A new method for estimating large-scale linear models with improved precision.
problem Estimating large-scale linear statistical models efficiently.
method Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), integrating Sketch-and-Solve and Iterative-Sketching methods.
result SLSE-FRS produces high-precision estimators, outperforming state-of-the-art methods.
New analysis proves sketching operators' RIP guarantees for mixture models without importance sampling.
problem Proving sketching operators' Restricted Isometry Property (RIP) for mixture models without assuming importance sampling.
method Proposed alternative analysis based on new deterministic bounds and concentration inequalities.
result Theoretical guarantees for sketching operators without importance sampling.
The paper sharpens the analysis of sketch-and-project methods using randomized singular value decomposition.
problem Improving convergence rates of sketch-and-project methods for solving linear systems and non-linear optimization problems.
method Developing a theoretical framework and new spectral bounds for the expected sketched projection matrix.
result The convergence rate improves linearly with sketch size and even faster with certain spectral decays.
Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation when the number of observations greatly exceeds the number of variables. In this p…
A new method improves convergence in low-rank approximation.
problem Efficiently solving large-scale numerical linear algebra problems.
method Error-Powered Sketched Inverse Iteration (EPSI) Method.
result Convergence rate improves at least linearly with sketch size.
Matrix sketching balances class sizes for better supervised classification performance.
problem Class imbalance in supervised classification leads to poor performance.
method Matrix sketching using random projections to rebalance class sizes.
result Rebalanced classes improve classification performance, especially for minority classes.
Unified bounds for sketched bilinear forms in machine learning and statistics.
problem Uniform bounds on sketched bilinear forms for modern analyses.
method Generic chaining and new techniques for handling suprema over pairs of sets.
result Improved convergence bounds for sketched Federated Learning and bandit algorithms.
Paper develops a method for estimating PFLM with minimized rates in high dimensions.
problem Estimating PFLM with minimized rates in high dimensions.
method Least square approach with mixed regularizations of function-norm and ℓ1-norm.
result Established optimal minimax rates of estimation for PFLM.
We consider statistical and algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. Prior results show that, from an \emph{algorithmic perspective}, when using sketching matrices constructed from random projections and leverage-score sampling, if the number of sampl…
New method solves constrained optimization problems efficiently.
problem Equality-constrained nonlinear, nonconvex optimization problems.
method Adaptive inexact Newton method with randomized iterative sketching.
result Global almost sure convergence and local linear/superlinear convergence.
Corrects bias in random sampling matrices for improved ML methods.
problem Inversion bias in random sampling matrices hampers ML applications.
method Corrects inversion bias for various random sampling methods.
result Establishes local convergence rates for sub-sampled Newton methods.
The paper analyzes sketching methods for regression, showing SRHT is superior.
problem Improving regression accuracy with sketching methods.
method Randomly projecting data and then performing regression.
result SRHT outperforms Gaussian projections in asymptotic analysis.
A new method reduces the cost of solving large-scale linear models.
problem Solving large-scale linear statistical models efficiently.
method Sequential Preconditioned Conjugate Gradient Method (SPCG).
result SPCG achieves OLS prediction accuracy with fewer iterations and less time.
The paper provides theoretical guarantees for hashing-based neural net compression.
problem Rigorous theoretical guarantees on neural net compression methods.
method Random linear sketching and HashedNets architecture.
result Provable guarantees on the performance of hashing-based neural net compression.
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, wi…
New method reduces linear regret in high-dimensional bandit problems.
problem Heavy spectral tails in streaming matrices lead to linear regret in sketch-based linear bandits.
method Dyadic Block Sketching, a multi-scale matrix sketching approach.
result Achieves sublinear regret bounds without prior knowledge of streaming matrix properties.
We consider statistical as well as algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data (X,Y)∈Rn×p×Rn, sketching algorithms use a sketching matrix, S∈Rr×n with $r \…
We accelerate the power method for strong low-rank approximation using fast sketching.
problem Efficiency bottleneck in power method for large target ranks.
method Developed an algorithmic and theoretical framework for accelerating the power method using fast sketching.
result Simple and provably efficient methods for singular value decomposition, low-rank factorization, and Nyström approximation.
A simple sketch improves online eigenvector and SDP problems.
problem Online eigenvector and semidefinite programming problems.
method Randomized mirror projection and mirror descent analysis.
result Regret bounds similar to MMW with reduced complexity.
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. T…
A new sketching method reduces tensor memory usage and enables efficient tensor operations.
problem Efficiently compressing and retaining tensor structure in large datasets.
method Higher-order Count Sketch (HCS) using multiple hash functions and tensor products.
result HCS achieves significant memory savings and efficient tensor operations.
Bagging stabilizes linear interpolators, improving their generalization performance.
problem Unstable linear interpolators fail on noisy data.
method Introduced multiplier-bootstrap-based bagged least square estimator.
result Bagging effectively mitigates variance, leading to bounded prediction risk.
Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study sketching from an optimization point of view: we first show that the iterative Hessia…
We improve prediction risk estimation for large datasets using sketching and ridge regression.
problem Estimating prediction risks for large datasets efficiently and accurately.
method Random matrix theory, generalized cross validation, sketched ridge regression ensembles, and ensemble trick.
result Consistent risk estimation and prediction intervals for large-scale datasets.
Newton-LESS sparsifies Gaussian sketching for faster optimization.
problem Computing the Hessian matrix in optimization is computationally expensive.
method Uses a sparsified version of a dense Gaussian sketching matrix.
result Achieves nearly the same convergence rate as dense Gaussian embeddings without the computational cost.
