arXiv subjects

Marco Loog

Publications and source records attributed to Marco Loog.

At least 19 recordsLinked to original sources

arXiv2024

Inductive Conformal Prediction under Data Scarcity: Exploring the Impacts of Nonconformity Measures

Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction quantifies how a test sample differs from the training data and the effectiveness of a conformal prediction interval may depend heavily on the precise measure employed. The impact of this choice has, however, not been widely explored, especially when dealing with limited amounts of data. The primary objective of this study is to evaluate the performance of various nonconformity measures (absolute error-based, normalized absolute error-based, and quantile-based measures) in terms of validity and efficiency when used in inductive conformal prediction. The focus is on small datasets, which is still a common setting in many real-world applications. Using synthetic and real-world data, we assess how different characteristics -- such as dataset size, noise, and dimensionality -- can affect the efficiency of conformal prediction intervals. Our results show that although there are differences, no single nonconformity measure consistently outperforms the others, as the effectiveness of each nonconformity measure is heavily influenced by the specific nature of the data. Additionally, we found that increasing dataset size does not always improve efficiency, suggesting the importance of fine-tuning models and, again, the need to carefully select the nonconformity measure for different applications.

cs.LG↗

arXiv2022

A Survey of Learning Curves with Bad Behavior: or How More Data Need Not Lead to Better Performance

Plotting a learner's generalization performance against the training set size results in a so-called learning curve. This tool, providing insight in the behavior of the learner, is also practically valuable for model selection, predicting the effect of more training data, and reducing the computational complexity of training. We set out to make the (ideal) learning curve concept precise and briefly discuss the aforementioned usages of such curves. The larger part of this survey's focus, however, is on learning curves that show that more data does not necessarily leads to better generalization performance. A result that seems surprising to many researchers in the field of artificial intelligence. We point out the significance of these findings and conclude our survey with an overview and discussion of open problems in this area that warrant further theoretical and empirical investigation.

cs.LG↗

arXiv2022

A view on model misspecification in uncertainty quantification

Estimating uncertainty of machine learning models is essential to assess the quality of the predictions that these models provide. However, there are several factors that influence the quality of uncertainty estimates, one of which is the amount of model misspecification. Model misspecification always exists as models are mere simplifications or approximations to reality. The question arises whether the estimated uncertainty under model misspecification is reliable or not. In this paper, we argue that model misspecification should receive more attention, by providing thought experiments and contextualizing these with relevant literature.

cs.LG↗

arXiv2022

An Analysis of Model-Based Reinforcement Learning From Abstracted Observations

Many methods for Model-based Reinforcement learning (MBRL) in Markov decision processes (MDPs) provide guarantees for both the accuracy of the model they can deliver and the learning efficiency. At the same time, state abstraction techniques allow for a reduction of the size of an MDP while maintaining a bounded loss with respect to the original problem. Therefore, it may come as a surprise that no such guarantees are available when combining both techniques, i.e., where MBRL merely observes abstract states. Our theoretical analysis shows that abstraction can introduce a dependence between samples collected online (e.g., in the real world). That means that, without taking this dependence into account, results for MBRL do not directly extend to this setting. Our result shows that we can use concentration inequalities for martingales to overcome this problem. This result makes it possible to extend the guarantees of existing MBRL algorithms to the setting with abstraction. We illustrate this by combining R-MAX, a prototypical MBRL algorithm, with abstraction, thus producing the first performance guarantees for model-based 'RL from Abstracted Observations': model-based reinforcement learning with an abstract model.

cs.LG↗

arXiv2022

On the reusability of samples in active learning

An interesting but not extensively studied question in active learning is that of sample reusability: to what extent can samples selected for one learner be reused by another? This paper explains why sample reusability is of practical interest, why reusability can be a problem, how reusability could be improved by importance-weighted active learning, and which obstacles to universal reusability remain. With theoretical arguments and practical demonstrations, this paper argues that universal reusability is impossible. Because every active learning strategy must undersample some areas of the sample space, learners that depend on the samples in those areas will learn more from a random sample selection. This paper describes several experiments with importance-weighted active learning that show the impact of the reusability problem in practice. The experiments confirmed that universal reusability does not exist, although in some cases -- on some datasets and with some pairs of classifiers -- there is sample reusability. Finally, this paper explores the conditions that could guarantee the reusability between two classifiers.

cs.LG↗

arXiv2022

Why Did This Model Forecast This Future? Closed-Form Temporal Saliency Towards Causal Explanations of Probabilistic Forecasts

