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Homework Overview:

This homework aims to evaluate the predictive performance of various machine learning

models using advanced statistical methods. The focus will be on applying and comparing

techniques such as probability distributions, sampling distributions, hypothesis testing,

and regression analysis to different datasets from domains like healthcare, finance, and

social sciences. The goal is to identify the strengths and limitations of each model in terms

of prediction accuracy and reliability.

Objectives:

o To evaluate the predictive accuracy of different machine learning models using advanced

statistical methods.

o To apply advanced statistical techniques and such as hypothesis testing, confidence

intervals, resampling methods to assess the models' performance.

Key Components:

o Model Selection: Choose a set of ML models to evaluate, such as linear regression,

decision trees, random forests, support vector machines, and neural networks.

o Dataset: Use a well$-$known dataset or collect your own data for the analysis. Ensure the

dataset is diverse and relevant to the problem you are addressing.

o Performance Metrics: Use metrics like accuracy, precision, recall, F$1-$score, ROC$-$AUC,

and mean squared error. These will be the primary measures for evaluating the models'

predictive power.

o Advanced Statistical Techniques:

Exploratory Data Analysis$($EDA$)$: Analyze and explore data to gain insights into

relationships, patterns, and model performance.

HypothesisTesting: Use hypothesis testing to compare the performance of different

models. For example, test if the difference in accuracy between two models is

statistically significant.

Confidence Intervals: Calculate confidence intervals for the performance metrics to

quantifythe uncertainty around these estimates.

Cross$-$Validation and Bias$-$Variance Trade$-$off: Use cross$-$validation to assess model

performance and balance bias and variance, reducing overfitting and improving

generalization.

ResamplingMethods: Apply techniques like cross$-$validation and boots trapping to assess

the stability and generalizability of the model predictions.

Expected Outcomes:

Insights into hidden patterns, relationships, and data quality issues using EDA.

A detailed comparison of machine learning models from a statistical perspective.

Insights into the predictive reliability of different models across various domains.

Potential guidelines for selecting the most appropriate model based on the

statistical analysis.