Search Results for author:
Found 26 papers, 2 papers with code
Black-Box $k$-to-$1$-PCA Reductions: Theory and Applications
The $k$-principal component analysis ($k$-PCA) problem is a fundamental algorithmic primitive that is widely-used in data analysis and dimensionality reduction applications.
Testing Calibration in Subquadratic Time
Motivated by [BGHN23], which proposed a rigorous framework for measuring distances to calibration, we initiate the algorithmic study of calibration through the lens of property testing.
Matrix Completion in Almost-Verification Time
In the well-studied setting where $\mathbf{M}$ has incoherent row and column spans, our algorithms complete $\mathbf{M}$ to high precision from $mr^{2+o(1)}$ observations in $mr^{3 + o(1)}$ time (omitting logarithmic factors in problem parameters), improving upon the prior state-of-the-art [JN15] which used $\approx mr^5$ samples and $\approx mr^7$ time.
Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Sampler
The development of efficient sampling algorithms catering to non-Euclidean geometries has been a challenging endeavor, as discretization techniques which succeed in the Euclidean setting do not readily carry over to more general settings.
ReSQueing Parallel and Private Stochastic Convex Optimization
We give a parallel algorithm obtaining optimization error $\epsilon_{\text{opt}}$ with $d^{1/3}\epsilon_{\text{opt}}^{-2/3}$ gradient oracle query depth and $d^{1/3}\epsilon_{\text{opt}}^{-2/3} + \epsilon_{\text{opt}}^{-2}$ gradient queries in total, assuming access to a bounded-variance stochastic gradient estimator.
Private Convex Optimization in General Norms
We propose a new framework for differentially private optimization of convex functions which are Lipschitz in an arbitrary norm $\|\cdot\|$.
Semi-Random Sparse Recovery in Nearly-Linear Time
We design a new iterative method tailored to the geometry of sparse recovery which is provably robust to our semi-random model.
Sharper Rates for Separable Minimax and Finite Sum Optimization via Primal-Dual Extragradient Methods
We generalize our algorithms for minimax and finite sum optimization to solve a natural family of minimax finite sum optimization problems at an accelerated rate, encapsulating both above results up to a logarithmic factor.
Robust Regression Revisited: Acceleration and Improved Estimation Rates
For the general case of smooth GLMs (e. g. logistic regression), we show that the robust gradient descent framework of Prasad et.
Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation
We leverage this result, together with additional techniques, to obtain the first almost-linear time algorithms for clustering mixtures of $k$ separated well-behaved distributions, nearly-matching the statistical guarantees of spectral methods.
Lower Bounds on Metropolized Sampling Methods for Well-Conditioned Distributions
We give lower bounds on the performance of two of the most popular sampling methods in practice, the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator, when applied to well-conditioned distributions.
List-Decodable Mean Estimation in Nearly-PCA Time
Our algorithm runs in time $\widetilde{O}(ndk)$ for all $k = O(\sqrt{d}) \cup \Omega(d)$, where $n$ is the size of the dataset.
Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration
We show that standard extragradient methods (i. e. mirror prox and dual extrapolation) recover optimal accelerated rates for first-order minimization of smooth convex functions.
Structured Logconcave Sampling with a Restricted Gaussian Oracle
For composite densities $\exp(-f(x) - g(x))$, where $f$ has condition number $\kappa$ and convex (but possibly non-smooth) $g$ admits an RGO, we obtain a mixing time of $O(\kappa d \log^3\frac{\kappa d}{\epsilon})$, matching the state-of-the-art non-composite bound; no composite samplers with better mixing than general-purpose logconcave samplers were previously known.
Coordinate Methods for Matrix Games
For linear regression with an elementwise nonnegative matrix, our guarantees improve on exact gradient methods by a factor of $\sqrt{\mathrm{nnz}(A)/(m+n)}$.
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.
Robust Sub-Gaussian Principal Component Analysis and Width-Independent Schatten Packing
We develop two methods for the following fundamental statistical task: given an $\epsilon$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix.
Composite Logconcave Sampling with a Restricted Gaussian Oracle
We consider sampling from composite densities on $\mathbb{R}^d$ of the form $d\pi(x) \propto \exp(-f(x) - g(x))dx$ for well-conditioned $f$ and convex (but possibly non-smooth) $g$, a family generalizing restrictions to a convex set, through the abstraction of a restricted Gaussian oracle.
Logsmooth Gradient Concentration and Tighter Runtimes for Metropolized Hamiltonian Monte Carlo
We show that the gradient norm $\|\nabla f(x)\|$ for $x \sim \exp(-f(x))$, where $f$ is strongly convex and smooth, concentrates tightly around its mean.
A Direct tilde{O}(1/epsilon) Iteration Parallel Algorithm for Optimal Transport
Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two $n$-dimensional distributions, is a fundamental primitive which arises in many learning and statistical settings.
Variance Reduction for Matrix Games
We present a randomized primal-dual algorithm that solves the problem $\min_{x} \max_{y} y^\top A x$ to additive error $\epsilon$ in time $\mathrm{nnz}(A) + \sqrt{\mathrm{nnz}(A)n}/\epsilon$, for matrix $A$ with larger dimension $n$ and $\mathrm{nnz}(A)$ nonzero entries.
A Direct $\tilde{O}(1/ε)$ Iteration Parallel Algorithm for Optimal Transport
Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two distributions, is a fundamental primitive which arises in many learning and statistical settings.
A Rank-1 Sketch for Matrix Multiplicative Weights
We show that a simple randomized sketch of the matrix multiplicative weight (MMW) update enjoys (in expectation) the same regret bounds as MMW, up to a small constant factor.
CoVeR: Learning Covariate-Specific Vector Representations with Tensor Decompositions
However, in addition to the text data itself, we often have additional covariates associated with individual corpus documents---e. g. the demographic of the author, time and venue of publication---and we would like the embedding to naturally capture this information.
Learning Covariate-Specific Embeddings with Tensor Decompositions
In addition to the text data itself, we often have additional covariates associated with individual documents in the corpus---e. g. the demographic of the author, time and venue of publication, etc.---and we would like the embedding to naturally capture the information of the covariates.
Learning Populations of Parameters
Consider the following estimation problem: there are $n$ entities, each with an unknown parameter $p_i \in [0, 1]$, and we observe $n$ independent random variables, $X_1,\ldots, X_n$, with $X_i \sim $ Binomial$(t, p_i)$.
