In this paper, we study the bias and high-order error bounds of the Linear Stochastic Approximation (LSA) algorithm with Polyak-Ruppert (PR) averaging under Markovian noise. We focus on the version of the algorithm with constant step size and propose a novel decomposition of the bias via a linearization technique. We a...
I. Levin, Alexey Naumov, Sergey Samsonov· AAAI Conference on Artificia...· 2 citations
In this article we prove that estimator stability, together with a gradient-growth condition on the expected fitted loss, is enough to provide concentration bounds for leave-one-out cross-validation in a general framework. In particular, we provide concentration bounds beyond Lipschitz continuity assumptions on the los...
In stochastic multi-armed bandits, rewards are generated by an unknown distribution; the world's reward uncertainty induces the exploration-exploitation trade-off. Thompson sampling (TS) addresses this trade-off elegantly, but requires knowing the reward model's parametric form to sample from its posterior and compute...
The automatic segmentation of human knee cartilage from 3D MR images is a useful yet challenging task due to the thin sheet structure of the cartilage with diffuse boundaries and inhomogeneous intensities. In this paper, we present an iterative multi-class learning method to segment the femoral, tibial and patellar car...
Quan Wang, Dijia Wu, Le Lu et al.· 0 citations
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A simple hedging principle shows how splitting initial wealth between two strategies achieves a best-of-both-worlds guarantee by retaining the smaller of their regrets and the larger of their growth rates.
Certified machine unlearning can be achieved through noise injection, with differential privacy guarantees obtained by calibrating the noise to worst-case sensitivity. Yet, the influence of individual training points is highly heterogeneous, making such uniform calibration unnecessarily conservative for most deletion r...
Generative Flow Networks (GFlowNets; GFNs) are a class of generative models that learn to sample compositional objects proportional to their a priori unknown value, their reward. We focus on the case where the reward has a specified, actionable structure, namely that it is submodular. We show submodularity can be harne...
Toeplitz covariance estimation is a classical signal processing problem, yet the geometry of the Gaussian maximum-likelihood objective remains only partially understood. Recent Newton-type, majorization-minimization, and gradient-based methods often solve the nonconvex problem globally with enough samples, but also rev...
We introduce Deep Jump Gaussian Processes (DJGP), a novel method for surrogate modeling of a piecewise continuous function on a high-dimensional domain. DJGP addresses the limitations of conventional Jump Gaussian Processes (JGP) in high-dimensional input spaces by integrating region-specific, locally linear projection...
We study the online stochastic difference-of-convex (DC) program $\min_{x \in R^n} F(x) = G(x) - H(x) + r_1(x) - r_2(x)$, which covers sparse learning with nonconvex penalties, robust regression with smooth robust losses, and non-negative positive--unlabeled learning. We propose \emph{momentum-based DCA} (MDCA), which...
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel Bayesian optimization framework tailored for hyperparameter tuning under uncertaint...
Markov chain Monte Carlo is one of the most useful tools for obtaining samples from complex distributions, such as posterior distributions in Bayesian inference. Bouncy particle sampler (BPS) is a method that performs sampling using uniform linear motion and elastic collisions. Since BPS does not require time discretiz...
Is your company’s AI sovereign? A practical guide for CIOs on AI vendor lock-in, EU Data Act switching, cloud sovereignty, and testing your exit plan before you need it. The post Sovereignty Is the Option to Leave appeared first on GPT-Lab.
