Related papers: Analytical confidence intervals for the number of …

This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled…

Automatic decision and prediction systems are increasingly deployed in applications where they significantly impact the livelihood of people, such as for predicting the creditworthiness of loan applicants or the recidivism risk of…

Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…

Inferring the means in the multivariate normal model $X \sim N_n(\theta, I)$ with unknown mean vector $\theta=(\theta_1,...,\theta_n)' \in \mathbb{R}^n$ and observed data $X=(X_1,...,X_n)'\in {\mathbb R}^n$ is a challenging task, known as…

Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile…

Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence…

In this research paper, we address the Distinct Elements estimation problem in the context of streaming algorithms. The problem involves estimating the number of distinct elements in a given data stream $\mathcal{A} = (a_1, a_2,\ldots,…

Fault tree analysis is a well-known technique in reliability engineering and risk assessment, which supports decision-making processes and the management of complex systems. Traditionally, fault tree (FT) models are built manually together…

We find arithmetic ability resides within a limited number of attention heads, with each head specializing in distinct operations. To delve into the reason, we introduce the Comparative Neuron Analysis (CNA) method, which identifies an…

We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how…

Multi-fidelity methods that use an ensemble of models to compute a Monte Carlo estimator of the expectation of a high-fidelity model can significantly reduce computational costs compared to single-model approaches. These methods use oracle…

This work introduces a novel and efficient Bayesian federated learning algorithm, namely, the Federated Averaging stochastic Hamiltonian Monte Carlo (FA-HMC), for parameter estimation and uncertainty quantification. We establish rigorous…

Collaborative filtering (CF), as a fundamental approach for recommender systems, is usually built on the latent factor model with learnable parameters to predict users' preferences towards items. However, designing a proper CF model for a…

We provide the first provably joint differentially private algorithm with formal utility guarantees for the problem of user-level privacy-preserving collaborative filtering. Our algorithm is based on the Frank-Wolfe method, and it…

A standing challenge in data privacy is the trade-off between the level of privacy and the efficiency of statistical inference. Here we conduct an in-depth study of this trade-off for parameter estimation in the $\beta$-model (Chatterjee,…

We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…

Recent progress in machine learning (ML) has made high-accuracy quantum chemistry (QC) calculations more accessible. Of particular interest are multifidelity machine learning (MFML) methods where training data from differing accuracies or…

This dissertation proves lower bounds on the inherent difficulty of deciding flow analysis problems in higher-order programming languages. We give exact characterizations of the computational complexity of 0CFA, the $k$CFA hierarchy, and…

In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary…

Ratio statistics--such as relative risk and odds ratios--play a central role in hypothesis testing, model evaluation, and decision-making across many areas of machine learning, including causal inference and fairness analysis. However,…