Data 102: Inference

Data102 Notes #

Here are my notes for the Fall 2022 offering of Data 102, Berkeley’s Inference for Data Science course.

Data 102 explores two major concepts: making decisions under uncertainty and modeling the real world. This is all about making assumptions– here are some definitions:

• Frequentist: $y$ (data) is random, $\theta$ (parameter) is fixed
• Bayesian: $y$ is random, $\theta$ is random
• Parametric: Make assumptions about the relationship between $\theta$ and $y$, then use these assumptions to find the best value of $\theta$ given $y$
• Nonparametric: Don’t make any assumptions, and find any good function $f$ such that $\theta = f(y)$

Table of Contents #

• Binary Decision Making

  Binary Decision Making is the simplest kind of decision we can make: 1 or 0, yes or now, true or...

  11/19/2023

  : Confusion matrix, sensitivity, specificity, TPR/FPR/FNR/FDP etc.
• Hypothesis Testing

  Hypothesis Testing Hypothesis testing is a form of (do we accept or reject the null hypothesis?). Formulate null hypothesis, alternate hypothesis,...

  11/19/2023

  : Null/alternative hypotheses, multiple hypothesis testing, controlling FWER/FDR, online decision making, likelihood ratios
• Decision Theory

  So far, in and , we've explored how to make as few mistakes as possible when making binary predictions. Intro...

  11/19/2023

  : Loss functions, risk, bias-variance tradeoff
• Parameter Estimation

  Suppose we observe $n$ data points ($x1$ to $xn$). Let $\theta$ be some unknown parameter that describes the distribution the data...

  11/19/2023

  : Likelihood, MLE, Bayesian parameter estimation, Bayesian hierarchical models
• Sampling

  Intro In practice, getting the exact probability of an inference is not required as long as we get a rough estimate...

  11/19/2023

  : Markov chains, MCMC, Metropolis-Hastings, Rejection sampling, Gibbs sampling
• Regression and GLMs

  Regression and GLMs

  Posterior Predictive Distribution Posterior Predictive Distribution: "if we saw some data, what future data might we expect?" $P(x{n+1}|x1,\cdots,xn)$ = $\int P(x{n+1}|\theta)P(\theta|x1,\cdots,xn)d\theta$ ...

  11/19/2023

  : Generalized linear models, posterior predictive check
• Nonparametric Methods

  What does nonparametric mean? Nonparametric methods make no assumptions about the distribution of the data or parameters; the null hypothesis is...

  11/19/2023

  : K-Nearest Neighbors, decision trees, random forests, neural networks, gradient ascent/descent
• Interpretability

  What do we look for in predictions? Accuracy: We want predictions to be close to the true values. Simplicity: We want the...

  11/19/2023

  : Interpretability, explainability
• Causality

  Prediction vs Causality Prediction: using $X$ data, can we guess what $y$ will be? Causation: does X cause y to...

  11/19/2023

  : Colliders, confounders, structural causal models, risk ratios, potential outcomes framework
• Concentration Inequalities

  The goal of concentration inequalities is to provide bounds on the probability of a random variable taking values in its...

  11/19/2023

  : Markov, Chebychev, Chernoff, Hoeffding
• Bandits

  Main idea: making repeated decisions based on feedback, factoring in the tradeoff between exploring new decisions or keeping existing good...

  11/19/2023

  : Multi-Armed Bandit Framework, UCB/ETC, Thomson Sampling, Regret
• Markov Decision Processes

  What is a Markov Decision Process? A Markov Decision Process is a Markov model that solves nondeterministic search problems (where an...

  11/19/2023

  : Value iteration, Q-value iteration, Policy iteration
• Reinforcement Learning

  Introduction Reinforcement Learning (RL) is an example of online planning, where agents have no prior knowledge of rewards or transitions and...

  11/19/2023

  : Q-Learning

How to contribute #

See the contributing guide

For the most part, these notes should be pretty complete in terms of content, but could use some cleaning up (as well as more examples).

Credits #

• Ben Cuan