Search Results for author: Kasper Green Larsen

Found 15 papers, 2 papers with code

The Fast Johnson-Lindenstrauss Transform is Even Faster

no code implementations4 Apr 2022 Ora Nova Fandina, Mikael Møller Høgsgaard, Kasper Green Larsen

In this work, we give a surprising new analysis of the Fast JL transform, showing that the $k \ln^2 n$ term in the embedding time can be improved to $(k \ln^2 n)/\alpha$ for an $\alpha = \Omega(\min\{\varepsilon^{-1}\ln(1/\varepsilon), \ln n\})$.

Dimensionality Reduction

Towards Optimal Lower Bounds for k-median and k-means Coresets

no code implementations25 Feb 2022 Vincent Cohen-Addad, Kasper Green Larsen, David Saulpic, Chris Schwiegelshohn

Given a set of points in a metric space, the $(k, z)$-clustering problem consists of finding a set of $k$ points called centers, such that the sum of distances raised to the power of $z$ of every data point to its closest center is minimized.

Optimality of the Johnson-Lindenstrauss Dimensionality Reduction for Practical Measures

no code implementations14 Jul 2021 Yair Bartal, Ora Nova Fandina, Kasper Green Larsen

They provided upper bounds on its quality for a wide range of practical measures and showed that indeed these are best possible in many cases.

Dimensionality Reduction

Compression Implies Generalization

no code implementations15 Jun 2021 Allan Grønlund, Mikael Høgsgaard, Lior Kamma, Kasper Green Larsen

The framework is simple and powerful enough to extend the generalization bounds by Arora et al. to also hold for the original network.

Generalization Bounds

CountSketches, Feature Hashing and the Median of Three

no code implementations3 Feb 2021 Kasper Green Larsen, Rasmus Pagh, Jakub Tětek

For $t > 1$, the estimator takes the median of $2t-1$ independent estimates, and the probability that the estimate is off by more than $2 \|v\|_2/\sqrt{s}$ is exponentially small in $t$.

Margins are Insufficient for Explaining Gradient Boosting

no code implementations NeurIPS 2020 Allan Grønlund, Lior Kamma, Kasper Green Larsen

We then explain the short comings of the $k$'th margin bound and prove a stronger and more refined margin-based generalization bound for boosted classifiers that indeed succeeds in explaining the performance of modern gradient boosters.

Optimal Learning of Joint Alignments with a Faulty Oracle

no code implementations21 Sep 2019 Kasper Green Larsen, Michael Mitzenmacher, Charalampos E. Tsourakakis

The goal is to recover $n$ discrete variables $g_i \in \{0, \ldots, k-1\}$ (up to some global offset) given noisy observations of a set of their pairwise differences $\{(g_i - g_j) \bmod k\}$; specifically, with probability $\frac{1}{k}+\delta$ for some $\delta > 0$ one obtains the correct answer, and with the remaining probability one obtains a uniformly random incorrect answer.

Optimal Minimal Margin Maximization with Boosting

no code implementations30 Jan 2019 Allan Grønlund, Kasper Green Larsen, Alexander Mathiasen

A common goal in a long line of research, is to maximize the smallest margin using as few base hypotheses as possible, culminating with the AdaBoostV algorithm by (R{\"a}tsch and Warmuth [JMLR'04]).

Fully Understanding the Hashing Trick

no code implementations NeurIPS 2018 Casper Benjamin Freksen, Lior Kamma, Kasper Green Larsen

We settle this question by giving tight asymptotic bounds on the exact tradeoff between the central parameters, thus providing a complete understanding of the performance of feature hashing.

Predicting Positive and Negative Links with Noisy Queries: Theory & Practice

1 code implementation19 Sep 2017 Charalampos E. Tsourakakis, Michael Mitzenmacher, Kasper Green Larsen, Jarosław Błasiok, Ben Lawson, Preetum Nakkiran, Vasileios Nakos

The {\em edge sign prediction problem} aims to predict whether an interaction between a pair of nodes will be positive or negative.

Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D

1 code implementation25 Jan 2017 Allan Grønlund, Kasper Green Larsen, Alexander Mathiasen, Jesper Sindahl Nielsen, Stefan Schneider, Mingzhou Song

We present all the existing work that had been overlooked and compare the various solutions theoretically.

Heavy hitters via cluster-preserving clustering

no code implementations5 Apr 2016 Kasper Green Larsen, Jelani Nelson, Huy L. Nguyen, Mikkel Thorup

Our main innovation is an efficient reduction from the heavy hitters to a clustering problem in which each heavy hitter is encoded as some form of noisy spectral cluster in a much bigger graph, and the goal is to identify every cluster.

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