Related papers: Optimal rates for density and mode estimation with…
For the Gaussian sequence model, we obtain non-asymptotic minimax rates of estimation of the linear, quadratic and the L2-norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates. The main…
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…
Variational Autoencoders (VAEs) are powerful generative models for learning latent representations. Standard VAEs generate dispersed and unstructured latent spaces by utilizing all dimensions, which limits their interpretability, especially…
The semantic matching capabilities of neural information retrieval can ameliorate synonymy and polysemy problems of symbolic approaches. However, neural models' dense representations are more suitable for re-ranking, due to their…
We study sparse principal components analysis in high dimensions, where $p$ (the number of variables) can be much larger than $n$ (the number of observations), and analyze the problem of estimating the subspace spanned by the principal…
In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse…
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…
Learning expressive representations for high-dimensional yet sparse features has been a longstanding problem in information retrieval. Though recent deep learning methods can partially solve the problem, they often fail to handle the…
The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
Sparse representations using data dictionaries provide an efficient model particularly for signals that do not enjoy alternate analytic sparsifying transformations. However, solving inverse problems with sparsifying dictionaries can be…
We study predictive density estimation under Kullback-Leibler loss in $\ell_0$-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. A surprise is the…
We study estimation of an $s$-sparse signal in the $p$-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely the rate scales with respect to…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…
Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…