8 problems

Let Forward Stagewise regression and the Lasso be the two fitting procedures discussed in the source, and let least-squares boosting be the procedure that repeatedly fits regressio…

Let ${\cal H}$ be a class of base classifiers and let ${\rm conv}({\cal H})$ denote its convex hull. Consider classifiers obtained in consecutive rounds of boosting, and let…

Let $\mathcal{F}_k$ denote sieve spaces used for boosting, and let the associated hyperparameters be selected from the data, for example by sample-splitting or cross-validation. Da…

Let $c_t$ be a neural classifier used in an iterative boosting procedure for density estimation, and consider the negative log-likelihood as the procedure progresses. Early-stoppin…

Let $c$ denote the parameter appearing in the assumptions governing the pure greedy algorithm (PGA), and let the convergence rate refer to the decay of the residual sequence under…

Let $m$ be the number of training examples and suppose the feature matrix has entries in $\{-1,0,+1\}$. Let $L$ denote the exponential loss and let…

Let $\bm{\lambda}^*$ be any weight vector and let $B=\|\bm{\lambda}^*\|_1$. For exponential loss $L$ and AdaBoost's iterates, quadratic convergence conjecture. For every…

Given $m$ labeled examples, a finite weak-hypothesis set of size $N$, the exponential loss … and AdaBoost's iterate $\bm{\lambda}^t$, let…