Research Portforlio
Research Interests
With my background in Mathematics and Statistics, I believe I am capable of performing a variety of relevant tasks.
Research Experiences
Robustness to Spurious Correlations via Distributionally Robust Optimization (DRO)
 Period: Apr  May, 2023
 Reference Information: ChenfengLi/DRO

Project Description:
This is a teamwork of three.
Review the theory of DRO.
Construct a colored MNIST dataset with spurious correlation (which are different between training and testing set). Build ERM (empirical risk minimization) and DRO models with and without regularization, apply to the dataset and evaluate the performance of each model.
Conclude the robustness of DRO model with strong regularization on the dataset and compile report.

My Position:
Project Leader

My responsibility:
Grouped the team, communicated with members and organized tasks.
Constructed the colored MNIST dataset. Wrote DRO models and apply to the dataset. Made comparison between DRO model with or without regularization and drew conclusion. Evaluate the DRO model with the general case of spurious variables.

Details:
For a supervised learning problem, with observed features \(X_1, \dots ,X_n\) and corresponding target \(Y\), we want to use the \(X\)'s that cause \(Y\) and avoid using those caused by \(Y\). We call the correlation between \(Y\) and \(X\)'s caused by \(Y\) as spurious correlations. The models with spurious correlation are possibly made wrong prediction.
The regular model (such as ERM) couldn't handle such problem, and we could consider DRO model. The idea of DRO is to grouped the data based on features, then minimize the risk of the wrost cases. We use colored MNIST dataset as an example.
MNIST is a dataset with images of handwritten digits and the corresponding numbers. For each image, label it as \(Y_i=0\) if the digits within 04 or \(Y_i=1\) if the digit within 59. Then colored the label 0 images with red and label 1 images green. For the training set, flip the color with probability 0.25, while for the testing set, flip the color with probability 0.8.
Under this setting, Image > Digit > Label \(Y\) > Color, where ">" denotes causation, and Image and Color are observed features. The correlation between label and color are spurious. If applying ERM, the model would learn this relationship from training set, but as such causation in testing set are different, the testing performance is poor.
To apply the DRO model, we separate the dataset into four subgroups based on color (red or green) and label (0 or 1). Then train a model that minimize the risk of the group with highest risk. This effectively eliminate the influence of spurious correlation. Moreover, to avoid overfitting, we use DRO model regularization. This model have satisfying training and testing accuracy.
Hierarchical Dirichlet Process (HDP)
 Period: Apr  May, 2023
 Reference Information: ChenfengLi/HDP

Project Description:
This is a giventopic final research of a Bayesian course. I worked at the stat team of eight.
Review the theory of HDP, Chinese Restaurant Franchise (CRF) and Slice Sampler (SS). Implement CRF sampling method for a clustering problem.
Construct a HDP model and implement SS for the same problem. Make comparison with the result of CRF method.
Make presentation and compile report.

My Position:
Researcher

My responsibility:
Constructed graphical model of HDP and made mathematical deduction for coding.
Cooperatively encoded the model.

Details:
Slice sampler (SS): For a probability distribution \(f(x)\) with two or more peaks, and small function value in between, some sampling method (such as Metropolisâ€“Hastings algorithm) may keep sampling values around one peak and ignore the others. Slice sampler is available for this situation. SS is an MCMC algorithm. For an initial \(x_0\), it first uniformly sample a value between 0 and \(f(x_0)\), then uniformly sample \(x_1\) from \(\{xf(x)>f(x_0)\}\), and repeat this process.
Chinese Restaurant Franchise (CRF): This is a generalization of Chinese Restaurant Process (CRP). In CRP each step choose either one of existing parameters or sample a new parameter. In CRF, it assumes an amount of Chinese restaurants sharing same distribution of parameter.
Hierarchical Dirichlet Process (HDP): This is a expansion of Dirichlet Process (DP), which is an nonparametric Bayesian. In HDP, we set a prior distribution for the base distribution of DP to reflect its variation. Therefore, HDP is more flexible than DP but more computational expensive.
In this research, for the clustering problem from the same given dataset, the performance of CRF is better than the HDP with SS.
Statistical Consulting
 Period: Sep  Nov, 2022
 Reference Information: ChenfengLi/Consulting

Description:
Consulting team of five. Provided consulting services to local clients with data issues.
Review the materials from clients after receiving the consulting request. Meet with them online and discuss detailed concerning of the problem, and provide brief suggestion instantly.
Delivered the final reports to clients. Make presentations to instructors and other consulting teams.
Completed three consulting missions duriing the period.