Private sketches protect linear regression data privacy.
problem Protecting sensitive information in linear regression.
method Release private sketches of datasets, compute approximate solutions.
result Private sketches maintain good approximation guarantees to the original problem.
Develops precise expressions for random projections for better machine learning tasks.
problem Improving the accuracy of dimensionality reduction in machine learning tasks.
method Exploits recent developments in spectral analysis of random matrices to derive accurate expressions for random projection matrices.
result Provides precise expressions that reflect the practical performance of sketching methods, including Gaussian and Rademacher sketches.
Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. We study two forms of sketching that…
Sublinear memory sketch finds nearest neighbors in streaming data.
problem Finding nearest neighbors in large datasets with limited memory.
method Combines LSH, online kernel density estimation, and compressed sensing to achieve sublinear memory.
result Achieves sublinear memory performance on stable queries, reporting nearest neighbors efficiently.
A new method reduces the complexity of tensor products from cubic to quadratic, improving both speed and accuracy.
problem Efficiently computing high-dimensional tensor products for polynomial kernels.
method Complex-to-Real (CtR) modification of sketches using complex random projections.
result Achieves state-of-the-art performance in accuracy and speed.
The paper shows how sketching data can simplify regression inference even when errors are heteroskedastic.
problem Performing robust inference with heteroskedastic errors using sketched data.
method Using random projections to sketch data, the paper shows that sketched estimates behave as if errors are homoskedastic.
result Estimation by random sampling does not have the same property, and sketched estimates are asymptotically normal with homoskedastic variance.
New algorithm converts data into sub-gaussian designs efficiently.
problem Efficiently converting large datasets into sub-gaussian random designs for robust performance.
method Algorithmic Gaussianization through sketching and averaging, using LESS embeddings.
result Efficient data sketches nearly indistinguishable from sub-gaussian designs.
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables memory-limited execution of several statistical analyses over streams, including online featu…
Improved estimator for least squares using random projections achieves smaller error.
problem Improving the accuracy of least squares solutions for large-scale problems.
method James-Stein estimator applied to Gaussian sketching of least squares problems.
result Upper and lower bounds match when SNR is small and data matrix is well-conditioned.
Paper proposes Nyström sketches for better adaptive compressive learning.
problem Improving adaptability of sketching for compressive learning.
method Data-dependent Nyström approximation for mean embedding.
result Excess risk can be controlled with geometric assumption.
New method improves Gaussian kernel approximations for high-frequency data.
problem Limited scalability of kernel-based models to large data sets.
method Local random feature approximations using Maclaurin expansions and polynomial sketches.
result Significant improvement in kernel approximations and downstream performance for high-frequency data.
Projection-cost preservation is a low-rank approximation guarantee which ensures that the cost of any rank-k projection can be preserved using a smaller sketch of the original data matrix. We present a general structural result outlining four sufficient conditions to achieve projection-cost preservation. These condit…
New algorithm reduces rank constrained optimization problems.
problem Rank constrained optimization problems in machine learning and statistics.
method Recursive Importance Sketching (RISRO) algorithm.
result RISRO offers clear advantages over existing algorithms and converges efficiently.
Improved sketching for logistic and ℓ1 regression with near-linear dimensions.
problem Efficiently approximate ℓ1 and logistic regression problems. method New sketching techniques achieving near-linear dimensions for both problems.
result Achieved near-linear sketching dimensions for ℓ1 and logistic regression. Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given n samples, the time and space complexity of computing the KRR estimate scale as O(n3) and O(n2) respectively, and so is prohibitive in many cases. We prop…
A fast sketching algorithm solves regularized least squares problems efficiently.
problem Solving large-scale optimization problems with convex or nonconvex regularization.
method Sketching for Regularized Optimization (SRO) algorithm that generates a sketch of the original data matrix and solves the sketched problem.
result General theoretical results for the approximation error between the original and sketched problems, including minimax rates for sparse signal estimation.
Unified methodology for statistical inference in least squares and PCA via randomized sketching.
problem Statistical inference in least squares and PCA problems.
method Randomized sketching and projections, asymptotic normality of quadratic forms.
result Unified statistical inference methods for various sketching distributions.
DBCL defends collaborative learning by sketching parameters to prevent gradient-based privacy inference attacks.
problem Privacy leaks in collaborative machine learning due to gradient-based attacks.
method Random matrix sketching applied to parameters, followed by re-generation of sketching after each iteration.
result DBCL prevents effective gradient-based privacy inference attacks without significant computational or accuracy costs.
This paper compresses large datasets for efficient machine learning.
problem Efficiently processing large datasets for machine learning.
method Constructing a sketch of the dataset using random features and averaging, then learning from the sketch.
result The approach can perform machine learning tasks without full dataset access, preserving both information and privacy.
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-speci…
We consider the problem of finding anomalies in high-dimensional data using popular PCA based anomaly scores. The naive algorithms for computing these scores explicitly compute the PCA of the covariance matrix which uses space quadratic in the dimensionality of the data. We give the first streaming algorithms that use …
Bayesian data sketching speeds up inference for large functional data.
problem Slow posterior computations in Bayesian varying coefficient models for large data.
method Compress functional response and predictor matrix using random linear transformation.
result Fully model-based Bayesian inference on compressed data.
Improved ridge regression with Frequent Directions for large-scale tasks.
problem Improving performance of ridge regression for large-scale data.
method Combines Frequent Directions with iterative optimization schemes.
result Achieves high accuracy in estimating bias and variance for sketched ridge regression.