15 problems

Let the data lie on the unit sphere, and let $\eta = \gamma/\lambda$ be the stability-threshold step size, where $\gamma$ is the step-size parameter and $\lambda$ is the relevant s…

Let $K\geq 3$. In the $K$-class setting, let \widehat{\boldsymbol{f}}(\text{\boldmath x}_i)\in\mathbb{R}^K denote the multinomial logistic-regression logits for the observed fe…

The missing-data logistic regression model is defined by observations $(\boldsymbol{Z},\boldsymbol{y})$ obtained under the missing-data model considered in the paper, with posterio…

A Simpson dataset is a $2\times 2\times 2$ dataset exhibiting Simpson's paradox; a pathological regularization regime is a set of regularization parameters for which the trend obta…

Let $x_1,\ldots,x_n$ be independent realizations of $N_p(0,\Sigma)$, and suppose that $p/n\to\kappa\in(0,1)$ and that the logistic-regression coefficient vector $\beta$ satisfies ……

Consider the logistic regression model with intercept … where $\theta_0\in\mathbb{R}$, the covariates are independent realizations…

Let $T$ be the corrected least-squares test statistic … Here $\hat{\boldsymbol{\beta}}^{\textrm{CLS}}$ is the corrected least-squares estimator, $\boldsymbol{e}_j$ is the $j$th sta…

Generality conjecture. The conclusions are generally true for rare-events data beyond the logistic regression model.

Consider logistic regression with responses $y_1,\ldots,y_n$, binomial totals $m_1,\ldots,m_n$, design matrix $X$, log-likelihood $l(\beta)$, and Jeffreys-prior penalized log-likel…

Let $\widetilde \ell_n^w(\boldsymbol{\beta})$ denote the weighted negative log-likelihood after elementwise clipping of the features, let $\boldsymbol{\beta}^*$ be the true regress…

Sample-complexity conjecture. The logistic regression procedure fails with high probability when

Let $m$ covariates index combinations of levels, and let ${\cal B}_{\Lambda(A_1 \otimes \dots \otimes A_m)}$ be the set of moves … Consider the subset for which every element of…

Let $m$ covariates index combinations of levels, and let $\Bj=(j_1,\dots,j_m)$ denote such a combination. Let $\bm{e}_{\Bj}$ be the array with $1$ at cell $(1,\Bj)$ and $-1$ at cel…

Let $m$ covariates index combinations of levels, and let ${\cal B}_{\Lambda(A_1 \otimes \dots \otimes A_m)}$ be the set of moves defined by arrays of the form … where $\Bj_i$ are c…

Let $n$ be the number of observations, $d$ the maximum graph degree, $p$ the number of vertices, and let $\theta^*_{\operatorname{min}}$ denote the minimum value of the model param…