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Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stages of sampling, and aims at regressing from probability…

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

Decentralized stochastic gradient descent (D-SGD) is an efficient method for large-scale distributed learning. Existing generalization studies mainly address expected results, achieving rates limited to $\mathcal{O}\left(\frac{1}{\delta…

Differentially private (DP) linear regression has received significant attention in the recent theoretical literature, with several approaches proposed to improve error rates. Our work considers the popular high-dimensional regime with…

In this paper, we present a multilevel Monte Carlo (MLMC) version of the Stochastic Gradient (SG) method for optimization under uncertainty, in order to tackle Optimal Control Problems (OCP) where the constraints are described in the form…

In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm,…

The performance of a deep neural network is highly dependent on its training, and finding better local optimal solutions is the goal of many optimization algorithms. However, existing optimization algorithms show a preference for descent…

We study gradient descent (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective,…

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…

Out-of-distribution (OOD) inputs can compromise the performance and safety of real world machine learning systems. While many methods exist for OOD detection and work well on small scale datasets with lower resolution and few classes, few…

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…

This paper proposes a novel approach to adaptive step sizes in stochastic gradient descent (SGD) by utilizing quantities that we have identified as numerically traceable -- the Lipschitz constant for gradients and a concept of the local…

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

Out-of-distribution (OOD) detection is a well-known challenge due to deep models often producing overconfident. In this paper, we reveal a key insight that trained classifiers tend to rely on sparse parameter contribution patterns, meaning…

Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Out-of-distribution detection is a common issue in deploying vision models in practice and solving it is an essential building block in safety critical applications. Most of the existing OOD detection solutions focus on improving the OOD…

Distributionally robust optimization (DRO) and invariant risk minimization (IRM) are two popular methods proposed to improve out-of-distribution (OOD) generalization performance of machine learning models. While effective for small models,…

When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…

Designing deep neural network classifiers that perform robustly on distributions differing from the available training data is an active area of machine learning research. However, out-of-distribution generalization for regression-the…