arXiv subjects

Marco Loog

Publications and source records attributed to Marco Loog.

At least 37 records · Page 2Linked to original sources

arXiv2020

A Brief Prehistory of Double Descent

In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a function of some (approximate) measure of its complexity $N$. With $N$ the number of features, these curves are also referred to as feature curves. A salient observation in [1] is that these curves can display, what they call, double descent: with increasing $N$, the risk initially decreases, attains a minimum, and then increases until $N$ equals $n$, where the training data is fitted perfectly. Increasing $N$ even further, the risk decreases a second and final time, creating a peak at $N=n$. This twofold descent may come as a surprise, but as opposed to what [1] reports, it has not been overlooked historically. Our letter draws attention to some original, earlier findings, of interest to contemporary machine learning.

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arXiv2020

Minimizers of the Empirical Risk and Risk Monotonicity

Plotting a learner's average performance against the number of training samples results in a learning curve. Studying such curves on one or more data sets is a way to get to a better understanding of the generalization properties of this learner. The behavior of learning curves is, however, not very well understood and can display (for most researchers) quite unexpected behavior. Our work introduces the formal notion of \emph{risk monotonicity}, which asks the risk to not deteriorate with increasing training set sizes in expectation over the training samples. We then present the surprising result that various standard learners, specifically those that minimize the empirical risk, can act \emph{non}monotonically irrespective of the training sample size. We provide a theoretical underpinning for specific instantiations from classification, regression, and density estimation. Altogether, the proposed monotonicity notion opens up a whole new direction of research.

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arXiv2019

A Distribution Dependent and Independent Complexity Analysis of Manifold Regularization

Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for models that add a convex data dependent regularization term to a supervised learning process, as is in particular done in Manifold regularization. We then compare the bound for those semi-supervised methods to purely supervised methods, and discuss a setting in which the semi-supervised method can only have a constant improvement, ignoring logarithmic terms. By viewing Manifold regularization as a kernel method we then derive Rademacher bounds which allow for a distribution dependent analysis. Finally we illustrate that these bounds may be useful for choosing an appropriate manifold regularization parameter in situations with very sparsely labeled data.

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arXiv2019

Making Learners (More) Monotone

Learning performance can show non-monotonic behavior. That is, more data does not necessarily lead to better models, even on average. We propose three algorithms that take a supervised learning model and make it perform more monotone. We prove consistency and monotonicity with high probability, and evaluate the algorithms on scenarios where non-monotone behaviour occurs. Our proposed algorithm $\text{MT}_{\text{HT}}$ makes less than $1\%$ non-monotone decisions on MNIST while staying competitive in terms of error rate compared to several baselines.

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arXiv2019

Robust importance-weighted cross-validation under sample selection bias

Cross-validation under sample selection bias can, in principle, be done by importance-weighting the empirical risk. However, the importance-weighted risk estimator produces sub-optimal hyperparameter estimates in problem settings where large weights arise with high probability. We study its sampling variance as a function of the training data distribution and introduce a control variate to increase its robustness to problematically large weights.

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arXiv2019

How to Manipulate CNNs to Make Them Lie: the GradCAM Case

Recently many methods have been introduced to explain CNN decisions. However, it has been shown that some methods can be sensitive to manipulation of the input. We continue this line of work and investigate the explanation method GradCAM. Instead of manipulating the input, we consider an adversary that manipulates the model itself to attack the explanation. By changing weights and architecture, we demonstrate that it is possible to generate any desired explanation, while leaving the model's accuracy essentially unchanged. This illustrates that GradCAM cannot explain the decision of every CNN and provides a proof of concept showing that it is possible to obfuscate the inner workings of a CNN. Finally, we combine input and model manipulation. To this end we put a backdoor in the network: the explanation is correct unless there is a specific pattern present in the input, which triggers a malicious explanation. Our work raises new security concerns, especially in settings where explanations of models may be used to make decisions, such as in the medical domain.

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arXiv2019

A review of domain adaptation without target labels

Domain adaptation has become a prominent problem setting in machine learning and related fields. This review asks the question: how can a classifier learn from a source domain and generalize to a target domain? We present a categorization of approaches, divided into, what we refer to as, sample-based, feature-based and inference-based methods. Sample-based methods focus on weighting individual observations during training based on their importance to the target domain. Feature-based methods revolve around on mapping, projecting and representing features such that a source classifier performs well on the target domain and inference-based methods incorporate adaptation into the parameter estimation procedure, for instance through constraints on the optimization procedure. Additionally, we review a number of conditions that allow for formulating bounds on the cross-domain generalization error. Our categorization highlights recurring ideas and raises questions important to further research.

