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In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes…
In this paper, within a unified framework of the condition number theory we present the explicit expression of the projected condition number of the equality constrained indefinite least squares problem. By setting specific norms and…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
We introduce several methods for assessing sensitivity to unmeasured confounding in marginal structural models; importantly we allow treatments to be discrete or continuous, static or time-varying. We consider three sensitivity models: a…
Simulation-based problems involving mixed-variable inputs frequently feature domains that are hierarchical, conditional, heterogeneous, or tree-structured. These characteristics pose challenges for data representation, modeling, and…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
The current research has two aims. First, to demonstrate the utility conditional nonparametric multilevel latent class analysis (NP-MLCA) for multi-site program evaluation using an empirical dataset. Second, to investigate how…
Various natural language processing tasks are structured prediction problems where outputs are constructed with multiple interdependent decisions. Past work has shown that domain knowledge, framed as constraints over the output space, can…
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
This paper introduces factored conditional filters, new filtering algorithms for simultaneously tracking states and estimating parameters in high-dimensional state spaces. The conditional nature of the algorithms is used to estimate…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
Computing the first few singular vectors of a large matrix is a problem that frequently comes up in statistics and numerical analysis. Given the presence of noise, exact calculation is hard to achieve, and the following problem is of…
In Constraint Programming, constraints are usually represented as predicates allowing or forbidding combinations of values. However, some algorithms exploit a finer representation: error functions. Their usage comes with a price though: it…
Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation. Sometimes additional information about the variables is known, and incorporating this…
Topological order has been proposed to go beyond Landau symmetry breaking theory for more than twenty years. But it is still a challenging problem to generally detect it in a generic many-body state. In this paper, we will introduce a…
Recent neural network-driven semantic role labeling (SRL) systems have shown impressive improvements in F1 scores. These improvements are due to expressive input representations, which, at least at the surface, are orthogonal to…
We discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice since most point pattern data consist…
Interconnected systems such as power systems and chemical processes are often required to satisfy safety properties in the presence of faults and attacks. Verifying safety of these systems, however, is computationally challenging due to…