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This paper provides a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Reliable outlier detection in high-dimensional data is crucial in modern science, yet it remains a challenging task. Traditional methods often break down in these settings due to their reliance on asymptotic behaviors with respect to sample…

A new dimension reduction methodology for change-point detection in functional means is developed in this paper. The major advantage and novelty of the proposed method is its efficiency in selecting basis functions that capture the change,…

The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…

We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…

In this paper, we present a dual representation of the influence functions, whose computational complexity scales with dataset size rather than model size. Both analytically and experimentally, we show that this representation can be an…

The performance of modern reinforcement learning algorithms critically relies on tuning ever-increasing numbers of hyperparameters. Often, small changes in a hyperparameter can lead to drastic changes in performance, and different…

We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the…

Attribution methods can provide powerful insights into the reasons for a classifier's decision. We argue that a key desideratum of an explanation method is its robustness to input hyperparameters which are often randomly set or empirically…

Many Bayesian inference problems involve high-dimensional models where the performance of standard importance sampling (IS) methods often degrades rapidly as the dimensionality increases. Classical analyses of IS typically rely on the…

Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called…

In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated…

Difference-in-differences is one of the most used identification strategies in empirical work in economics. This chapter reviews a number of important, recent developments related to difference-in-differences. First, this chapter reviews…

In this paper, we conduct performance evaluation for Ultra-Dense Networks (UDNs), and identify which modelling factors play major roles and minor roles. From our study, we draw the following conclusions. First, there are 3 factors/models…

The sensitivity analysis of biological system models can significantly contribute to identifying and explaining influences of internal or external changes on model and its elements. We propose here a comprehensive framework to study…

Language models are commonly fine-tuned via reinforcement learning to alter their behavior or elicit new capabilities. Datasets used for these purposes, and particularly human preference datasets, are often noisy. The relatively small size…

Prototypical network (PN) is a simple yet effective few shot learning strategy. It is a metric-based meta-learning technique where classification is performed by computing Euclidean distances to prototypical representations of each class.…

The behaviors of deep neural networks (DNNs) are notoriously resistant to human interpretations. In this paper, we propose Hypergradient Data Relevance Analysis, or HYDRA, which interprets the predictions made by DNNs as effects of their…

The scores of distance-based outlier detection methods are difficult to interpret, making it challenging to determine a cut-off threshold between normal and outlier data points without additional context. We describe a generic…