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arXiv2019

Semi-Generative Modelling: Covariate-Shift Adaptation with Cause and Effect Features

Current methods for covariate-shift adaptation use unlabelled data to compute importance weights or domain-invariant features, while the final model is trained on labelled data only. Here, we consider a particular case of covariate shift which allows us also to learn from unlabelled data, that is, combining adaptation with semi-supervised learning. Using ideas from causality, we argue that this requires learning with both causes, $X_C$, and effects, $X_E$, of a target variable, $Y$, and show how this setting leads to what we call a semi-generative model, $P(Y,X_E|X_C,θ)$. Our approach is robust to domain shifts in the distribution of causal features and leverages unlabelled data by learning a direct map from causes to effects. Experiments on synthetic data demonstrate significant improvements in classification over purely-supervised and importance-weighting baselines.

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arXiv2019

An introduction to domain adaptation and transfer learning

In machine learning, if the training data is an unbiased sample of an underlying distribution, then the learned classification function will make accurate predictions for new samples. However, if the training data is not an unbiased sample, then there will be differences between how the training data is distributed and how the test data is distributed. Standard classifiers cannot cope with changes in data distributions between training and test phases, and will not perform well. Domain adaptation and transfer learning are sub-fields within machine learning that are concerned with accounting for these types of changes. Here, we present an introduction to these fields, guided by the question: when and how can a classifier generalize from a source to a target domain? We will start with a brief introduction into risk minimization, and how transfer learning and domain adaptation expand upon this framework. Following that, we discuss three special cases of data set shift, namely prior, covariate and concept shift. For more complex domain shifts, there are a wide variety of approaches. These are categorized into: importance-weighting, subspace mapping, domain-invariant spaces, feature augmentation, minimax estimators and robust algorithms. A number of points will arise, which we will discuss in the last section. We conclude with the remark that many open questions will have to be addressed before transfer learners and domain-adaptive classifiers become practical.

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arXiv2019

The Pessimistic Limits and Possibilities of Margin-based Losses in Semi-supervised Learning

Consider a classification problem where we have both labeled and unlabeled data available. We show that for linear classifiers defined by convex margin-based surrogate losses that are decreasing, it is impossible to construct any semi-supervised approach that is able to guarantee an improvement over the supervised classifier measured by this surrogate loss on the labeled and unlabeled data. For convex margin-based loss functions that also increase, we demonstrate safe improvements are possible.

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arXiv2018

Learning an MR acquisition-invariant representation using Siamese neural networks

Generalization of voxelwise classifiers is hampered by differences between MRI-scanners, e.g. different acquisition protocols and field strengths. To address this limitation, we propose a Siamese neural network (MRAI-NET) that extracts acquisition-invariant feature vectors. These can consequently be used by task-specific methods, such as voxelwise classifiers for tissue segmentation. MRAI-NET is tested on both simulated and real patient data. Experiments show that MRAI-NET outperforms voxelwise classifiers trained on the source or target scanner data when a small number of labeled samples is available.

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arXiv2018

Distance Based Source Domain Selection for Sentiment Classification

Automated sentiment classification (SC) on short text fragments has received increasing attention in recent years. Performing SC on unseen domains with few or no labeled samples can significantly affect the classification performance due to different expression of sentiment in source and target domain. In this study, we aim to mitigate this undesired impact by proposing a methodology based on a predictive measure, which allows us to select an optimal source domain from a set of candidates. The proposed measure is a linear combination of well-known distance functions between probability distributions supported on the source and target domains (e.g. Earth Mover's distance and Kullback-Leibler divergence). The performance of the proposed methodology is validated through an SC case study in which our numerical experiments suggest a significant improvement in the cross domain classification error in comparison with a random selected source domain for both a naive and adaptive learning setting. In the case of more heterogeneous datasets, the predictability feature of the proposed model can be utilized to further select a subset of candidate domains, where the corresponding classifier outperforms the one trained on all available source domains. This observation reinforces a hypothesis that our proposed model may also be deployed as a means to filter out redundant information during a training phase of SC.

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arXiv2018

A Benchmark and Comparison of Active Learning for Logistic Regression

Logistic regression is by far the most widely used classifier in real-world applications. In this paper, we benchmark the state-of-the-art active learning methods for logistic regression and discuss and illustrate their underlying characteristics. Experiments are carried out on three synthetic datasets and 44 real-world datasets, providing insight into the behaviors of these active learning methods with respect to the area of the learning curve (which plots classification accuracy as a function of the number of queried examples) and their computational costs. Surprisingly, one of the earliest and simplest suggested active learning methods, i.e., uncertainty sampling, performs exceptionally well overall. Another remarkable finding is that random sampling, which is the rudimentary baseline to improve upon, is not overwhelmed by individual active learning techniques in many cases.