Forecasting tasks surrounding the dynamics of low-level human behavior are of significance to multiple research domains. In such settings, methods for explaining specific forecasts can enable domain experts to gain insights into the predictive relationships between behaviors. In this work, we introduce and address the following question: given a probabilistic forecasting model how can we identify observed windows that the model considers salient when making its forecasts? We build upon a general definition of information-theoretic saliency grounded in human perception and extend it to forecasting settings by leveraging a crucial attribute of the domain: a single observation can result in multiple valid futures. We propose to express the saliency of an observed window in terms of the differential entropy of the resulting predicted future distribution. In contrast to existing methods that either require explicit training of the saliency mechanism or access to the internal states of the forecasting model, we obtain a closed-form solution for the saliency map for commonly used density functions in probabilistic forecasting. We empirically demonstrate how our framework can recover salient observed windows from head pose features for the sample task of speaking-turn forecasting using a synthesized conversation dataset.

cs.LG↗

arXiv2022

Enhancing Classifier Conservativeness and Robustness by Polynomiality

We illustrate the detrimental effect, such as overconfident decisions, that exponential behavior can have in methods like classical LDA and logistic regression. We then show how polynomiality can remedy the situation. This, among others, leads purposefully to random-level performance in the tails, away from the bulk of the training data. A directly related, simple, yet important technical novelty we subsequently present is softRmax: a reasoned alternative to the standard softmax function employed in contemporary (deep) neural networks. It is derived through linking the standard softmax to Gaussian class-conditional models, as employed in LDA, and replacing those by a polynomial alternative. We show that two aspects of softRmax, conservativeness and inherent gradient regularization, lead to robustness against adversarial attacks without gradient obfuscation.

cs.LG↗

arXiv2021

Social Processes: Self-Supervised Meta-Learning over Conversational Groups for Forecasting Nonverbal Social Cues

Free-standing social conversations constitute a yet underexplored setting for human behavior forecasting. While the task of predicting pedestrian trajectories has received much recent attention, an intrinsic difference between these settings is how groups form and disband. Evidence from social psychology suggests that group members in a conversation explicitly self-organize to sustain the interaction by adapting to one another's behaviors. Crucially, the same individual is unlikely to adapt similarly across different groups; contextual factors such as perceived relationships, attraction, rapport, etc., influence the entire spectrum of participants' behaviors. A question arises: how can we jointly forecast the mutually dependent futures of conversation partners by modeling the dynamics unique to every group? In this paper, we propose the Social Process (SP) models, taking a novel meta-learning and stochastic perspective of group dynamics. Training group-specific forecasting models hinders generalization to unseen groups and is challenging given limited conversation data. In contrast, our SP models treat interaction sequences from a single group as a meta-dataset: we condition forecasts for a sequence from a given group on other observed-future sequence pairs from the same group. In this way, an SP model learns to adapt its forecasts to the unique dynamics of the interacting partners, generalizing to unseen groups in a data-efficient manner. Additionally, we first rethink the task formulation itself, motivating task requirements from social science literature that prior formulations have overlooked. For our formulation of Social Cue Forecasting, we evaluate the empirical performance of our SP models against both non-meta-learning and meta-learning approaches with similar assumptions. The SP models yield improved performance on synthetic and real-world behavior datasets.

cs.LG↗

arXiv2021

Resolution learning in deep convolutional networks using scale-space theory

Resolution in deep convolutional neural networks (CNNs) is typically bounded by the receptive field size through filter sizes, and subsampling layers or strided convolutions on feature maps. The optimal resolution may vary significantly depending on the dataset. Modern CNNs hard-code their resolution hyper-parameters in the network architecture which makes tuning such hyper-parameters cumbersome. We propose to do away with hard-coded resolution hyper-parameters and aim to learn the appropriate resolution from data. We use scale-space theory to obtain a self-similar parametrization of filters and make use of the N-Jet: a truncated Taylor series to approximate a filter by a learned combination of Gaussian derivative filters. The parameter sigma of the Gaussian basis controls both the amount of detail the filter encodes and the spatial extent of the filter. Since sigma is a continuous parameter, we can optimize it with respect to the loss. The proposed N-Jet layer achieves comparable performance when used in state-of-the art architectures, while learning the correct resolution in each layer automatically. We evaluate our N-Jet layer on both classification and segmentation, and we show that learning sigma is especially beneficial for inputs at multiple sizes.

cs.CV↗

arXiv2021

The Shape of Learning Curves: a Review

Learning curves provide insight into the dependence of a learner's generalization performance on the training set size. This important tool can be used for model selection, to predict the effect of more training data, and to reduce the computational complexity of model training and hyperparameter tuning. This review recounts the origins of the term, provides a formal definition of the learning curve, and briefly covers basics such as its estimation. Our main contribution is a comprehensive overview of the literature regarding the shape of learning curves. We discuss empirical and theoretical evidence that supports well-behaved curves that often have the shape of a power law or an exponential. We consider the learning curves of Gaussian processes, the complex shapes they can display, and the factors influencing them. We draw specific attention to examples of learning curves that are ill-behaved, showing worse learning performance with more training data. To wrap up, we point out various open problems that warrant deeper empirical and theoretical investigation. All in all, our review underscores that learning curves are surprisingly diverse and no universal model can be identified.

