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Post-hoc model-agnostic interpretation methods such as partial dependence plots can be employed to interpret complex machine learning models. While these interpretation methods can be applied regardless of model complexity, they can produce…
Estimating the strength of dependency between two variables is fundamental for exploratory analysis and many other applications in data mining. For example: non-linear dependencies between two continuous variables can be explored with the…
The probabilistic characterization of the relationship between two or more random variables calls for a notion of dependence. Dependence modeling leads to mathematical and statistical challenges, and recent developments in extremal…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex. This dependency complex exposes multi-attribute interactions and enables homological…
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…
This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical…
The ability to remove unwanted dependencies from data is crucial in various domains, including fairness, robust learning, and privacy protection. In this work, we propose an encoder-based approach that learns a representation independent of…
Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. While traditionally studied within Euclidean spaces, contemporary applications…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
In many experimental contexts, it is necessary to statistically remove the impact of instrumental effects in order to physically interpret measurements. This task has been extensively studied in particle physics, where the deconvolution…
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…
Many real-world datasets can be divided into groups according to certain salient features (e.g. grouping images by subject, grouping text by font, etc.). Often, machine learning tasks require that these features be represented separately…
Spectral unmixing is one of the most important quantitative analysis tasks in hyperspectral data processing. Conventional physics-based models are characterized by clear interpretation. However they may not be suitable for analyzing scenes…
Hazard and survival functions are natural, interpretable targets in time-to-event prediction, but their inherent non-additivity fundamentally limits standard additive explanation methods. We introduce Survival Functional Decomposition…
We introduce Matched Machine Learning, a framework that combines the flexibility of machine learning black boxes with the interpretability of matching, a longstanding tool in observational causal inference. Interpretability is paramount in…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
A fundamental challenge in observational causal inference is that assumptions about unconfoundedness are not testable from data. Assessing sensitivity to such assumptions is therefore important in practice. Unfortunately, some existing…