Search Results for author:
Found 24 papers, 2 papers with code
Faster Sublinear Algorithms using Conditional Sampling
In contrast to prior algorithms for the classic model, our algorithms have time, space and sample complexity that is polynomial in the dimension and polylogarithmic in the number of points.
Ten Steps of EM Suffice for Mixtures of Two Gaussians
In the finite sample regime, we show that, under a random initialization, $\tilde{O}(d/\epsilon^2)$ samples suffice to compute the unknown vectors to within $\epsilon$ in Mahalanobis distance, where $d$ is the dimension.
A Converse to Banach's Fixed Point Theorem and its CLS Completeness
Our first result is a strong converse of Banach's theorem, showing that it is a universal analysis tool for establishing global convergence of iterative methods to unique fixed points, and for bounding their convergence rate.
Efficient Statistics, in High Dimensions, from Truncated Samples
We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples.
Optimal Learning of Mallows Block Model
The main result of the paper is a tight sample complexity bound for learning Mallows and Generalized Mallows Model.
Efficient Truncated Statistics with Unknown Truncation
Our main result is a computationally and sample efficient algorithm for estimating the parameters of the Gaussian under arbitrary unknown truncation sets whose performance decays with a natural measure of complexity of the set, namely its Gaussian surface area.
Constant-Expansion Suffices for Compressed Sensing with Generative Priors
Using this theorem we can show that a matrix concentration inequality known as the Weight Distribution Condition (WDC), which was previously only known to hold for Gaussian matrices with logarithmic aspect ratio, in fact holds for constant aspect ratios too.
Estimation and Inference with Trees and Forests in High Dimensions
We prove that if only $r$ of the $d$ features are relevant for the mean outcome function, then shallow trees built greedily via the CART empirical MSE criterion achieve MSE rates that depend only logarithmically on the ambient dimension $d$.
Truncated Linear Regression in High Dimensions
As a corollary, our guarantees imply a computationally efficient and information-theoretically optimal algorithm for compressed sensing with truncation, which may arise from measurement saturation effects.
The Complexity of Constrained Min-Max Optimization
In this paper, we provide a characterization of the computational complexity of the problem, as well as of the limitations of first-order methods in constrained min-max optimization problems with nonconvex-nonconcave objectives and linear constraints.
Computationally and Statistically Efficient Truncated Regression
We provide a computationally and statistically efficient estimator for the classical problem of truncated linear regression, where the dependent variable $y = w^T x + \epsilon$ and its corresponding vector of covariates $x \in R^k$ are only revealed if the dependent variable falls in some subset $S \subseteq R$; otherwise the existence of the pair $(x, y)$ is hidden.
Optimal Approximation -- Smoothness Tradeoffs for Soft-Max Functions
A soft-max function has two main efficiency measures: (1) approximation - which corresponds to how well it approximates the maximum function, (2) smoothness - which shows how sensitive it is to changes of its input.
Robust Learning of Optimal Auctions
The proposed algorithms operate beyond the setting of bounded distributions that have been studied in prior works, and are guaranteed to obtain a fraction $1-O(\alpha)$ of the optimal revenue under the true distribution when the distributions are MHR.
Last-Iterate Convergence of Saddle-Point Optimizers via High-Resolution Differential Equations
However, the convergence properties of these methods are qualitatively different, even on simple bilinear games.
First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems
We consider the problem of computing an equilibrium in a class of \textit{nonlinear generalized Nash equilibrium problems (NGNEPs)} in which the strategy sets for each player are defined by equality and inequality constraints that may depend on the choices of rival players.
Estimation of Standard Auction Models
We provide efficient estimation methods for first- and second-price auctions under independent (asymmetric) private values and partial observability.
What Makes A Good Fisherman? Linear Regression under Self-Selection Bias
In known-index self-selection, the identity of the observed model output is observable; in unknown-index self-selection, it is not.
Efficient Truncated Linear Regression with Unknown Noise Variance
In this paper, we provide the first computationally and statistically efficient estimators for truncated linear regression when the noise variance is unknown, estimating both the linear model and the variance of the noise.
STay-ON-the-Ridge: Guaranteed Convergence to Local Minimax Equilibrium in Nonconvex-Nonconcave Games
In particular, our method is not designed to decrease some potential function, such as the distance of its iterate from the set of local min-max equilibria or the projected gradient of the objective, but is designed to satisfy a topological property that guarantees the avoidance of cycles and implies its convergence.
Learning and Covering Sums of Independent Random Variables with Unbounded Support
In this work, we address two questions: (i) Are there general families of SIIRVs with unbounded support that can be learned with sample complexity independent of both $n$ and the maximal element of the support?
Deterministic Nonsmooth Nonconvex Optimization
In particular, we prove a lower bound of $\Omega(d)$ for any deterministic algorithm.
The Computational Complexity of Finding Stationary Points in Non-Convex Optimization
Finding approximate stationary points, i. e., points where the gradient is approximately zero, of non-convex but smooth objective functions $f$ over unrestricted $d$-dimensional domains is one of the most fundamental problems in classical non-convex optimization.
Tree of Attacks: Jailbreaking Black-Box LLMs Automatically
In this work, we present Tree of Attacks with Pruning (TAP), an automated method for generating jailbreaks that only requires black-box access to the target LLM.
Transfer Learning Beyond Bounded Density Ratios
We also provide a discrete analogue of our transfer inequality on the Boolean Hypercube $\{-1, 1\}^n$, and study its connections with the recent problem of Generalization on the Unseen of Abbe, Bengio, Lotfi and Rizk (ICML, 2023).
