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Found 34 papers, 8 papers with code
Worst-case Performance of Popular Approximate Nearest Neighbor Search Implementations: Guarantees and Limitations
Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees.
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.
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 $n$.
Generalization Bounds for Data-Driven Numerical Linear Algebra
Our techniques are general, and provide generalization bounds for many other recently proposed data-driven algorithms in numerical linear algebra, covering both sketching-based and multigrid-based methods.
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.
Few-Shot Data-Driven Algorithms for Low Rank Approximation
Recently, data-driven and learning-based algorithms for low rank matrix approximation were shown to outperform classical data-oblivious algorithms by wide margins in terms of accuracy.
Targeted Supervised Contrastive Learning for Long-Tailed Recognition
This forces all classes, including minority classes, to maintain a uniform distribution in the feature space, improves class boundaries, and provides better generalization even in the presence of long-tail data.
Ranked #22 on
Long-tail Learning
on CIFAR-10-LT (ρ=100)
Embeddings and labeling schemes for A*
In particular, we consider heuristics induced by norm embeddings and distance labeling schemes, and provide lower bounds for the tradeoffs between the number of dimensions or bits used to represent each graph node, and the running time of the A* algorithm.
(Optimal) Online Bipartite Matching with Degree Information
For the bipartite version of a stochastic graph model due to Chung, Lu, and Vu where the expected values of the offline degrees are known and used as predictions, we show that MinPredictedDegree stochastically dominates any other online algorithm, i. e., it is optimal for graphs drawn from this model.
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.
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.
Faster Kernel Matrix Algebra via Density Estimation
In particular, we consider estimating the sum of kernel matrix entries, along with its top eigenvalue and eigenvector.
Addressing Feature Suppression in Unsupervised Visual Representations
However, contrastive learning is susceptible to feature suppression, i. e., it may discard important information relevant to the task of interest, and learn irrelevant features.
Online Page Migration with ML Advice
In contrast, we show that if the algorithm is given a prediction of the input sequence, then it can achieve a competitive ratio that tends to $1$ as the prediction error rate tends to $0$.
Space and Time Efficient Kernel Density Estimation in High Dimensions
We instantiate our framework with the Laplacian and Exponential kernels, two popular kernels which possess the aforementioned property.
Estimating Entropy of Distributions in Constant Space
We consider the task of estimating the entropy of $k$-ary distributions from samples in the streaming model, where space is limited.
Learning-Based Low-Rank Approximations
Our experiments show that, for multiple types of data sets, a learned sketch matrix can substantially reduce the approximation loss compared to a random matrix $S$, sometimes by one order of magnitude.
Scalable Nearest Neighbor Search for Optimal Transport
Our extensive experiments, on real-world text and image datasets, show that Flowtree improves over various baselines and existing methods in either running time or accuracy.
Data Structures and Algorithms
Neural Embeddings for Nearest Neighbor Search Under Edit Distance
The edit distance between two sequences is an important metric with many applications.
Composable Core-sets for Determinant Maximization: A Simple Near-Optimal Algorithm
In this work, first we provide a theoretical approximation guarantee of $O(C^{k^2})$ for the Greedy algorithm in the context of composable core-sets; Further, we propose to use a Local Search based algorithm that while being still practical, achieves a nearly optimal approximation bound of $O(k)^{2k}$; Finally, we implement all three algorithms and show the effectiveness of our proposed algorithm on standard data sets.
Sample-Optimal Low-Rank Approximation of Distance Matrices
Recent work by Bakshi and Woodruff (NeurIPS 2018) showed it is possible to compute a rank-$k$ approximation of a distance matrix in time $O((n+m)^{1+\gamma}) \cdot \mathrm{poly}(k, 1/\epsilon)$, where $\epsilon>0$ is an error parameter and $\gamma>0$ is an arbitrarily small constant.
Learning-Based Frequency Estimation Algorithms
Estimating the frequencies of elements in a data stream is a fundamental task in data analysis and machine learning.
Scalable Fair Clustering
In the fair variant of $k$-median, the points are colored, and the goal is to minimize the same average distance objective while ensuring that all clusters have an "approximately equal" number of points of each color.
Learning Space Partitions for Nearest Neighbor Search
Space partitions of $\mathbb{R}^d$ underlie a vast and important class of fast nearest neighbor search (NNS) algorithms.
Composable Core-sets for Determinant Maximization Problems via Spectral Spanners
We show that for many objective functions one can use a spectral spanner, independent of the underlying functions, as a core-set and obtain almost optimal composable core-sets.
Approximate Nearest Neighbor Search in High Dimensions
The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X, D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$).
Practical Data-Dependent Metric Compression with Provable Guarantees
We introduce a new distance-preserving compact representation of multi-dimensional point-sets.
On the Fine-Grained Complexity of Empirical Risk Minimization: Kernel Methods and Neural Networks
We also give similar hardness results for computing the gradient of the empirical loss, which is the main computational burden in many non-convex learning tasks.
Fast recovery from a union of subspaces
We address the problem of recovering a high-dimensional but structured vector from linear observations in a general setting where the vector can come from an arbitrary union of subspaces.
Practical and Optimal LSH for Angular Distance
Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
Nearly Optimal Deterministic Algorithm for Sparse Walsh-Hadamard Transform
Moreover, we design a deterministic and non-adaptive $\ell_1/\ell_1$ compressed sensing scheme based on general lossless condensers that is equipped with a fast reconstruction algorithm running in time $k^{1+\alpha} (\log N)^{O(1)}$ (for the GUV-based condenser) and is of independent interest.
