Related papers: Intrinsic Dimension Correlation: uncovering nonlin…

The increasing application of deep-learning is accompanied by a shift towards highly non-linear statistical models. In terms of their geometry it is natural to identify these models with Riemannian manifolds. The further analysis of the…

Recent work has found that neural networks with stronger generalization tend to exhibit higher representational alignment with one another across architectures and training paradigms. In this work, we show that models with stronger…

Multimodal deep learning methods capture synergistic features from multiple modalities and have the potential to improve accuracy for stress detection compared to unimodal methods. However, this accuracy gain typically comes from high…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

Multiple modalities can provide more valuable information than single one by describing the same contents in various ways. Hence, it is highly expected to learn effective joint representation by fusing the features of different modalities.…

Multimodal learning has mainly focused on learning large models on, and fusing feature representations from, different modalities for better performances on downstream tasks. In this work, we take a detour from this trend and study the…

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such…

Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…

When pre-processing observational data via matching, we seek to approximate each unit with maximally similar peers that had an alternative treatment status--essentially replicating a randomized block design. However, as one considers a…

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…

In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear(in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

A plethora of networks is being collected in a growing number of fields, including disease transmission, international relations, social interactions, and others. As data streams continue to grow, the complexity associated with these highly…

Recent years have seen rapid progress at the intersection between causality and machine learning. Motivated by scientific applications involving high-dimensional data, in particular in biomedicine, we propose a deep neural architecture for…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

In this study, we measure the Intrinsic Dimension (ID) of token embedding to estimate the intrinsic dimensions of the manifolds spanned by the representations, so as to evaluate their redundancy quantitatively compared to their extrinsic…

Following the recent success of word embeddings, it has been argued that there is no such thing as an ideal representation for words, as different models tend to capture divergent and often mutually incompatible aspects like…

Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…