Related papers: Universal coding, intrinsic volumes, and metric co…
We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard…
The intrinsic volumes induced by a stationary Poisson k-flat process inside a compact and convex sampling window are considered. Using techniques from stochastic analysis, more precisely calculus with multiple stochastic integrals and a…
Uncertainty quantification for neural operators remains an open problem in the infinite-dimensional setting due to the lack of finite-sample coverage guarantees over functional outputs. While conformal prediction offers finite-sample…
We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
Learning high-dimensional distributions is often done with explicit likelihood modeling or implicit modeling via minimizing integral probability metrics (IPMs). In this paper, we expand this learning paradigm to stochastic orders, namely,…
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…
In this paper, we study the approximation problem for functions in the Gaussian-weighted Sobolev space $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed smoothness $\alpha \in \mathbb{N}$ with error measured in the Gaussian-weighted space…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
We use Gaussian stochastic weight averaging (SWAG) to assess the model-form uncertainty associated with neural-network-based function approximation relevant to fluid flows. SWAG approximates a posterior Gaussian distribution of each weight,…
Skew-symmetric functions are a class of functions defined on a product space $M \times M$ that are antisymmetric with respect to the order of their inputs. In [13], the authors proved that non-deterministic skew-symmetric Gaussian fields…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
Motivated by the growing application of wireless multi-access networks with stringent delay constraints, we investigate the Gaussian multiple access channel (MAC) in the finite blocklength regime. Building upon information spectrum…
The asymptotic law for the expected nodal volume of random non-Gaussian monochromatic band-limited functions is determined in vast generality. Our methods combine microlocal analytic techniques and modern probability theory. A particularly…
A stochastic incremental subgradient algorithm for the minimization of a sum of convex functions is introduced. The method sequentially uses partial subgradient information and the sequence of partial subgradients is determined by a general…
Though learning has become a core component of modern information processing, there is now ample evidence that it can lead to biased, unsafe, and prejudiced systems. The need to impose requirements on learning is therefore paramount,…
Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…
This article presents a theoretical study of uncertainty functionals on general measurable spaces. These functionals are fundamental in experimental design and global sensitivity analysis, where they are used to quantify variability and…
Shortened abstract: Given a constrained minimization problem, under what conditions does there exist a related, unconstrained problem having the same minimum points? This basic question in global optimization motivates this paper, which…