Related papers: Archetypal Analysis++: Rethinking the Initializati…
We present PPI++: a computationally lightweight methodology for estimation and inference based on a small labeled dataset and a typically much larger dataset of machine-learning predictions. The methods automatically adapt to the quality of…
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…
K-Means is one of the most used algorithms for data clustering and the usual clustering method for benchmarking. Despite its wide application it is well-known that it suffers from a series of disadvantages; it is only able to find local…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
The role of AI-generated synthetic data has recently been expanded to support realistic Monte Carlo simulations. However, guidance is limited on generating data with multilevel structures and designing simulations based on such data. This…
Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…
Anderson Acceleration (AA) is a popular acceleration technique to enhance the convergence of fixed-point iterations. The analysis of AA approaches typically focuses on the convergence behavior of a corresponding fixed-point residual, while…
The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate rational approximations to given data. While AAA can often produce rational approximations…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
In matrix sensing, we first numerically identify the sensitivity to the initialization rank as a new limitation of the implicit bias of gradient flow. We will partially quantify this phenomenon mathematically, where we establish that the…
This paper aims to address few-shot segmentation. While existing prototype-based methods have achieved considerable success, they suffer from uncertainty and ambiguity caused by limited labeled examples. In this work, we propose attentional…
The identification of black-box nonlinear state-space models requires a flexible representation of the state and output equation. Artificial neural networks have proven to provide such a representation. However, as in many identification…
In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of…
Traditionally, practitioners initialize the {\tt k-means} algorithm with centers chosen uniformly at random. Randomized initialization with uneven weights ({\tt k-means++}) has recently been used to improve the performance over this…
A recent trend in probabilistic inference emphasizes the codification of models in a formal syntax, with suitable high-level features such as individuals, relations, and connectives, enabling descriptive clarity, succinctness and…
Estimation and inference for the Average Treatment Effect (ATE) is a cornerstone of causal inference and often serves as the foundation for developing procedures for more complicated settings. Although traditionally analyzed in a batch…
Matrix trace estimation is ubiquitous in machine learning applications and has traditionally relied on Hutchinson's method, which requires $O(\log(1/\delta)/\epsilon^2)$ matrix-vector product queries to achieve a $(1 \pm…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…