相关论文: Analysis vs. synthesis sparsity for $\alpha$-shear…

Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an…

Shearlet systems have been introduced as directional representation systems, which provide optimally sparse approximations of a certain model class of functions governed by anisotropic features while allowing faithful numerical realizations…

We present a sparse analogue to stochastic gradient descent that is guaranteed to perform well under similar conditions to the lasso. In the linear regression setup with irrepresentable noise features, our algorithm recovers the support set…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…

In this paper we present the framework of symmetry in nonparametric regression. This generalises the framework of covariate sparsity, where the regression function depends only on at most $s < d$ of the covariates, which is a special case…

In Artificial Intelligence, interpreting the results of a Machine Learning technique often termed as a black box is a difficult task. A counterfactual explanation of a particular "black box" attempts to find the smallest change to the input…

Sparse attention reduces the quadratic complexity of full self-attention but faces two challenges: (1) an attention gap, where applying sparse attention to full-attention-trained models causes performance degradation due to train-inference…

We introduce the Sparsity Roofline, a visual performance model for evaluating sparsity in neural networks. The Sparsity Roofline jointly models network accuracy, sparsity, and theoretical inference speedup. Our approach does not require…

The main contribution of this paper is a mathematical definition of statistical sparsity, which is expressed as a limiting property of a sequence of probability distributions. The limit is characterized by an exceedance measure~$H$ and a…

Frame is the corner stone for designing decomposition and reconstruction operations in signal processing. Famous frames include wavelets, curvelets,and Gabor. A celebrated result indicates that if a synthesis frame is chosen for…

We construct a classifier which attains the rate of convergence $\log n/n$ under sparsity and margin assumptions. An approach close to the one met in approximation theory for the estimation of function is used to obtain this result. The…

This paper considers the sample-efficiency of preference learning, which models and predicts human choices based on comparative judgments. The minimax optimal estimation error rate $\Theta(d/n)$ in classical estimation theory requires that…

The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest…

While CNNs naturally lend themselves to densely sampled data, and sophisticated implementations are available, they lack the ability to efficiently process sparse data. In this work we introduce a suite of tools that exploit sparsity in…

Analysis sparsity is a common prior in inverse problem or machine learning including special cases such as Total Variation regularization, Edge Lasso and Fused Lasso. We study the geometry of the solution set (a polyhedron) of the analysis…

Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…

Discrepancy theory provides powerful tools for producing higher-quality objects which "beat the union bound" in fundamental settings throughout combinatorics and computer science. However, this quality has often come at the price of more…

Finding a basis/coordinate system that can efficiently represent an input data stream by viewing them as realizations of a stochastic process is of tremendous importance in many fields including data compression and computational…