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Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…
Outlier or anomaly detection is an important task in data analysis. We discuss the problem from a geometrical perspective and provide a framework that exploits the metric structure of a data set. Our approach rests on the manifold…
Learning representations for pixel-based control has garnered significant attention recently in reinforcement learning. A wide range of methods have been proposed to enable efficient learning, leading to sample complexities similar to those…
Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
With the rise of large language models (LLMs) for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric…
Developing an understanding of high-dimensional data can be facilitated by visualizing that data using dimensionality reduction. However, the low-dimensional embeddings are often difficult to interpret. To facilitate the exploration and…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the…
High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
In the realm of visual recognition, data augmentation stands out as a pivotal technique to amplify model robustness. Yet, a considerable number of existing methodologies lean heavily on heuristic foundations, rendering their intrinsic…
Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches…
Non-linear dimensionality reduction (NDR) methods such as LLE and t-SNE are popular with visualization researchers and experienced data analysts, but present serious problems of interpretation. In this paper, we present DimReader, a…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
Sensor data analysis plays a key role in health assessment of critical equipment. Such data are multivariate and exhibit nonlinear relationships. This paper describes how one can exploit nonlinear dimension reduction techniques, such as the…
Supervised (linear) embedding models like Wsabie and PSI have proven successful at ranking, recommendation and annotation tasks. However, despite being scalable to large datasets they do not take full advantage of the extra data due to…
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
Low-dimensional projections of text embeddings support visual analysis of document collections, but their spatial organization may not reflect the relationships an analyst intends to examine. Existing semantic interaction approaches encode…
Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features.…