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arXiv2018

Single Shot Active Learning using Pseudo Annotators

Standard myopic active learning assumes that human annotations are always obtainable whenever new samples are selected. This, however, is unrealistic in many real-world applications where human experts are not readily available at all times. In this paper, we consider the single shot setting: all the required samples should be chosen in a single shot and no human annotation can be exploited during the selection process. We propose a new method, Active Learning through Random Labeling (ALRL), which substitutes single human annotator for multiple, what we will refer to as, pseudo annotators. These pseudo annotators always provide uniform and random labels whenever new unlabeled samples are queried. This random labeling enables standard active learning algorithms to also exhibit the exploratory behavior needed for single shot active learning. The exploratory behavior is further enhanced by selecting the most representative sample via minimizing nearest neighbor distance between unlabeled samples and queried samples. Experiments on real-world datasets demonstrate that the proposed method outperforms several state-of-the-art approaches.

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arXiv2018

MR Acquisition-Invariant Representation Learning

Voxelwise classification approaches are popular and effective methods for tissue quantification in brain magnetic resonance imaging (MRI) scans. However, generalization of these approaches is hampered by large differences between sets of MRI scans such as differences in field strength, vendor or acquisition protocols. Due to this acquisition related variation, classifiers trained on data from a specific scanner fail or under-perform when applied to data that was acquired differently. In order to address this lack of generalization, we propose a Siamese neural network (MRAI-net) to learn a representation that minimizes the between-scanner variation, while maintaining the contrast between brain tissues necessary for brain tissue quantification. The proposed MRAI-net was evaluated on both simulated and real MRI data. After learning the MR acquisition invariant representation, any supervised classification model that uses feature vectors can be applied. In this paper, we provide a proof of principle, which shows that a linear classifier applied on the MRAI representation is able to outperform supervised convolutional neural network classifiers for tissue classification when little target training data is available.

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arXiv2018

Effects of sampling skewness of the importance-weighted risk estimator on model selection

Importance-weighting is a popular and well-researched technique for dealing with sample selection bias and covariate shift. It has desirable characteristics such as unbiasedness, consistency and low computational complexity. However, weighting can have a detrimental effect on an estimator as well. In this work, we empirically show that the sampling distribution of an importance-weighted estimator can be skewed. For sample selection bias settings, and for small sample sizes, the importance-weighted risk estimator produces overestimates for datasets in the body of the sampling distribution, i.e. the majority of cases, and large underestimates for data sets in the tail of the sampling distribution. These over- and underestimates of the risk lead to suboptimal regularization parameters when used for importance-weighted validation.

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arXiv2018

A Variance Maximization Criterion for Active Learning

Active learning aims to train a classifier as fast as possible with as few labels as possible. The core element in virtually any active learning strategy is the criterion that measures the usefulness of the unlabeled data based on which new points to be labeled are picked. We propose a novel approach which we refer to as maximizing variance for active learning or MVAL for short. MVAL measures the value of unlabeled instances by evaluating the rate of change of output variables caused by changes in the next sample to be queried and its potential labelling. In a sense, this criterion measures how unstable the classifier's output is for the unlabeled data points under perturbations of the training data. MVAL maintains, what we refer to as, retraining information matrices to keep track of these output scores and exploits two kinds of variance to measure the informativeness and representativeness, respectively. By fusing these variances, MVAL is able to select the instances which are both informative and representative. We employ our technique both in combination with logistic regression and support vector machines and demonstrate that MVAL achieves state-of-the-art performance in experiments on a large number of standard benchmark datasets.

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arXiv2017

Supervised Classification: Quite a Brief Overview

The original problem of supervised classification considers the task of automatically assigning objects to their respective classes on the basis of numerical measurements derived from these objects. Classifiers are the tools that implement the actual functional mapping from these measurements---also called features or inputs---to the so-called class label---or output. The fields of pattern recognition and machine learning study ways of constructing such classifiers. The main idea behind supervised methods is that of learning from examples: given a number of example input-output relations, to what extent can the general mapping be learned that takes any new and unseen feature vector to its correct class? This chapter provides a basic introduction to the underlying ideas of how to come to a supervised classification problem. In addition, it provides an overview of some specific classification techniques, delves into the issues of object representation and classifier evaluation, and (very) briefly covers some variations on the basic supervised classification task that may also be of interest to the practitioner.

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