My Position:
Consultant

My responsibility:
Participate in the whole consulting process.

Details:
First client is Mr. Kwang from UChicago Medicine. This client wanted to study the effect of a medication for COVID patients on the requirement of ventilation. We advised to apply logistic regression, and provided suggestions on grouping the patients and strengthen the analysis result.
Second client is Ms. Wang from UChicago BSD. This client wanted to study the effect of HCBS (a kind of healthcare service) on PostAcute Care (PAC) based on a dataset with 700,000 observations, and she was interested in using fixed effects (FE) with propensity scores (PS) weighting in the model. We suggested to use logistic regression model without PS weighting.
Third client is Ms. Gan from UChicago Hospital. This client wanted to learn if the distance between the middle point of the chest and left entricle is significant accross different age group and other physical factors. We pointed out an issue of the covariate choice (BMI should not be included as it is a function of weight and height), advised linear regression model and provided the number of samples should be collected.
The current situation and feasible development direction of Chinese medicine
 Period: Jun  Dec, 2021
 Reference Information: ChenfengLi/Chinesemedicine

Description:
Teamwork of four for the capstone project at the Chung Chi College, CUHK. The language of this research is Chinese (traditional).
This research is to study the situation and problems encountered of the Chinese medicine, and raise suggestions for its development.
The research process included reviewing relevant papers, interviewing specialists and practitioners, collecting and analyzing the public preception through questionaires, and further discussion about development. Then we compiled reports and made presentation.

My Position:
Data Analyst

My major responsibility:
Review the research related to public preception about Chinese medicine.
Design and distribute online and paperbased questionaire. Process regression analyze and visualize by charts. Draw analysis conclusion and make reflection.

Details:
In general, we analyzed the medical, econimical and cultural value of Chinese medicine and concluded that it is worth developing. According to the data result we noticed that the public have positive view in Chinese medicine. However, the Chinese medicine faces many issues, such as nonscientific theory, treatment effectiveness, qualify of products and lack of talent. We raised suggestions such as pharmacological analysis, patent protection, commercialization.
In data analysis part, I wanted to study the effect of ages and education level on the idea of Chinese medicine (overall, theory, effectiveness and choice), and the perception of some specific symptoms, the advantages and shortages of Chinese medicine. Therefore, I designed a questionaire with 10 questions (required 12 minutes to finish), and distributed online and onsite with the help of teammates.
We collected 153 valid answers. I used linear regression on the first problem. As the ages and education level were ordinal categorical variables, and to analyze the difference between each two neighbor categories, I encoded with staircase dummy variables. The result showed that generally, the age had positive effect ,and education level had weak negative effect on perception. Besides, I found people thought Chinese medicine is more effective in treating minor and chronic diseases.
The limitation in this analysis is that the sample size is small, especially for the elderly group, and many people rejected to answer, which may cause bias on result. Besides, we can choose more covariates (such as income level).
A General Review of Facial Recognition Technology
 Period: Sep  Dec, 2020
 Reference Information: ChenfengLi/FacialRecognition

My Position:
Independent Researcher

Description:
This is an independent project.
Review the theories and applications of several facial detection and recognition methods proposed in the past decades.
Implement a facial recognition model through Convolution Neural Network (CNN).

Details:
This is my first research project.
I divided the review part into two, detection and recognition. In detection part I provided some personal thinking and reviewed ViolaJones Algorithm, CNN and Multitask Cascade Convolutional Network. In recognition part I reviewed Eigenface and CNN.
In the inplementation part I chose a dataset with 2,749 face images (of size 62*47) from 52 individuals from Sklearn (fetch_lfw_people with 20 minimum faces), and then constructed a CNN model through tensorflow. Split the data with training, validation and testing sets at a ratio 8:1:1. Achieve a testing accuracy of 91.7%.