Chenfeng LI

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 hand-written digits and the corresponding numbers. For each image, label it as \(Y_i=0\) if the digits within 0-4 or \(Y_i=1\) if the digit within 5-9. 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.

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 Metropolis–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 \(\{x|f(x)>f(x_0)\}\), 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.

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 health-care service) on Post-Acute 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 Medicine. 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.

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 non-scientific 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 1-2 minutes to finish), and distributed online and on-site 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).

This is my first research project, when I was new on machine learning.

I divided the review part into two, detection and recognition. In detection part I provided some personal thinking and reviewed Viola-Jones Algorithm, CNN and Multi-task Cascade Convolutional Network. In recognition part I reviewed Eigenface and CNN.

In the inplementation part I chose a dataset with 2,370 face images (of size 50*37) from 34 individuals from Sklearn (fetch_lfw_people with 30 minimum faces, resize = 0.4), 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 80.6%.