arXiv subjects

Juraj Marusic

Publications and source records attributed to Juraj Marusic.

3 recordsLinked to original sources

arXiv2026

Differentially Private Hyperparameter Tuning using Local Bayesian Optimization

Hyperparameter tuning is a key component of machine learning procedures, but when validation data contain sensitive user information, search mechanisms can leak private information through the selected configuration. Existing differentially private hyperparameter tuning methods often rely on near-random search, while prior differentially private Bayesian optimization approaches are typically global and, therefore, scale poorly with the hyperparameter dimensionality. We study differentially private hyperparameter tuning using local Bayesian optimization, focusing on settings where the validation objective is available only through noisy black box evaluations and gradients are unavailable or impractical to compute. We introduce DP-GIBO, a differentially private local Bayesian optimization framework that privately approximates gradients using a Gaussian Process surrogate. Under suitable conditions, we prove that DP-GIBO converges to a locally optimal hyperparameter configuration up to a privacy-dependent error, with dimensional dependence that is polynomial rather than exponential.Empirically, we show that DP-GIBO provides scalable private hyperparameter tuning across multiple tasks, substantially outperforming non-private random search and global Bayesian optimization baselines in moderate-to-high-dimensional hyperparameter spaces.

stat.ML↗

arXiv2026

Variational Deep Learning via Implicit Regularization

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of architecture, hyperparameters, and optimization procedure. However, deep neural networks can be surprisingly non-robust, resulting in overconfident predictions and poor out-of-distribution generalization. Bayesian deep learning addresses this via model averaging, but typically requires significant computational resources as well as carefully elicited priors to avoid overriding the benefits of implicit regularization. Instead, in this work, we propose to regularize variational neural networks solely by relying on the implicit bias of (stochastic) gradient descent. We theoretically characterize this inductive bias in overparametrized linear models as generalized variational inference and demonstrate the importance of the choice of parametrization. Empirically, our approach demonstrates strong in- and out-of-distribution performance without additional hyperparameter tuning and with minimal computational overhead.

cs.LG↗

arXiv2025

A theoretical framework for M-posteriors: frequentist guarantees and robustness properties

We provide a theoretical framework for a wide class of generalized posteriors that can be viewed as the natural Bayesian posterior counterpart of the class of M-estimators in the frequentist world. We call the members of this class M-posteriors and show that they are asymptotically normally distributed under mild conditions on the M-estimation loss and the prior. In particular, an M-posterior contracts in probability around a normal distribution centered at an M-estimator, showing frequentist consistency and suggesting some degree of robustness depending on the reference M-estimator. We formalize the robustness properties of the M-posteriors by a new characterization of the posterior influence function and a novel definition of breakdown point adapted for posterior distributions. We illustrate the wide applicability of our theory in various popular models and illustrate their empirical relevance in some numerical examples.

math.ST↗