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Found 18 papers, 2 papers with code
Statistical Barriers to Affine-equivariant Estimation
We investigate the quantitative performance of affine-equivariant estimators for robust mean estimation.
Diagnosing Transformers: Illuminating Feature Spaces for Clinical Decision-Making
These findings showcase the utility of SUFO in enhancing trust and safety when using transformers in medicine, and we believe SUFO can aid practitioners in evaluating fine-tuned language models for other applications in medicine and in more critical domains.
Optimal PAC Bounds Without Uniform Convergence
In this paper, we address this issue by providing optimal high probability risk bounds through a framework that surpasses the limitations of uniform convergence arguments.
The One-Inclusion Graph Algorithm is not Always Optimal
In one of the first COLT open problems, Warmuth conjectured that this prediction strategy always implies an optimal high probability bound on the risk, and hence is also an optimal PAC algorithm.
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.
Estimation of Standard Auction Models
We provide efficient estimation methods for first- and second-price auctions under independent (asymmetric) private values and partial observability.
Uniform Approximations for Randomized Hadamard Transforms with Applications
We use our inequality to then derive improved guarantees for two applications in the high-dimensional regime: 1) kernel approximation and 2) distance estimation.
Terminal Embeddings in Sublinear Time
\end{equation*} When $X, Y$ are both Euclidean metrics with $Y$ being $m$-dimensional, recently (Narayanan, Nelson 2019), following work of (Mahabadi, Makarychev, Makarychev, Razenshteyn 2018), showed that distortion $1+\epsilon$ is achievable via such a terminal embedding with $m = O(\epsilon^{-2}\log n)$ for $n := |T|$.
Adversarial Examples in Multi-Layer Random ReLU Networks
We consider the phenomenon of adversarial examples in ReLU networks with independent gaussian parameters.
A single gradient step finds adversarial examples on random two-layers neural networks
Daniely and Schacham recently showed that gradient descent finds adversarial examples on random undercomplete two-layers ReLU neural networks.
Optimal Mean Estimation without a Variance
Concretely, given a sample $\mathbf{X} = \{X_i\}_{i = 1}^n$ from a distribution $\mathcal{D}$ over $\mathbb{R}^d$ with mean $\mu$ which satisfies the following \emph{weak-moment} assumption for some ${\alpha \in [0, 1]}$: \begin{equation*} \forall \|v\| = 1: \mathbb{E}_{X \thicksim \mathcal{D}}[\lvert \langle X - \mu, v\rangle \rvert^{1 + \alpha}] \leq 1, \end{equation*} and given a target failure probability, $\delta$, our goal is to design an estimator which attains the smallest possible confidence interval as a function of $n, d,\delta$.
On Adaptive Distance Estimation
Our memory consumption is $\tilde O((n+d)d/\epsilon^2)$, slightly more than the $O(nd)$ required to store $X$ in memory explicitly, but with the benefit that our time to answer queries is only $\tilde O(\epsilon^{-2}(n + d))$, much faster than the naive $\Theta(nd)$ time obtained from a linear scan in the case of $n$ and $d$ very large.
Data Structures and Algorithms
Optimal Robust Linear Regression in Nearly Linear Time
We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \langle X, w^* \rangle + \epsilon$ (with $X \in \mathbb{R}^d$ and $\epsilon$ independent), in which an $\eta$ fraction of the samples have been adversarially corrupted.
Fast Mean Estimation with Sub-Gaussian Rates
We propose an estimator for the mean of a random vector in $\mathbb{R}^d$ that can be computed in time $O(n^4+n^2d)$ for $n$ i. i. d.~samples and that has error bounds matching the sub-Gaussian case.
Nearly Optimal Robust Matrix Completion
Finally, an application of our result to the robust PCA problem (low-rank+sparse matrix separation) leads to nearly linear time (in matrix dimensions) algorithm for the same; existing state-of-the-art methods require quadratic time.
Thresholding based Efficient Outlier Robust PCA
That is, given a data matrix $M^*$, where $(1-\alpha)$ fraction of the points are noisy samples from a low-dimensional subspace while $\alpha$ fraction of the points can be arbitrary outliers, the goal is to recover the subspace accurately.
Nearly-optimal Robust Matrix Completion
Finally, an application of our result to the robust PCA problem (low-rank+sparse matrix separation) leads to nearly linear time (in matrix dimensions) algorithm for the same; existing state-of-the-art methods require quadratic time.
