Life of Chang

An Analysis of Superbowl TV Shows

Mon, 01 Jan 0001 00:00:00 +0000

1. TV, halftime shows, and the Big Game

# Import pandas
import pandas as pd

# Load the CSV data into DataFrames
super_bowls = pd.read_csv('datasets/super_bowls.csv')
tv = pd.read_csv('datasets/tv.csv')
halftime_musicians = pd.read_csv('datasets/halftime_musicians.csv')

# Display the first five rows of each DataFrame
display(super_bowls.head())
display(tv.head())
display(halftime_musicians.head())

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Anatomy of a Significance Test

Mon, 01 Jan 0001 00:00:00 +0000

Anatomy of a Significance Test

The Goal

We want to test the difference between attributes of 2 sub-populations relative to randomly mixed sub-populations and provide numerical evidence.

The Null Hypothesis

The following equivalent statements are the null hypothesis, H0 that we are testing.

H0:The sub-populations P1 and P2 were randomly draw from the same population
H0:The sub-populations P1 and P2 were created randomly by assigning units in the same population to each of P1 and P2
H0:The sub-populations P1 and P2 were randomly generated.

Note that that H0 is weaker to be stated in the form of a(𝒫1) = a(𝒫2), although still correct. That’s why we shouldn’t state H0 in terms of equivalence of attribute value.

Bootstrap-t Confidence Interval

Mon, 01 Jan 0001 00:00:00 +0000

Bootstrap-t Confidence Interval

We want to approximate the sampling distribution of a pivotal quantity with bootstrap distribution so that we could construct a confidence interval. The method is similar to approximating a sampling distribution of a pivotal quantity using a t-distribution.

The Step-By-Step Approach

Given a sample 𝒮, an attribute a(𝒮), and standard error $$\widehat {SD}[\tilde a(\mathcal S)]$$, calculate a(𝒮) and standard error $$\widehat {SD}[\tilde a(\mathcal S)]$$ based on the sample.

Chang Liu

Mon, 01 Jan 0001 00:00:00 +0000

Hi! I’m Chang, a thesis-based Master’s student specializing in computer vision within the Systems Design Engineering department at the University of Waterloo. I’m co-supervised by Prof. Sirisha Rambhatla and Prof. Alexander Wong as part of the Vision and Image Processing (VIP) Lab and Critical ML Lab.

My ultimate vision is to develop safe and highly capable models that effectively combine multiple modalities, including vision, language, audio, and more. My current research focuses on unsupervised image segmentation, particularly under distribution shifts, with applications in manufacturing and self-driving. This work aligns with my broader vision as I incorporate language as an additional modality to tackle the distributional shift challenge.

Grade 5 Students in California

Mon, 01 Jan 0001 00:00:00 +0000

Stardardized Test Scores of Grade 5 Students in California

Describing the Data

The data contains the average standardized test scores of grade 5 students in each school in California in the school year of 1998 through 1999. On top of the scores, information are collected on areas such as the number of students enrolled in the school, number of computers per classroom, the percentage of students in school that qualify for a reduced price lunch, and the percentage of students whose first language is not English in the school.

Projects

Mon, 01 Jan 0001 00:00:00 +0000

Checkout my GitHub for coding projects

Towards Smaller Diffusion Models - Gaussian Mixture Masks and UNet Scaling

#Diffusion Models #Deep Learning #Research

Denoising diffusion probabilistic models (DDPMs) have demonstrated superior image generation capabilities but suffer from slow inference and high computational costs. As a first step to address these challenges, we propose two novel modifications to enhance small-scale diffusion models- Gaussian mixture masks and scaled skip connections. More details in the report or poster.

Statistical Sampling

Mon, 01 Jan 0001 00:00:00 +0000

Sample

Sample Definitions

A sample S is a subset of the population. A sample has n < < N units.
An sample attribute a(𝒮) is an estimate of the population attribute a(𝒫)
$$ a(\mathcal S) = \widehat{a(\mathcal P)} = a(\hat{\mathcal P})$$ Sample error is the difference between the sample estimate a(𝒮) and the population attribute a(𝒫) (the estimand). For numerical attributes , sample error is determined mathematically. For graphical attributes, sample error is not determined precisely but it is still conceptually applicable. error = a(𝒮) − a(𝒫) Fisher consistency happens if the sample 𝒮 is equal to the population 𝒫 so the sample error is zero, meaning the estimation is sometimes consistent.

What is Influence?

Mon, 01 Jan 0001 00:00:00 +0000

Influence

Influence Definition

Influence of a variate yu on the population attribute when a variate yu is removed from the population is measured by the following expression:

Δ(α,u) = α(y1, …, yu − 1, yu, yu + 1, …, yN) − α(y1, …, yu − 1, yu + 1, …, yN) for each unit u in the population, and α is an arbitrary population attribute. Note the first part of the equation contains the unit u, and the unit u is removed in the second part of the equation.