Related papers: A global Lipschitz stability perspective for under…

Biclustering is a powerful unsupervised learning technique for simultaneously identifying coherent subsets of rows and columns in a data matrix, thus revealing local patterns that may not be apparent in global analyses. However, most…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…

We generalize the notion of average Lipschitz smoothness proposed by Ashlagi et al. (COLT 2021) by extending it to H\"older smoothness. This measure of the "effective smoothness" of a function is sensitive to the underlying distribution and…

Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine…

Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…

Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness and stability…

Universal approximation serves as the foundation of neural network learning algorithms. However, some networks establish their universal approximation property by demonstrating that the iterative errors converge in probability measure…

We show that parametric models trained by a stochastic gradient method (SGM) with few iterations have vanishing generalization error. We prove our results by arguing that SGM is algorithmically stable in the sense of Bousquet and Elisseeff.…

We present a new PAC-Bayesian generalization bound. Standard bounds contain a $\sqrt{L_n \cdot \KL/n}$ complexity term which dominates unless $L_n$, the empirical error of the learning algorithm's randomized predictions, vanishes. We manage…

We consider a typical learning problem of point estimations for modeling of nonlinear functions or dynamical systems in which generalization, i.e., verifying a given learned model, can be embedded as an integral part of the learning process…

Despite their widespread use in practice, the asymptotic properties of Bayesian penalized splines have not been investigated so far. We close this gap and study posterior concentration rates for Bayesian penalized splines in a Gaussian…

We study a sequential binary prediction setting where the forecaster is evaluated in terms of the calibration distance, which is defined as the $L_1$ distance between the predicted values and the set of predictions that are perfectly…

Bayesian reinforcement learning (BRL) is a method that merges principles from Bayesian statistics and reinforcement learning to make optimal decisions in uncertain environments. As a model-based RL method, it has two key components: (1)…

To improve the predictive capacity of system models in the input-output sense, this paper presents a framework for model updating via learning of modeling uncertainties in locally (and thus also in globally) Lipschitz nonlinear systems.…

Linear programming is widely used for decision-making in science, engineering, and operations research, yet in many modern applications the coefficients entering the constraints and objective are not known exactly and must be learned from…

Rehearsal approaches enjoy immense popularity with Continual Learning (CL) practitioners. These methods collect samples from previously encountered data distributions in a small memory buffer; subsequently, they repeatedly optimize on the…

We propose a Bayesian neural network-based continual learning algorithm using Variational Inference, aiming to overcome several drawbacks of existing methods. Specifically, in continual learning scenarios, storing network parameters at each…

We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimation error under the Dudley distance between the latent joint distribution and the data joint distribution with appropriately specified architecture of the neural…