07-380 Lec6 adds one constraint to an LP, x ∈ ℤᴺ, and the vertex solution may no longer be an integer. Searching the integer points near the LP solution is not guaranteed to work either. The fix: drop the integer constraint (relaxation) to get an LP lower bound, split on a fractional coordinate into xᵢ ≤ floor and xᵢ ≥ ceil, and keep every subproblem in a priority queue ordered by LP objective. The first all-integer solution popped is optimal.
07-380 Lec7 frames PCA as low-rank optimization: approximate the data with a matrix of rank at most r. For a unit vector v, each point's reconstruction error equals ‖x‖² minus the squared projection length, so minimizing reconstruction error and maximizing projected variance are the same problem. Lagrange multipliers show the answer is an eigenvector of the covariance matrix, which you can also read straight off the V in the SVD. The site lists the LoRA paper as reading; its ΔW = BA applies the same low-rank idea to weight updates.
Lecture 8 swaps MLE's argmax p(D|θ) for argmax p(θ|D). The prior p(θ) multiplies the likelihood, and after taking the negative log it becomes an extra term in the objective. A trick coin shows data overwhelming the prior, a Beta prior estimates a click rate, and Gaussian and Laplace priors on linear-regression weights turn into L2 and L1 regularization.
Lecture 9 stops learning p(y|x) directly. Instead it learns the class prior p(y) and the class-conditional p(x|y), then inverts them with Bayes rule. The price is stronger assumptions; the payoff is the ability to generate new data and more stability with little data. Naive Bayes uses conditional independence to make the parameters estimable, GDA uses multivariate Gaussians for continuous features, and whether the covariances match decides a linear or a curved boundary.
The Lec10 slides are not on the 07-380 course site yet, so this guide uses only the PR6 Bayes Nets pre-reading and the 15-281 Bayes Net Demo. A joint distribution can answer any query, but nobody hands it to you and it is too big to store; a Bayes net writes it as a product of 'node given parents' tables, and every missing edge is an independence assumption.
The course site's schedule splits 07-380's first ten lectures into Reasoning Under Certainty, Optimization and Reasoning Under Uncertainty: prove things with logic and plan with search, then write problems as constrained objectives, and finally let a prior in with MAP and turn to probabilistic models. HW1 tests logic plus search, HW2 planning plus LP graphing, HW3 writing solvers plus PCA and MAP derivations.
Break the research workflow into three actions — find, read, write — and pick one tool for each: Google Scholar for discovery, Moonlight AI for reading comprehension, and CorTeX for collaborative writing. All three offer free tiers and together cover the full pipeline from literature search to manuscript submission.
30 minutes a day for 12 weeks — combine shadowing, scenario practice, and AI apps to go from 'I understand but can't speak' to holding your own in meetings.
A/B testing turns a product change into an estimate with uncertainty. A useful report covers effect size, confidence, guardrails, randomization, and launch risk.
Large-sample normal approximation describes the behavior of estimators, not raw data. It is useful, but dependence, boundaries, and distribution shift can make it unreliable.
Bayesian inference updates uncertainty about an unknown parameter by combining prior belief with the likelihood from observed data, producing a posterior distribution.
Bias checks whether an estimator is centered correctly, variance checks sampling fluctuation, MSE combines both, and consistency asks whether the estimator approaches truth as sample size grows.
Bootstrap estimates uncertainty by resampling from the observed sample with replacement, rebuilding many sample-like datasets, and watching the statistic fluctuate.
Chi-square tests compare observed counts with expected counts. First decide whether the problem is goodness-of-fit for one categorical variable or independence for two categorical variables.
Distributions are names for data-generating situations, not formula cards. Learn when Bernoulli, Binomial, Poisson, and Normal distributions fit a problem.
A confidence interval puts a point estimate back inside sampling fluctuation. Computing bounds is only the first step; you also need to explain standard error, critical values, and coverage.
Data type determines the statistical tools you can use. Start with categorical, numeric, count, and time-ordered data, then choose summaries that fit the question.