Search Results for author:
Found 29 papers, 6 papers with code
A Simple and Practical Method for Reducing the Disparate Impact of Differential Privacy
Our theoretical results center on the private mean estimation problem, while our empirical results center on extensive experiments on private data synthesis to demonstrate the effectiveness of stratification on a variety of private mechanisms.
Improved Active Learning via Dependent Leverage Score Sampling
We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage.
Moments, Random Walks, and Limits for Spectrum Approximation
We study lower bounds for the problem of approximating a one dimensional distribution given (noisy) measurements of its moments.
Dimensionality Reduction for General KDE Mode Finding
There has been particular interest in efficient methods for solving the problem when $D$ is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known.
Active Learning for Single Neuron Models with Lipschitz Non-Linearities
Namely, we can collect samples via statistical \emph{leverage score sampling}, which has been shown to be near-optimal in other active learning scenarios.
Active Linear Regression for $\ell_p$ Norms and Beyond
By combining this with our techniques for $\ell_p$ regression, we obtain an active regression algorithm making $\tilde O(d^{1+\max\{1, p/2\}}/\mathrm{poly}(\epsilon))$ queries for such loss functions, including the Tukey and Huber losses, answering another question of [CD21].
Correlation Sketches for Approximate Join-Correlation Queries
The increasing availability of structured datasets, from Web tables and open-data portals to enterprise data, opens up opportunities~to enrich analytics and improve machine learning models through relational data augmentation.
The Statistical Cost of Robust Kernel Hyperparameter Turning
This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise.
Hutch++: Optimal Stochastic Trace Estimation
This improves on the ubiquitous Hutchinson's estimator, which requires $O(1/\epsilon^2)$ matrix-vector products.
Fast and Near-Optimal Diagonal Preconditioning
In this paper, we revisit the decades-old problem of how to best improve $\mathbf{A}$'s condition number by left or right diagonal rescaling.
Graph Learning for Inverse Landscape Genetics
Our main contribution is an efficient algorithm for \emph{inverse landscape genetics}, which is the task of inferring this graph from measurements of genetic similarity at different locations (graph nodes).
The Statistical Cost of Robust Kernel Hyperparameter Tuning
This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise.
Fourier Sparse Leverage Scores and Approximate Kernel Learning
Bounding Fourier sparse leverage scores under various measures is of pure mathematical interest in approximation theory, and our work extends existing results for the uniform measure [Erd17, CP19a].
Projection-Cost-Preserving Sketches: Proof Strategies and Constructions
In this note we illustrate how common matrix approximation methods, such as random projection and random sampling, yield projection-cost-preserving sketches, as introduced in [FSS13, CEM+15].
Sample Efficient Toeplitz Covariance Estimation
In addition to results that hold for any Toeplitz $T$, we further study the important setting when $T$ is close to low-rank, which is often the case in practice.
Simple Heuristics Yield Provable Algorithms for Masked Low-Rank Approximation
In particular, for rank $k' > k$ depending on the $public\ coin\ partition\ number$ of $W$, the heuristic outputs rank-$k'$ $L$ with cost$(L) \leq OPT + \epsilon \|A\|_F^2$.
A Universal Sampling Method for Reconstructing Signals with Simple Fourier Transforms
We formalize this intuition by showing that, roughly, a continuous signal from a given class can be approximately reconstructed using a number of samples proportional to the *statistical dimension* of the allowed power spectrum of that class.
Inferring Networks From Random Walk-Based Node Similarities
In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i. e., commute times) or personalized PageRank scores.
Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees
Qualitatively, our results are twofold: on the one hand, we show that random Fourier feature approximation can provably speed up kernel ridge regression under reasonable assumptions.
Learning Networks from Random Walk-Based Node Similarities
In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i. e., commute times) or personalized PageRank scores.
Minimizing Polarization and Disagreement in Social Networks
We perform an empirical study of our proposed methods on synthetic and real-world data that verify their value as mining tools to better understand the trade-off between of disagreement and polarization.
Recursive Sampling for the Nystrom Method
We give the first algorithm for kernel Nystrom approximation that runs in linear time in the number of training points and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions.
Stability of the Lanczos Method for Matrix Function Approximation
In exact arithmetic, the method's error after $k$ iterations is bounded by the error of the best degree-$k$ polynomial uniformly approximating $f(x)$ on the range $[\lambda_{min}(A), \lambda_{max}(A)]$.
Data Structures and Algorithms Numerical Analysis
Recursive Sampling for the Nyström Method
We give the first algorithm for kernel Nystr\"om approximation that runs in *linear time in the number of training points* and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions.
Principal Component Projection Without Principal Component Analysis
To achieve our results, we first observe that ridge regression can be used to obtain a "smooth projection" onto the top principal components.
Input Sparsity Time Low-Rank Approximation via Ridge Leverage Score Sampling
Our method is based on a recursive sampling scheme for computing a representative subset of $A$'s columns, which is then used to find a low-rank approximation.
Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition
We give the first provable runtime improvement on Simultaneous Iteration: a simple randomized block Krylov method, closely related to the classic Block Lanczos algorithm, gives the same guarantees in just $\tilde{O}(1/\sqrt{\epsilon})$ iterations and performs substantially better experimentally.
Dimensionality Reduction for k-Means Clustering and Low Rank Approximation
We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error.
Uniform Sampling for Matrix Approximation
In addition to an improved understanding of uniform sampling, our main proof introduces a structural result of independent interest: we show that every matrix can be made to have low coherence by reweighting a small subset of its rows.
