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Found 8 papers, 0 papers with code
Optimal Embedding Dimension for Sparse Subspace Embeddings
We use this to construct the first oblivious subspace embedding with $O(d)$ embedding dimension that can be applied faster than current matrix multiplication time, and to obtain an optimal single-pass algorithm for least squares regression.
Exact Matching of Random Graphs with Constant Correlation
Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi graphs marginally, identified with their adjacency matrices.
Random Graph Matching with Improved Noise Robustness
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges.
Restricted Isometry Property under High Correlations
Matrices satisfying the Restricted Isometry Property (RIP) play an important role in the areas of compressed sensing and statistical learning.
Restricted Eigenvalue from Stable Rank with Applications to Sparse Linear Regression
This construction allows incorporating a fixed matrix that has an easily {\em verifiable} condition into the design process, and allows for generation of {\em compressed} design matrices that have a lower storage requirement than a standard design matrix.
Errors-in-variables models with dependent measurements
Under sparsity and restrictive eigenvalue type of conditions, we show that one is able to recover a sparse vector $\beta^* \in \mathbb{R}^m$ from the model given a single observation matrix $X$ and the response vector $y$.
Spectral Norm of Random Kernel Matrices with Applications to Privacy
In this paper, we initiate the study of non-asymptotic spectral theory of random kernel matrices.
High dimensional errors-in-variables models with dependent measurements
Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* + \epsilon \\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$ design matrix with independent subgaussian row vectors, $\epsilon \in \mathbb{R}^f$ is a noise vector and $W$ is a mean zero $f \times m$ random noise matrix with independent subgaussian column vectors, independent of $X_0$ and $\epsilon$.
