相关论文: $\ell_1$-Based Adaptive Identification under Quant…

Adaptive experimental designs have gained popularity in clinical trials and online experiments. Unlike traditional, fixed experimental designs, adaptive designs can dynamically adjust treatment randomization probabilities and other design…

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…

Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…

Time-to-event outcomes are commonly used as primary endpoints in randomized clinical trials. Despite this, relatively little work incorporates baseline covariate information while also accounting for stratified randomization, a common form…

We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…

This paper develops a unified framework for partial identification and inference in stratified experiments with attrition, accommodating both equal and heterogeneous treatment shares across strata. For equal-share designs, we apply recent…

Dynamical systems with binary-valued observations are widely used in information industry, technology of biological pharmacy and other fields. Though there have been much efforts devoted to the identification of such systems, most of the…

Capture-recapture experiments are widely used to estimate the abundance of a finite population. Based on capture-recapture data, the empirical likelihood (EL) method has been shown to outperform the conventional conditional likelihood (CL)…

P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…

Despite many applications, dimensionality reduction in the $\ell_1$-norm is much less understood than in the Euclidean norm. We give two new oblivious dimensionality reduction techniques for the $\ell_1$-norm which improve exponentially…

$\ell_1$ mean filtering is a conventional, optimization-based method to estimate the positions of jumps in a piecewise constant signal perturbed by additive noise. In this method, the $\ell_1$ norm penalizes sparsity of the first-order…

In this paper we provide a complementary set of results to those we present in our companion work \cite{Stojnicl1HidParasymldp} regarding the behavior of the so-called partial $\ell_1$ (a variant of the standard $\ell_1$ heuristic often…

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…

This paper considers real-time control and learning problems for finite-dimensional linear systems under binary-valued and randomly disturbed output observations. This has long been regarded as an open problem because the exact values of…

We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…

This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…

Reuse of data in adaptive workflows poses challenges regarding overfitting and the statistical validity of results. Previous work has demonstrated that interacting with data via differentially private algorithms can mitigate overfitting,…

Overfitting is the bane of data analysts, even when data are plentiful. Formal approaches to understanding this problem focus on statistical inference and generalization of individual analysis procedures. Yet the practice of data analysis…

We investigate the difference between using an $\ell_1$ penalty versus an $\ell_1$ constraint in generalized eigenvalue problems, such as principal component analysis and discriminant analysis. Our main finding is that an $\ell_1$ penalty…