24 problems

Let GF denote the Gaussian gradient flow method and CBO the consensus-based optimization method for approximating Gaussian mixture target distributions, with multiple particles use…

Let $V_{\mu^0}$ be the variational information matrix at the true parameter $\mu^0$. Consider models with unequal component weights or non-identity covariance matrices, and suppose…

Consider the maximizers of the variational-Laplace objective $I_j^{(n)}$ in the exponential-family setting described above, with the normalized objective converging in probability…

Variance-offset conjecture. Variance inflation induced by sequential updates offsets the usual variance underestimation associated with KL-based variational approximations.

Let the sampling problem have a target density whose complexity may be measured, for example, by its number of modes, and let the problem dimension be the number of variables in th…

Consider the non-Gaussian component of the posterior measure arising in the GP-PDE collocation method, where collocation points impose nonlinear PDE observations. Dense-collocation…

Consider the logistic regression model with crossed random effects, with intercept and slope estimates $\widehat{\underline{\beta}}_{0}$ and $\widehat{\underline{\beta}}_{1}$ from…

Consider diffusion neural networks for image-generation tasks, in particular U-nets with convolutional layers, and graphical models having locality and invariance structures. U-net…

Let $(\boldsymbol{x},\boldsymbol{\theta})\sim\mu(\boldsymbol{x},\boldsymbol{\theta})\propto\exp\{\langle\boldsymbol{\sigma},\boldsymbol{A}\boldsymbol{\sigma}\rangle/2\}$, with the…

Let…

Suppose $\boldsymbol{Y}=\boldsymbol{u}\boldsymbol{u}^{\mathsf T}+\boldsymbol{J}$, where $\boldsymbol{J}\sim\operatorname{GOE}(d)$ and $u_i\sim_{\mathrm{iid}}\pi_0$ for a distributi…

Let $\boldsymbol{A}=\beta\boldsymbol{J}$, where $\boldsymbol{J}$ is a symmetric random matrix whose off-diagonal elements are independent, have variance $1/d$, and satisfy some mom…

Conjecture on GB-SVGD rates. The convergence rates of GB-SVGD can be improved even in the regime $n \ll KT$. The paper establishes provably fast convergence guarantees for finite-p…

Let BBVI denote black-box variational inference, and let the mean-field variational family be the class of variational distributions whose coordinates are independent. Under mild a…

Let $\boldsymbol{x}_{i}^{(t)}$ evolve according to the finite-particle system defined by the Gaussian-Stein dynamics above, and let the corresponding mean-field limit be the associ…

Let $N$ be a Hawkes process with link functions $phi=(phi_k)_k$ and parameter $f_0=(nu_0,h_0)$ satisfying Assumption (ass-psi), and suppose the hierarchical squared exponential Gau…

Let $T\geq2$, let $\theta^*$ be the unique minimum of $\mathrm{KL}(\mathrm{q}(\mathbf{x};\theta)\mathbin{\|}\mathrm{p}(\mathbf{x}))$, and define the local Hessian mismatch ratio ……

Let a stochastic mixture have component family $\mathrm{q}(\mathbf{x};\theta)$ and mixing distribution $\psi(\theta)$. Call it unbiased when its mixture density satisfies…

Let $\mathrm{q}(\mathbf{x};\theta)$ be a component family and let $\psi(\theta)$ be a mixing distribution. Sampling is defined by unbiasedness in the limit of infinitely many compo…

Higher-derivative extension conjecture. A similar result would hold under the assumption of a uniform bound on the $k^{\text{th}}$ derivative of $f_n$.

Higher-order derivative conjecture. Bounds on higher-order derivatives would also suffice in place of the imposed bound on the second derivative.

Gumbel-softmax convergence conjecture. The Gumbel-softmax approximation does not hurt variational Bayes convergence.

The TRW bound concerns an upper bound on the log-partition function for graphical models with discrete variables, with known tree weights. The proposed variational approach is base…

The multi-graph stochastic block model consists of multiple network layers sharing node class assignments, with layer-specific connection probability matrices; variational approxim…