Author name cluster

Raphael Sznitman

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5 papers

2 author rows

TMLR Journal 2024 Journal Article

Hyperbolic Random Forests

Lars Doorenbos
Pablo Márquez Neila
Raphael Sznitman
Pascal Mettes

Hyperbolic space is becoming a popular choice for representing data due to the hierarchical structure - whether implicit or explicit - of many real-world datasets. Along with it comes a need for algorithms capable of solving fundamental tasks, such as classification, in hyperbolic space. Recently, multiple papers have investigated hyperbolic alternatives to hyperplane-based classifiers, such as logistic regression and SVMs. While effective, these approaches struggle with more complex hierarchical data. We, therefore, propose to generalize the well-known random forests to hyperbolic space. We do this by redefining the notion of a split using horospheres. Since finding the globally optimal split is computationally intractable, we find candidate horospheres through a large-margin classifier. To make hyperbolic random forests work on multi-class data and imbalanced experiments, we furthermore outline new methods for combining classes based on the lowest common ancestor and class-balanced large-margin losses. Experiments on standard and new benchmarks show that our approach outperforms both conventional random forest algorithms and recent hyperbolic classifiers.

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NeurIPS Conference 2017 Conference Paper

Learning Active Learning from Data

Ksenia Konyushkova
Raphael Sznitman
Pascal Fua

In this paper, we suggest a novel data-driven approach to active learning (AL). The key idea is to train a regressor that predicts the expected error reduction for a candidate sample in a particular learning state. By formulating the query selection procedure as a regression problem we are not restricted to working with existing AL heuristics; instead, we learn strategies based on experience from previous AL outcomes. We show that a strategy can be learnt either from simple synthetic 2D datasets or from a subset of domain-specific data. Our method yields strategies that work well on real data from a wide range of domains.

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ICML Conference 2015 Conference Paper

Bayesian Multiple Target Localization

Purnima Rajan
Weidong Han 0004
Raphael Sznitman
Peter I. Frazier
Bruno Jedynak

We consider the problem of quickly localizing multiple targets by asking questions of the form “How many targets are within this set" while obtaining noisy answers. This setting is a generalization to multiple targets of the game of 20 questions in which only a single target is queried. We assume that the targets are points on the real line, or in a two dimensional plane for the experiments, drawn independently from a known distribution. We evaluate the performance of a policy using the expected entropy of the posterior distribution after a fixed number of questions with noisy answers. We derive a lower bound for the value of this problem and study a specific policy, named the dyadic policy. We show that this policy achieves a value which is no more than twice this lower bound when answers are noise-free, and show a more general constant factor approximation guarantee for the noisy setting. We present an empirical evaluation of this policy on simulated data for the problem of detecting multiple instances of the same object in an image. Finally, we present experiments on localizing multiple faces simultaneously on real images.

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ICML Conference 2013 Conference Paper

An Optimal Policy for Target Localization with Application to Electron Microscopy

Raphael Sznitman
Aurélien Lucchi
Peter I. Frazier
Bruno Jedynak
Pascal Fua

This paper considers the task of finding a target location by making a limited number of sequential observations. Each observation results from evaluating an imperfect classifier of a chosen cost and accuracy on an interval of chosen length and position. Within a Bayesian framework, we study the problem of minimizing an objective that combines the entropy of the posterior distribution with the cost of the questions asked. In this problem, we show that the one-step lookahead policy is Bayes-optimal for any arbitrary time horizon. Moreover, this one-step lookahead policy is easy to compute and implement. We then use this policy in the context of localizing mitochondria in electron microscope images, and experimentally show that significant speed ups in acquisition can be gained, while maintaining near equal image quality at target locations, when compared to current policies.

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IROS Conference 2011 Conference Paper

Visual tracking using the sum of conditional variance

Rogério Richa
Raphael Sznitman
Russell H. Taylor
Gregory D. Hager

The goal of this paper is to introduce a direct visual tracking method based on an image similarity measure called the sum of conditional variance (SCV). The SCV was originally proposed in the medical imaging domain for registering multi-modal images. In the context of visual tracking, the SCV is invariant to non-linear illumination variations, multi-modal and computationally inexpensive. Compared to information theoretic tracking methods, it requires less iterations to converge and has a significantly larger convergence radius. The novelty in this paper is a generalization of the efficient second-order minimization formulation for tracking using the SCV, allowing us to combine the efficient second-order approximation of the Hessian with a similarity metric invariant to non-linear illumination variations. The result is a visual tracking method that copes with non-linear illumination variations without requiring the estimation of photometric correction parameters at every iteration. We demonstrate the superior performance of the proposed method through comparative studies and tracking experiments under challenging illumination conditions and rapid motions.

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