52 problems

Bridgeless limit-interchange conjecture. In general, the same result remains true when the order of the limits is swapped, at least for bridgeless estimators for every $q\in[1,2]$…

Simultaneous-limit conjecture. We conjecture that

Let $T$involve Bernoulli random tensor entries, and let $d_{i_{1},\dots,i_{k-m}}$ denote the degree of a tuple $(i_{1},\dots,i_{k-m})$, namely … Assume…

Dimension-equality conjecture. For all weights $w$ and levels $N$,

Let $D(\theta):=\sup_{y\in\mathbb R^m}\psi_1(y)$ be the Case 1.2 dual value, where $\theta>0$ is the regularization parameter. Let $V$ be the primal value and $W$ the limiting lowe…

Generalization conjecture. It may be possible to derive a generalization of the proposition to an arbitrary regularization schedule in which the term

Over-regularization conjecture. The lower bound imposed on the $\mathcal{A}_i$ in the regularization analysis could be replaced by requiring the $\mathcal{A}_i$ to be larger than t…

Let $m_k$ be the regularized Taylor model at iterate $\bm{x}_k$, let $\bm{x}_*$ be the limit minimizer, and call a local minimizer of $m_k$ persistent if it can be continuously tra…

In the setting of quadratically regularized optimal transport, let the support of the optimal coupling be partitioned into sections, and let $d$ denote the underlying dimension and…

Let KRAS denote the kernel adversarial estimator, and consider the source conditions imposed in the paper. An iterated Tikhonov KRAS estimator is obtained by applying Tikhonov regu…

Let an adaptive iterated KRAS estimator be an iterated Tikhonov KRAS estimator whose regularization or stopping choice is selected adaptively, as in the adaptive LRAS procedure dis…

Let $t$ be a positive integer, and let a $t$-iterated Tikhonov KRAS estimator mean the KRAS estimator obtained by applying Tikhonov regularization for $t$ iterations. Let Assumptio…

Let $\lambda_2$ be the quadratic regularization parameter in the empirical KLIEP loss with an elastic net penalty, and let the sample sizes and dimensions be fixed. Fixed-small-…

Consider the Poisson problem … with solution $u^*\in H^t_0$, forcing term $\xi\in H^{-s}$, and reproducing-kernel Hilbert space $\mathcal{H}_K=H^q$ for some $q>t$, where $t=2-s$. L…

Let $Z(\lambda)$ denote the marginal likelihood for a regularized linear regression model, with ridge, lasso, and group lasso corresponding to their respective regularizers. Quasic…

Trade-off invariance principle. For all but some exceptional $\alpha\in[0,+\infty)^m$, if $\inf_{u\in U}H_{\alpha}(u)>-\infty$, then there exist…

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…

Min-norm interpolators and estimators are considered in an overparameterized regime, where the number of parameters may exceed the number of observations and interpolation is possi…

Let $p<3/2$. The $L^p\to L^\infty$ regularization rate of the heat equation is said to be the rate obtained by heat-flow smoothing from $L^p$ data. Landau regularization conjecture…

Consider training neural networks with quadratic regularization terms. Loshchilov–Hutter conjecture. The quadratic regularization terms contribute to the low generalization error i…

Conjecture on correlated features. Fully avoiding correlated features may be detrimental for learning tasks.

For inverting real Laplace transforms, let $f_r^{(1)}$ and $f_r^{(2)}$ be two closely related regularized solutions depending on the regularization parameter and additional method…

Let $(X,\omega)$ be a compact Kähler space, and let $\varphi$ be an $\omega$-psh function on $X$. Smooth regularization conjecture. The function $\varphi$ can be written as the poi…

Let $\Sigma$ be the design covariance matrix, let $L$ be the penalty matrix, and let $\lambda_2$ be the quadratic-penalty parameter. Write $\gmin(A)$ for the minimum eigenvalue of…

Let $B_j$ denote the matrices associated with the punctures, let $epsilon>0$ be the smearing width, and consider the series expansion arising from the regularized determinant of th…