Related papers: Stable Sparse Subspace Embedding for Dimensionalit…
In the era of large foundation models, the quality of embeddings has become a central determinant of downstream task performance and overall system capability. Yet widely used dense embeddings are often extremely high-dimensional, incurring…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
We consider the smoothed version of sliced average variance estimation (SAVE) dimension reduction method for dealing with spatially dependent data that are observations of a strongly mixing random field. We propose kernel estimators for the…
$t$-SNE is an embedding method that the data science community has widely Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space…
Different unsupervised models for dimensionality reduction like PCA, LLE, Shannon's mapping, tSNE, UMAP, etc. work on different principles, hence, they are difficult to compare on the same ground. Although they are usually good for…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We propose a probabilistic framework for interpreting and developing hard thresholding sparse signal reconstruction methods and present several new algorithms based on this framework. The measurements follow an underdetermined linear model,…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt…
Standard Adjacency Spectral Embedding (ASE) relies on a global low-rank assumption often incompatible with the sparse, transitive structure of real-world networks, causing local geometric features to be 'smeared'. To address this, we…
Parametric embedding methods such as parametric t-SNE (pt-SNE) have been widely adopted for data visualization and out-of-sample data embedding without further computationally expensive optimization or approximation. However, the…
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…
For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach…
Continual Reinforcement Learning (CRL) is essential for developing agents that can learn, adapt, and accumulate knowledge over time. However, a fundamental challenge persists as agents must strike a delicate balance between plasticity,…
Recently sparse coding have been highly successful in image classification mainly due to its capability of incorporating the sparsity of image representation. In this paper, we propose an improved sparse coding model based on linear spatial…
In this paper, redundant random matrix ensembles (abbreviated as redundant random ensembles) are defined and their stopping set (SS) weight distributions are analyzed. A redundant random ensemble consists of a set of binary matrices with…
We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such…
We propose a versatile framework based on random search, Sparse-RS, for score-based sparse targeted and untargeted attacks in the black-box setting. Sparse-RS does not rely on substitute models and achieves state-of-the-art success rate and…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
Sparse linear regression is one of the classic problems in the field of statistics, which has deep connections and high intersections with optimization, computation, and machine learning. To address the effective handling of…