Notes in EEN100: Theory and exercises

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Status	Last Update	Fields
Published	09/16/2023	Assume that \(X\) is \((\nu,b)\)-sub-exponential with mean \(\mu\). Provide a bound for \(\mathbb{P}[X - \mu > t]\).
Published	09/23/2023	Bernstein bound for \(X = \sum_{i=1}^n X_i\)
Published	09/16/2023	Markov's inequality
Published	09/16/2023	Chebyshev's inequality
Published	09/17/2023	Chernoff bound
Published	09/16/2023	Sub-Gaussian random variable
Published	09/16/2023	Properties of \( X = \sum_{k=1}^n X_i \) where \(X_1, X_2, \dotsc, X_n\) are independent sub-Gaussian random variables with parameters \(\sigma_1, \si…
Published	09/16/2023	Let \(X\) be \(\sigma\)-sub-Gaussian. Provide bounds for the probabilities \( \mathbb{P}[X-\mathbb{E}[X] >t] \) and \( \mathbb{P}[\l…
Published	09/16/2023	Sub-exponential random variable
Published	09/16/2023	Let \(X_1,\dotsc,X_n\) be independent sub-exponential random variables with parameters \((\nu_1, b_1),(\nu_2, b_2),\dotsc,(\mu_n, b_n)\) then. What ca…
Published	09/20/2023	Lindeberg-Lévy CLT
Published	09/16/2023	SLLN
Published	09/22/2023	Berry-Esseen CLT
Published	09/16/2023	Hoeffding's bound
Published	09/16/2023	Large-deviation inequality for sub-exp. random variables
Published	09/16/2023	Bernstein's condition
Published	09/18/2023	Bernstein bound (for mgf and tail)
Published	09/17/2023	Let \(X,Y\) be two independent Rademacher vectors (iid uniform \(\pm 1\) entries).What can be said about \(\cos \theta(X,Y) = \frac{Y^\mathsf{T}X}{\lV…
Published	09/17/2023	Operator norm of \(A \in \mathbb{R}^{m \times n}\)
Published	09/17/2023	Rayleigh-Ritz theorem
Published	09/17/2023	Covering
Published	09/17/2023	Packing
Published	09/17/2023	Covering-packing bounds
Published	09/17/2023	Bounds on \(N(\varepsilon, \mathcal B^n)\): \(\varepsilon\)-covering number of the Euclidean ball
Published	09/17/2023	Bounds on operator norm by \(\varepsilon\)-cover
Published	09/17/2023	Concentration bounds for norm of matrix with independent \(\sigma\)-sub-Gaussian entries
Published	09/23/2023	How to extend two-sided matrix bounds if the sub-Gaussian rows \(X_i\) have covariance matrix \(\Sigma\)?
Published	09/23/2023	Support of \(x \in \mathbb R^n\)
Published	09/23/2023	\(s\)-sparse vector
Published	09/23/2023	Equivalent conditions for recovery of \(s\)-sparse solution of \(Az = y\)
Published	09/23/2023	Uniqueness of solution to (P0)
Published	09/23/2023	\(\ell_q\) norm
Published	09/23/2023	Problem (P1) and conditions on uniqueness
Published	09/24/2023	Restricted null space property (RNP)
Published	09/27/2023	RIP implies RNP
Published	09/27/2023	RIP and orthogonal vectors
Published	09/28/2023	Upper and lower bound on \(\ell_1\)-norm using \(\ell_2\)-norm (lemma 1-2).
Published	09/27/2023	Conditions under a row sub-Gaussian random matrix satisfies RIP
Removal Requested	09/27/2023	Sub exponential bound for row-wise sub-Gaussian random matrix
Removal Requested	09/27/2023	RIP for row sub-Gaussian matrices
Published	09/28/2023	\(s\)-sparse approximation error
Published	09/27/2023	Relaxed basis pursuit (LASSO)
Published	09/28/2023	Stable and robust RIP
Published	09/27/2023	P0 problem in matrix reconstruction
Published	09/27/2023	Nuclear norm of \(Z\)
Published	09/27/2023	P1 problem in matrix recovery
Published	09/27/2023	Frobenius norm
Published	09/27/2023	Rank-restricted isometry property
Published	09/27/2023	Uniqueness of solution to P1 in matrix recovery
Published	09/28/2023	Rank restricted isometry propery and sub-Gaussianity
New Card	10/08/2023	Supervised learning sets (\(\mathcal X, \mathcal Y, \mathcal S, \mathcal H, ...\))
New Card	10/08/2023	Loss function and population loss
New Card	10/08/2023	Empirical risk minimization (ERM)
New Card	10/08/2023	Probably approximately correct
New Card	10/08/2023	PAC learnability
New Card	10/08/2023	\(\epsilon\)-representative sample
New Card	10/08/2023	Representative training set and ERM correctness
Status	Last Update	Fields