Related papers: On UMAP's true loss function

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…

Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…

The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an…

The objective of deep metric learning (DML) is to learn embeddings that can capture semantic similarity and dissimilarity information among data points. Existing pairwise or tripletwise loss functions used in DML are known to suffer from…

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

Compressive imaging aims to recover a latent image from under-sampled measurements, suffering from a serious ill-posed inverse problem. Recently, deep neural networks have been applied to this problem with superior results, owing to the…

Two-dimensional data maps can visually reveal information about the relations between data instances. Popular techniques to construct data maps are t-SNE and UMAP. The resulting point-based visualizations, though, provide information only…

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a…

The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which…

Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric…

In this paper, we present SIMAP, a novel layer integrated into deep learning models, aimed at enhancing the interpretability of the output. The SIMAP layer is an enhanced version of Simplicial-Map Neural Networks (SMNNs), an explainable…

Motivation: Network-based analyses of omics data are widely used, and while many of these methods have been adapted to single-cell scenarios, they often remain memory- and space-intensive. As a result, they are better suited to batch data…

Generative Recommendation (GR) has recently transitioned from atomic item-indexing to Semantic ID (SID)-based frameworks to capture intrinsic item relationships and enhance generalization. However, the adoption of high-granularity SIDs…

Machine unlearning poses the challenge of ``how to eliminate the influence of specific data from a pretrained model'' in regard to privacy concerns. While prior research on approximated unlearning has demonstrated accuracy and efficiency in…

The rapid adoption of generative AI has driven an explosion in the size of datasets consumed and produced by AI models. Traditional methods for unstructured data visualization, such as t-SNE and UMAP, have not kept up with the pace of…

Gibbs sampling is a workhorse for Bayesian inference but has several limitations when used for parameter estimation, and is often much slower than non-sampling inference methods. SAME (State Augmentation for Marginal Estimation)…

Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…

Embedding-based neural retrieval is a prevalent approach to address the semantic gap problem which often arises in product search on tail queries. In contrast, popular queries typically lack context and have a broad intent where additional…

Optimising a ranking-based metric, such as Average Precision (AP), is notoriously challenging due to the fact that it is non-differentiable, and hence cannot be optimised directly using gradient-descent methods. To this end, we introduce an…