Related papers: Convex hierarchical testing of interactions
In this paper we develop a novel nonparametric framework to test the independence of two random variables $\mathbf{X}$ and $\mathbf{Y}$ with unknown respective marginals $H(dx)$ and $G(dy)$ and joint distribution $F(dx dy)$, based on {\it…
The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…
We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and…
Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
We investigate a class of methods for selective inference that condition on a selection event. Such methods follow a two-stage process. First, a data-driven (sub)collection of hypotheses is chosen from some large universe of hypotheses.…
Models with many signals, high-dimensional models, often impose structures on the signal strengths. The common assumption is that only a few signals are strong and most of the signals are zero or close (collectively) to zero. However, such…
Bilevel optimization problems involve two nested objectives, where an upper-level objective depends on a solution to a lower-level problem. When the latter is non-convex, multiple critical points may be present, leading to an ambiguous…
Large-scale testing is crucial in pandemic containment, but resources are often prohibitively constrained. We study the optimal application of pooled testing for populations that are heterogeneous with respect to an individual's infection…
As autonomous vehicle technology advances, the precise assessment of safety in complex traffic scenarios becomes crucial, especially in mixed-vehicle environments where human perception of safety must be taken into account. This paper…
An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates…
Network structure optimization is a fundamental task in complex network analysis. However, almost all the research on Bayesian optimization is aimed at optimizing the objective functions with vectorial inputs. In this work, we first present…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
Understanding how features interact with each other is of paramount importance in many scientific discoveries and contemporary applications. Yet interaction identification becomes challenging even for a moderate number of covariates. In…
This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…
Investigating the relation between the structure and behavior of complex biological networks often involves posing the following two questions: Is a hypothesized structure of a regulatory network consistent with the observed behavior? And…
We argue that many general evaluation problems can be viewed through the lens of voting theory. Each task is interpreted as a separate voter, which requires only ordinal rankings or pairwise comparisons of agents to produce an overall…
The domain of metaheuristic optimization has become vibrant due to a flood of new algorithms using a new nature-inspired metaphor but lacking clear methodological novelty. The Criticism behind the development of these algorithms has reached…
Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…
This paper addresses the multiple two-sample test problem in a graph-structured setting, which is a common scenario in fields such as Spatial Statistics and Neuroscience. Each node $v$ in fixed graph deals with a two-sample testing problem…