Related papers: Dictionary-based Manifold Learning
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…
In this paper, we propose a supervised dictionary learning algorithm that aims to preserve the local geometry in both dimensions of the data. A graph-based regularization explicitly takes into account the local manifold structure of the…
Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…
Learning an explainable classifier often results in low accuracy model or ends up with a huge rule set, while learning a deep model is usually more capable of handling noisy data at scale, but with the cost of hard to explain the result and…
Visual data is used in numerous different scientific workflows ranging from remote sensing to ecology. As the amount of observation data increases, the challenge is not just to make accurate predictions but also to understand the underlying…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
Manifold hypotheses are typically used for tasks such as dimensionality reduction, interpolation, or improving classification performance. In the less common problem of manifold estimation, the task is to characterize the geometric…
Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and geometrical…
Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a…
Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…
Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…
The advent of big data has vast potential for discovery in natural phenomena ranging from climate science to medicine, but overwhelming complexity stymies insight. Existing theory is often not able to succinctly describe salient phenomena,…
We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between…
Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited…
We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any…
Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…
Gradient-based interpretations often require an anchor point of comparison to avoid saturation in computing feature importance. We show that current baselines defined using static functions--constant mapping, averaging or blurring--inject…
We are interested in derivative-free optimization of high-dimensional functions. The sample complexity of existing methods is high and depends on problem dimensionality, unlike the dimensionality-independent rates of first-order methods.…
Sparse dictionary learning (DL) has emerged as a powerful approach to extract semantically meaningful concepts from the internals of large language models (LLMs) trained mainly in the text domain. In this work, we explore whether DL can…
Machine Learning algorithms are good tools for both classification and prediction purposes. These algorithms can further be used for scientific discoveries from the enormous data being collected in our era. We present ways of discovering…