Multi-Instance Kernels

By Thomas Gärtner, Peter A. Flach, Adam Kowalczyk, Alex Smola. 2002

574 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistical Learning Theory

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Moreover, the empirical version of (3.49) and (3.40) coincides with that of classical set kernel of Haussler (1999) and Gärtner et al. (2002) (see also Kondor and Jebara (2003)).”
Towards a Neural Statistician (2016, methodology): “Typical approaches involve adapting kernel based methods such as support measure machines [24], support distribution machines [26] and multiple-instance-kernels [7].”
Learning Theory for Distribution Regression (2014, background): “…the covariates xi to have finite doubling dimension (Kpotufe, 2011).3 One can define kernel learning algorithms on bags based on set kernels (Gärtner et al., 2002) by computing the similarity of the sets/bags of samples representing the input distributions; set kernels are also called…”
Distribution Kernel Methods for Multiple-Instance Learning (2013, methodology): “A related MI kernel is the average-normalized set kernel (Gärtner et al. 2002), which is equivalent to an “empirical” mean map computed using samples from distributions.”
Video Representation Learning Using Discriminative Pooling (2018, methodology): “While all these schemes share similar motivations as ours, we cast our MIL problem in the setting of normalized set kernels [15] and reduce the formulation to standard SVM setup which can be solved rapidly.”
A Kernel Method for the Two-Sample-Problem (2006, methodology): “The present work synthesizes and expands on results of Gretton et al. (2007a,b), Smola et al. (2007), and Song et al.”
Attention-based Deep Multiple Instance Learning (2018, neutral): “[1] (Andrews et al., 2003), [2] (G¨artner et al., 2002), [3] (Zhang & Goldman, 2002) [4] (Zhou et al., 2009) [5] (Wei et al., 2017)”
Multi-Level Active Prediction of Useful Image Annotations for Recognition (2008, methodology): “We integrate our active selection method with the SVM-based MIL approach given in [22], which uses a Normalized Set Kernel (NSK) to describe bags based on t he average representation of instances within them.”
Weakly supervised histopathology cancer image segmentation and classification (2014, methodology): “In the machine learning community, many MIL methods have been developed in recent years such as Diverse Density (DD) (Maron and Lozano-Pérez, 1997), Citation-kNN (Wang et al., 2000), EM-DD (Zhang and Goldman, 2001), MI-Kernels (Gärtner et al., 2002), SVM-based methods (Andrews et al., 2003), and ens”
Revisiting Multiple-Instance Learning Via Embedded Instance Selection (2008, methodology): “The MI algorithms were MILES, MISMO (SVM with the MI polynomial kernel [12]), mi-SVM [1], Citation-KNN [24], EMDD [29], Adaboost + Optimal Ball [2], MIBoost [27] (with the WEKA REPTree decision tree learner, with no automatic pruning but depth-limited to 3 levels, as the base classifier), MILR [27] ”
Confidence-Rated Multiple Instance Boosting for Object Detection (2014, methodology): “The approach performs well when compared to [12, 18].”
Multiple instance classification: Review, taxonomy and comparative study (2013, methodology): “In [14] the authors prove that if the instances ~x are separable in the space induced by the instance-level kernel, then the bags are also separable in the space induced by the bag-level kernel defined in Eq.”
A Kernel Two-Sample Test (2012, methodology): “The solution proposed by G̈artner et al. (2002) is to map the ensemblesXi := {xi1, . . . ,ximi}, where i is the ensemble index andmi the number of elements in theith ensemble, jointly into feature space via φ(Xi) := 1 mi mi ∑ j=1 φ(xi j ), and to use the latter as the basis for a kernel method.”
Revisiting multiple instance neural networks (2016, methodology): “Dataset MI-Kernel [25] miGraph [26] miFV [27] mi-Net MI-Net MI-Net with DS MI-Net with RC”
Non-I.I.D. Multi-Instance Dimensionality Reduction by Learning a Maximum Bag Margin Subspace (2010, methodology): “Most recent multi-instance methods (Gartner et al. 2002) (Andrews, Tsochantaridis, and Hofmann 2003) (Zhou and Zhang 2003) treat instances in each bag as independently and identically distributed (i.i.d.), which ignore the valuable structure information conveyed by instances in a bag.”