Related papers: MoDaH achieves rate optimal batch correction
An important aspect of large-scale structure data analysis is the presence of non-negligible theoretical uncertainties, which become increasingly important on small scales. We show how to incorporate these uncertainties in realistic power…
Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…
This paper studies the problem of clustering in the two-component Gaussian mixture model where the centers are separated by $2\Delta$ for some $\Delta>0$. We characterize the exact phase transition threshold, given by $$ \bar{\Delta}_n^{2}…
Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
Discrete Collision Detection (DCD) is a fundamental task in several domains including particle-based physics simulations. Efficient DCD uses indexing structures such as Bounding Volume Hierarchy (BVH), but accelerating irregular BVH…
Clustered data arise naturally in many scientific and applied research settings where units are grouped within clusters. They are commonly analyzed using linear mixed models to account for within-cluster correlations. This article focuses…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…
This paper presents a novel adaptation of the Stochastic Gradient Descent (SGD), termed AdaBatchGrad. This modification seamlessly integrates an adaptive step size with an adjustable batch size. An increase in batch size and a decrease in…
Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple…
In this paper, we present enhanced analysis for sign-based optimization algorithms with momentum updates. Traditional sign-based methods, under the separable smoothness assumption, guarantee a convergence rate of $\mathcal{O}(T^{-1/4})$,…
The advantages of adaptive experiments have led to their rapid adoption in economics, other fields, as well as among practitioners. However, adaptive experiments pose challenges for causal inference. This note suggests a BOLS (batched…
Here, we explore the problem of error propagation mitigation in modular digital twins as a sequential decision process. Building on a companion study that used a Hidden Markov Model (HMM) to infer latent error regimes from surrogate-physics…
We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…
Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in…
Conformal inference provides a rigorous statistical framework for uncertainty quantification in machine learning, enabling well-calibrated prediction sets with precise coverage guarantees for any classification model. However, its reliance…
The choice of batch-size in a stochastic optimization algorithm plays a substantial role for both optimization and generalization. Increasing the batch-size used typically improves optimization but degrades generalization. To address the…
In mixture models, anisotropic noise within each cluster is widely present in real-world data. This work investigates both computationally efficient procedures and fundamental statistical limits for clustering in high-dimensional…
We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…