Related papers: Sharp oracle inequalities and slope heuristic for …
In this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L1 penalized least absolute deviation method. Different…
Stochastic proximal point methods have recently garnered renewed attention within the optimization community, primarily due to their desirable theoretical properties. Notably, these methods exhibit a convergence rate that is independent of…
We initiate the systematic study of decision-theoretic metrics in the design and analysis of algorithms with machine-learned predictions. We introduce approaches based on both deterministic measures such as distance-based evaluation, that…
This paper considers smooth strongly convex and strongly concave (SC-SC) stochastic saddle point (SSP) problems. Suppose there is an arbitrary oracle that in expectation returns an $\epsilon$-solution in the sense of certain gaps, which can…
Stochastic rounding (SR) is a probabilistic rounding mode that mitigates errors in large-scale numerical computations, especially when prone to stagnation effects. Beyond numerical analysis, SR has shown significant benefits in practical…
We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their…
This paper addresses the challenge of probabilistic parameter estimation given measurement uncertainty in real-time. We provide a general formulation and apply this to pose estimation for an autonomous visual landing system. We present…
We develop theory for using heuristics to solve computationally hard problems in differential privacy. Heuristic approaches have enjoyed tremendous success in machine learning, for which performance can be empirically evaluated. However,…
As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse…
Ultra high-throughput sequencing of transcriptomes (RNA-Seq) has enabled the accurate estimation of gene expression at individual isoform level. However, systematic biases introduced during the sequencing and mapping processes as well as…
High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we…
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. Progress is measured by the Pareto stationarity gap $\mathcal{G}(x)$, the norm of the best convex…
We study high-dimensional linear models and the $\ell_1$-penalized least squares estimator, also known as the Lasso estimator. In literature, oracle inequalities have been derived under restricted eigenvalue or compatibility conditions. In…
We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the…
We provide dual algorithms for sampling the space of abstract simplicial complexes on a fixed number of vertices. We develop a generative and descriptive sampler designed with heuristics to help balance the combinatorial multiplicities of…
This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on…
In this work, we consider solving optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Sequential Quadratic Programming method to find both first- and second-order stationary…
In this paper we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently…