242745
Speaker
Zhibo DaiGeorgia Tech

My thesis studies two topics. In the first part, we study the spectrum reconstruction technique. As is known to all, eigenvalues play an important role in many research fields and are foundation to many practical techniques such like PCA (Principal Component Analysis). We believe that related algorithms should perform better with more accurate spectrum estimation. There was an approximation formula proposed by Prof. Matzinger. However, they didn't give any proof. In our research, we show why the formula works. And when both number of features and dimension of space go to infinity, we find the order of error for the approximation formula, which is related to a constant C-the ratio of dimension of space and number of features.

In the second part, we focus on some applications of Naive Bayes models in text classification problems. Especially we focus on two special situations: 1) there is insufficient data for model training; 2) partial labeling problem. We choose Naive Bayes as our base model and do some improvement on the model to achieve better performance in those two situations. To improve model performance and to utilize as many information as possible, we introduce a correlation factor, which somehow relaxes the conditional independence assumption of Naive Bayes. The new estimates are biased estimation compared to the traditional Naive Bayes estimate, but have much smaller variance, which give us a better prediction result.

Bordered Floer Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, April 15, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sally CollinsGeorgia Tech

Bordered Floer homology, due to Lipshitz, Ozsváth, and Thurston, is a Heegaard Floer homology theory for 3-manifolds with connected boundary. This theory associates to the boundary surface (with suitable parameterization) a differential graded algebra A(Z). Our invariant comes in two versions: a left differential (type D) module over A(Z), or its dual, a right A-infinity (type A) module over A(Z). In this talk, we will focus on the case of 3-manifolds with torus boundary, and will explicitly describe how to compute type D structures of knot complements.

Tropical convex hulls of infinite sets

Series
Algebra Seminar
Time
Monday, April 13, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Cvetelina HillGeorgia Tech

In this talk we will explore the interplay between tropical convexity and its classical counterpart. In particular, we will focus on the tropical convex hull of convex sets and polyhedral complexes. We give a vertex description of the tropical convex hull of a line segment and of a ray in Rn/R1 and show that tropical convex hull and classical convex hull commute in R3/R1. Finally, we prove results on the dimension of tropical convex fans and give an upper bound on the dimension of the tropical convex hull of tropical curves under certain hypothesis. 

The talk will be held online via Bluejeans, use the following link to join the meeting.

Pages