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Found 18 papers, 1 papers with code
Better and Simpler Lower Bounds for Differentially Private Statistical Estimation
First, we prove that for any $\alpha \le O(1)$, estimating the covariance of a Gaussian up to spectral error $\alpha$ requires $\tilde{\Omega}\left(\frac{d^{3/2}}{\alpha \varepsilon} + \frac{d}{\alpha^2}\right)$ samples, which is tight up to logarithmic factors.
SPAIC: A sub-$μ$W/Channel, 16-Channel General-Purpose Event-Based Analog Front-End with Dual-Mode Encoders
Low-power event-based analog front-ends (AFE) are a crucial component required to build efficient end-to-end neuromorphic processing systems for edge computing.
A faster and simpler algorithm for learning shallow networks
We revisit the well-studied problem of learning a linear combination of $k$ ReLU activations given labeled examples drawn from the standard $d$-dimensional Gaussian measure.
Data Structures for Density Estimation
We study statistical/computational tradeoffs for the following density estimation problem: given $k$ distributions $v_1, \ldots, v_k$ over a discrete domain of size $n$, and sampling access to a distribution $p$, identify $v_i$ that is "close" to $p$.
Learned Interpolation for Better Streaming Quantile Approximation with Worst-Case Guarantees
An $\varepsilon$-approximate quantile sketch over a stream of $n$ inputs approximates the rank of any query point $q$ - that is, the number of input points less than $q$ - up to an additive error of $\varepsilon n$, generally with some probability of at least $1 - 1/\mathrm{poly}(n)$, while consuming $o(n)$ space.
Krylov Methods are (nearly) Optimal for Low-Rank Approximation
In particular, for Spectral LRA, we show that any algorithm requires $\Omega\left(\log(n)/\varepsilon^{1/2}\right)$ matrix-vector products, exactly matching the upper bound obtained by Krylov methods [MM15, BCW22].
Query lower bounds for log-concave sampling
Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower bounds for this task has remained elusive, with lower bounds previously known only in dimension one.
Robustness Implies Privacy in Statistical Estimation
We study the relationship between adversarial robustness and differential privacy in high-dimensional algorithmic statistics.
Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks
However, those simulations involve neural networks for the 'combine' function of size polynomial or even exponential in the number of graph nodes $n$, as well as feature vectors of length linear in $n$.
Improved Approximations for Euclidean $k$-means and $k$-median, via Nested Quasi-Independent Sets
Motivated by data analysis and machine learning applications, we consider the popular high-dimensional Euclidean $k$-median and $k$-means problems.
Triangle and Four Cycle Counting with Predictions in Graph Streams
We propose data-driven one-pass streaming algorithms for estimating the number of triangles and four cycles, two fundamental problems in graph analytics that are widely studied in the graph data stream literature.
Private High-Dimensional Hypothesis Testing
Our results improve over the previous best work of Canonne et al.~\cite{CanonneKMUZ20} for both computationally efficient and inefficient algorithms, and even our computationally efficient algorithm matches the optimal \emph{non-private} sample complexity of $O\left(\frac{\sqrt{d}}{\alpha^2}\right)$ in many standard parameter settings.
Tight and Robust Private Mean Estimation with Few Users
In particular, we provide a nearly optimal trade-off between the number of users and the number of samples per user required for private mean estimation, even when the number of users is as low as $O(\frac{1}{\varepsilon}\log\frac{1}{\delta})$.
Randomized Dimensionality Reduction for Facility Location and Single-Linkage Clustering
Random dimensionality reduction is a versatile tool for speeding up algorithms for high-dimensional problems.
Almost Tight Approximation Algorithms for Explainable Clustering
Next, we study the $k$-means problem in this context and provide an $O(k \log k)$-approximation algorithm for explainable $k$-means, improving over the $O(k^2)$ bound of Dasgupta et al. and the $O(d k \log k)$ bound of \cite{laber2021explainable}.
Learning-based Support Estimation in Sublinear Time
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements.
Metric Transforms and Low Rank Matrices via Representation Theory of the Real Hyperrectangle
This completes the theory of Manhattan to Manhattan metric transforms initiated by Assouad in 1980.
Optimal terminal dimensionality reduction in Euclidean space
$$ We show that a strictly stronger version of this statement holds, answering one of the main open questions of [MMMR18]: "$\forall y\in X$" in the above statement may be replaced with "$\forall y\in\mathbb R^d$", so that $f$ not only preserves distances within $X$, but also distances to $X$ from the rest of space.
