Related papers: An Optimal Design Framework for Lasso Sign Recover…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…
This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…
We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field contain some a priori assumptions about the error corrupting…
We revisit Cox's proportional hazard models and LASSO in the aim of improving feature selection in survival analysis. Unlike traditional methods relying on cross-validation or BIC, the penalty parameter $\lambda$ is directly tuned for…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…
We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…
Algorithm designers typically assume that the input data is correct, and then proceed to find "optimal" or "sub-optimal" solutions using this input data. However this assumption of correct data does not always hold in practice, especially…
We introduce a novel LLM based solution design approach that utilizes combinatorial optimization and sampling. Specifically, a set of factors that influence the quality of the solution are identified. They typically include factors that…
We study the design of a decentralized two-sided matching market in which agents' search is guided by the platform. There are finitely many agent types, each with (potentially random) preferences drawn from known type-specific…
We study the property of the Fused Lasso Signal Approximator (FLSA) for estimating a blocky signal sequence with additive noise. We transform the FLSA to an ordinary Lasso problem. By studying the property of the design matrix in the…
In many engineered systems, optimization is used for decision making at time-scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly…
We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the $\ell_{2}$-prediction error and the $\ell_{1}$-risk of the lasso and the Dantzig selector are…
Generative modeling of crystal structures is significantly challenged by the complexity of input data, which constrains the ability of these models to explore and discover novel crystals. This complexity often confines de novo design…
We propose a novel two-stage subsampling algorithm based on optimal design principles. In the first stage, we use a density-based clustering algorithm to identify an approximating design space for the predictors from an initial subsample.…
We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable…
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…
Faced with data-driven policies, individuals will manipulate their features to obtain favorable decisions. While earlier works cast these manipulations as undesirable gaming, recent works have adopted a more nuanced causal framing in which…