Mathematics & Statisticshttp://hdl.handle.net/10211.3/1224902020-07-10T05:13:27Z2020-07-10T05:13:27ZGaussian Process Models for Computer VisionFrank, Hakeemhttp://hdl.handle.net/10211.3/2168572020-06-29T21:59:58Z2020-06-29T00:00:00ZGaussian Process Models for Computer Vision
Frank, Hakeem
Supervised learning is the task of finding a function f(x) that maps an input x to an output y using observed data. Gaussian process models approach supervised learning by assuming a probability distribution over a space of possible functions, using observed data to update the space of functions to consider using Bayes the- orem, and taking the expected value over the space of functions to get an estimate for f(x). While Gaussian process models are commonly used in time series and regression domains, they can extend to classification tasks using a response function and variational inference. This thesis investigates Gaussian process models for image classification tasks with an emphasis on kernels that are effective for the high dimensional nature of image data. Specifically, stationary and non-stationary kernels are compared with each other and their performance is analyzed on image recognition tasks. The models are evaluated on high-resolution aerial images, a handwritten digit dataset, and a dataset of X-ray images of patients exhibiting signs of pneumonia.
2020-06-29T00:00:00ZExperiences of Community College Students in a Co-requisite Statistics Course in a Community CollegeHernandez, Vanessahttp://hdl.handle.net/10211.3/2168532020-06-29T20:49:10Z2020-06-29T00:00:00ZExperiences of Community College Students in a Co-requisite Statistics Course in a Community College
Hernandez, Vanessa
Due to recent policy changes in California (AB 705), colleges have been tasked to restructure their courses to support all studentsâ€™ placement into college-level mathematics courses, with support for those students who may have been previously placed in developmental mathematics. This exploratory study describes studentsâ€™ experiences in a co-requisite statistics course at one community college. Specifically, this study investigates the different supports and resources these students were provided and if and how these helped them to be successful. The study is framed through the instructional triangle (Cohen, Raudenbush, & Ball, 2003) and studentsâ€™ instructional experiences (Cawley, 2018). Students were asked to fill out three surveys during Fall 2019 in relation to their experience in their courses. Findings show that supports included the purposeful use of the support course, review worksheets, and group work. Important resources include time as it relates to pacing in the parent course. In addition, the study elaborates on experiences of students repeating the course after having taken it previously without support and describes what these students found valuable to their learning and success. Implications from this study indicate that the co-requisite model is a step in the right direction. Recommendations are made to streamline coordination of coursework in order to create equitable student learning outcomes by ensuring students are provided the best opportunities for support.
2020-06-29T00:00:00ZHuman Impact on a Simple Climate ModelSecor, Samanthahttp://hdl.handle.net/10211.3/2168512020-06-27T01:31:34Z2020-06-26T00:00:00ZHuman Impact on a Simple Climate Model
Secor, Samantha
In this thesis, we use a system of nonlinear differential equations to model the average temperature and the percentage of glacial volume on Earth. We first make sense of the model itself, down to its geophysical properties so that we can interpret the real-world meaning of its mathematical representation. We then evaluate the model algebraically to determine the locations of the equilibrium solutions and to come up with a form for which we can run simulations. To understand numerically, we conduct various differential equation transformations that are easier to comprehend. We can then use the results to categorize all of the equilibrium points and note interesting behavior within the linearized and nonlinearized models. Lastly, we modify the initial conditions to understand how human activity would affect the model. We simulate the results over time to determine how soon drastic events would take place.
2020-06-26T00:00:00ZPlay for the Point or Go for the Win: Expected Goals in the National Hockey LeaguePaerels, Taylorhttp://hdl.handle.net/10211.3/2168012020-06-20T00:36:55Z2020-06-19T00:00:00ZPlay for the Point or Go for the Win: Expected Goals in the National Hockey League
Paerels, Taylor
Research in expected goals has consistently overlooked the difference in how tied games are played in regulation versus overtime, thus making for a widely unstudied distinction. This study's data set involved limiting attempts to the final five minutes of regulation or overtime with the scores either tied or showing a one goal difference.
Two modeling types have been used in the study of expected goals: logistic regression and, more recently, gradient boosting. Both methods were subsequently used in this work alongside a new, additional method: generalized additive modeling. In using all three types of models, the expected goals could be calculated differently based on which variables were being used. Nine different variables were included in the models: distance and angle relative to the goal, type of shot taken, numerical difference in players on the rink for each team, potential use of overtime, potential use of a rebound, potential use of a rush, and existence of teams as potential inter-conference and/or inter-division rivals.
Conducting logistic regression first, ten models were prepared with the comparison of significance and AUC values. Findings determined the best model to be one with a cubic distance term and a quadratic angular term. The four best models from logistic regression were then recalculated in the GAM with the cubic distance, cubic angle model proven best. A gradient boosted decision tree was also created, but it demonstrated a lower AUC. In all cases, the expected goal percentage in overtime was twice that of the regulation situations. More research is necessary to expand the findings on gradient boosting as a superior method of modeling expected goals or if generalized additive models can perform the same task as effectively.
2020-06-19T00:00:00Z