cs.LG↗

arXiv2021

Nearest Neighbor-based Importance Weighting

Importance weighting is widely applicable in machine learning in general and in techniques dealing with data covariate shift problems in particular. A novel, direct approach to determine such importance weighting is presented. It relies on a nearest neighbor classification scheme and is relatively straightforward to implement. Comparative experiments on various classification tasks demonstrate the effectiveness of our so-called nearest neighbor weighting (NNeW) scheme. Considering its performance, our procedure can act as a simple and effective baseline method for importance weighting.

cs.LG↗

arXiv2020

ReproducedPapers.org: Openly teaching and structuring machine learning reproducibility

We present ReproducedPapers.org: an open online repository for teaching and structuring machine learning reproducibility. We evaluate doing a reproduction project among students and the added value of an online reproduction repository among AI researchers. We use anonymous self-assessment surveys and obtained 144 responses. Results suggest that students who do a reproduction project place more value on scientific reproductions and become more critical thinkers. Students and AI researchers agree that our online reproduction repository is valuable.

cs.CY↗

arXiv2020

Respecting Domain Relations: Hypothesis Invariance for Domain Generalization

In domain generalization, multiple labeled non-independent and non-identically distributed source domains are available during training while neither the data nor the labels of target domains are. Currently, learning so-called domain invariant representations (DIRs) is the prevalent approach to domain generalization. In this work, we define DIRs employed by existing works in probabilistic terms and show that by learning DIRs, overly strict requirements are imposed concerning the invariance. Particularly, DIRs aim to perfectly align representations of different domains, i.e. their input distributions. This is, however, not necessary for good generalization to a target domain and may even dispose of valuable classification information. We propose to learn so-called hypothesis invariant representations (HIRs), which relax the invariance assumptions by merely aligning posteriors, instead of aligning representations. We report experimental results on public domain generalization datasets to show that learning HIRs is more effective than learning DIRs. In fact, our approach can even compete with approaches using prior knowledge about domains.

cs.LG↗

arXiv2020

Black Magic in Deep Learning: How Human Skill Impacts Network Training

How does a user's prior experience with deep learning impact accuracy? We present an initial study based on 31 participants with different levels of experience. Their task is to perform hyperparameter optimization for a given deep learning architecture. The results show a strong positive correlation between the participant's experience and the final performance. They additionally indicate that an experienced participant finds better solutions using fewer resources on average. The data suggests furthermore that participants with no prior experience follow random strategies in their pursuit of optimal hyperparameters. Our study investigates the subjective human factor in comparisons of state of the art results and scientific reproducibility in deep learning.

cs.CV↗

arXiv2020

Improvability Through Semi-Supervised Learning: A Survey of Theoretical Results

Semi-supervised learning is a setting in which one has labeled and unlabeled data available. In this survey we explore different types of theoretical results when one uses unlabeled data in classification and regression tasks. Most methods that use unlabeled data rely on certain assumptions about the data distribution. When those assumptions are not met in reality, including unlabeled data may actually decrease performance. Studying such methods, it therefore is particularly important to have an understanding of the underlying theory. In this review we gather results about the possible gains one can achieve when using semi-supervised learning as well as results about the limits of such methods. More precisely, this review collects the answers to the following questions: What are, in terms of improving supervised methods, the limits of semi-supervised learning? What are the assumptions of different methods? What can we achieve if the assumptions are true? Finally, we also discuss the biggest bottleneck of semi-supervised learning, namely the assumptions they make.

cs.LG↗

arXiv2020

Consistency and Finite Sample Behavior of Binary Class Probability Estimation

In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Based on existing literature on excess risk bounds and proper scoring rules, we derive a class probability estimator based on empirical risk minimization. We then derive fairly general conditions under which this estimator will converge, in the L1-norm and in probability, to the true class probabilities. Our main contribution is to present a way to derive finite sample L1-convergence rates of this estimator for different surrogate loss functions. We also study in detail which commonly used loss functions are suitable for this estimation problem and finally discuss the setting of model-misspecification as well as a possible extension to asymmetric loss functions.

cs.LG↗

arXiv2020

Semi-Supervised Learning, Causality and the Conditional Cluster Assumption

While the success of semi-supervised learning (SSL) is still not fully understood, Schölkopf et al. (2012) have established a link to the principle of independent causal mechanisms. They conclude that SSL should be impossible when predicting a target variable from its causes, but possible when predicting it from its effects. Since both these cases are somewhat restrictive, we extend their work by considering classification using cause and effect features at the same time, such as predicting disease from both risk factors and symptoms. While standard SSL exploits information contained in the marginal distribution of all inputs (to improve the estimate of the conditional distribution of the target given inputs), we argue that in our more general setting we should use information in the conditional distribution of effect features given causal features. We explore how this insight generalises the previous understanding, and how it relates to and can be exploited algorithmically for SSL.

stat.ML↗

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.

cs.LG↗