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Found 22 papers, 3 papers with code
Optimal Algorithms for Augmented Testing of Discrete Distributions
We provide lower bounds to indicate that the improvements in sample complexity achieved by our algorithms are information-theoretically optimal.
Statistical-Computational Trade-offs for Density Estimation
In particular, if an algorithm uses $O(n/\log^c k)$ samples for some constant $c>0$ and polynomial space, then the query time of the data structure must be at least $k^{1-O(1)/\log \log k}$, i. e., close to linear in the number of distributions $k$.
A Bi-metric Framework for Fast Similarity Search
In both cases we show that, as long as the proxy metric used to construct the data structure approximates the ground-truth metric up to a bounded factor, our data structure achieves arbitrarily good approximation guarantees with respect to the ground-truth metric.
Efficiently Computing Similarities to Private Datasets
We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function $f$ and a large high-dimensional private dataset $X \subset \mathbb{R}^d$, output a differentially private (DP) data structure which approximates $\sum_{x \in X} f(x, y)$ for any query $y$.
Improved Frequency Estimation Algorithms with and without Predictions
In particular, their learning-augmented frequency estimation algorithm uses a learned heavy-hitter oracle which predicts which elements will appear many times in the stream.
A Near-Linear Time Algorithm for the Chamfer Distance
For any two point sets $A, B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A, B)=\sum_{a \in A} \min_{b \in B} d_X(a, b)$, where $d_X$ is the underlying distance measure (e. g., the Euclidean or Manhattan distance).
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.
Improved Space Bounds for Learning with Experts
We give improved tradeoffs between space and regret for the online learning with expert advice problem over $T$ days with $n$ experts.
Sub-quadratic Algorithms for Kernel Matrices via Kernel Density Estimation
We build on the recent Kernel Density Estimation framework, which (after preprocessing in time subquadratic in $n$) can return estimates of row/column sums of the kernel matrix.
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 $n$.
Learning-Augmented Algorithms for Online Linear and Semidefinite Programming
We show that if the predictor is accurate, we can efficiently bypass these impossibility results and achieve a constant-factor approximation to the optimal solution, i. e., consistency.
Hardness and Algorithms for Robust and Sparse Optimization
We further show fine-grained hardness of robust regression through a reduction from the minimum-weight $k$-clique conjecture.
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.
Learning-Augmented $k$-means Clustering
$k$-means clustering is a well-studied problem due to its wide applicability.
Dimensionality Reduction for Wasserstein Barycenter
In order to cope with this "curse of dimensionality," we study dimensionality reduction techniques for the Wasserstein barycenter problem.
Cluster Tree for Nearest Neighbor Search
In addition, we show theoretically and empirically that ClusterTree finds partitions which are superior to those found by RP trees in preserving the cluster structure of the input dataset.
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.
Adversarial Robustness of Streaming Algorithms through Importance Sampling
In this paper, we introduce adversarially robust streaming algorithms for central machine learning and algorithmic tasks, such as regression and clustering, as well as their more general counterparts, subspace embedding, low-rank approximation, and coreset construction.
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.
Using Dimensionality Reduction to Optimize t-SNE
t-SNE is a popular tool for embedding multi-dimensional datasets into two or three dimensions.
Testing Properties of Multiple Distributions with Few Samples
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution.
