Related papers: Distance Assessment and Hypothesis Testing of High…

The paper demonstrates the use of variational autoencoders for graphical representation of a large database containing process-microstructure relationships. Correlating microstructural features to processing is an essential first step to…

A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…

Neural networks are powerful predictive models, but they provide little insight into the nature of relationships between predictors and outcomes. Although numerous methods have been proposed to quantify the relative contributions of input…

In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…

Unsupervised learning-based anomaly detection in latent space has gained importance since discriminating anomalies from normal data becomes difficult in high-dimensional space. Both density estimation and distance-based methods to detect…

Wireless signal strength based localization can enable robust localization for robots using inexpensive sensors. For this, a location-to-signal-strength map has to be learned for each access point in the environment. Due to the ubiquity of…

Data augmentation is an essential technique for improving recognition accuracy in object recognition using deep learning. Methods that generate mixed data from multiple data sets, such as mixup, can acquire new diversity that is not…

The goal of anomaly detection is to identify examples that deviate from normal or expected behavior. We tackle this problem for images. We consider a two-phase approach. First, using normal examples, a convolutional autoencoder (CAE) is…

In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…

We present a method which tests whether or not two datasets (one of which could be Monte Carlo generated) might come from the same distribution. Our method works in arbitrarily high dimensions.

In machine learning, the performance of a classifier depends on both the classifier model and the separability/complexity of datasets. To quantitatively measure the separability of datasets, we create an intrinsic measure -- the…

Network data is a major object data type that has been widely collected or derived from common sources such as brain imaging. Such data contains numeric, topological, and geometrical information, and may be necessarily considered in certain…

This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…

In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…

Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…

Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…

Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…

Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…

Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of…