Related papers: Nonparametric Trace Regression in High Dimensions …

The semantics are derived from textual data that provide representations for Machine Learning algorithms. These representations are interpretable form of high dimensional sparse matrix that are given as an input to the machine learning…

Despite advances in representation learning, high-dimensional classification remains challenging in low-sample-size regimes, where the dominant signal may vary across applications and labeled data are often limited. We propose a…

Constructing good representations is critical for learning complex tasks in a sample efficient manner. In the context of meta-learning, representations can be constructed from common patterns of previously seen tasks so that a future task…

We study the interplay between surrogate methods for structured prediction and techniques from multitask learning designed to leverage relationships between surrogate outputs. We propose an efficient algorithm based on trace norm…

In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

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…

We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

Multi-task representation learning (MTRL) is an approach that learns shared latent representations across related tasks, facilitating collaborative learning that improves the overall learning efficiency. This paper studies MTRL for…

This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding.…

The sequential data observed in earth science can be regarded as paths in multidimensional space. To read the path effectively, it is useful to convert it into a sequence of numbers called the signature, which can faithfully describe the…

We propose trace pursuit for model-free variable selection under the sufficient dimension reduction paradigm. Two distinct algorithms are proposed: stepwise trace pursuit and forward trace pursuit. Stepwise trace pursuit achieves selection…

Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…

Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered.…

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…

Current progress in artificial intelligence is centered around so-called large language models that consist of neural networks processing long sequences of high-dimensional vectors called tokens. Statistical physics provides powerful tools…

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation.…

The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…