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We introduce a novel scheme for choosing the regularization parameter in high-dimensional linear regression with Lasso. This scheme, inspired by Lepski's method for bandwidth selection in non-parametric regression, is equipped with both…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…
We consider the nonparametric regression and the classification problems for $\psi$-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association, $\ldots$. A penalized estimation…
Partial label learning (PLL) aims to solve the problem where each training instance is associated with a set of candidate labels, one of which is the correct label. Most PLL algorithms try to disambiguate the candidate label set, by either…
Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric implying linear relationships between the variables at hand, or non-linear PCA is…
Reinforcement learning (RL) commonly relies on scalar rewards with limited ability to express temporal, conditional, or safety-critical goals, and can lead to reward hacking. Temporal logic expressible via the more general class of…
Penalized methods are applied to quasi likelihood analysis for stochastic differential equation models. In this paper, we treat the quasi likelihood function and the associated statistical random field for which a polynomial type large…
Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods,…
When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which…
We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide…
Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of…
Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…
As medical devices become more complex, they routinely collect extensive and complicated data. While classical regressions typically examine the relationship between an outcome and a vector of predictors, it becomes imperative to identify…
We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property…
Quantum nonlocality is often judged by violations of Bell-type inequalities for a given state. The computation of such violations is a global task, requiring evaluation of global correlations and subsequent testing against a Bell…
A large body of research has focused on theory and computation for variable selection techniques for high dimensional data. There has been substantially less work in the big tall data paradigm, where the number of variables may be large,…
The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…
Meta-analysis allows rigorous aggregation of estimates and uncertainty across multiple studies. When a given study reports multiple estimates, such as log odds ratios (ORs) or log relative risks (RRs) across exposure groups, accounting for…
Solving optimization problems is a key task for which quantum computers could possibly provide a speedup over the best known classical algorithms. Particular classes of optimization problems including semi-definite programming (SDP) and…