Meelis Kull

Kacper Sokol, Meelis Kull, Jeffrey Chan et al.

While data-driven predictive models are a strictly technological construct, they may operate within a social context in which benign engineering choices entail implicit, indirect and unexpected real-life consequences. Fairness of such systems -- pertaining both to individuals and groups -- is one relevant consideration in this space; algorithms can discriminate people across various protected characteristics regardless of whether these properties are included in the data or discernible through proxy variables. To date, this notion has predominantly been studied for a fixed model, often under different classification thresholds, striving to identify and eradicate undesirable, discriminative and possibly unlawful aspects of its operation. Here, we backtrack on this fixed model assumption to propose and explore a novel definition of cross-model fairness where individuals can be harmed when one predictor is chosen ad hoc from a group of equally well performing models, i.e., in view of utility-based model multiplicity. Since a person may be classified differently across models that are otherwise considered equivalent, this individual could argue for a predictor granting them the most favourable outcome, employing which may have adverse effects on other people. We introduce this scenario with a two-dimensional example and linear classification; then, we present a comprehensive empirical study based on real-life predictive models and data sets that are popular with the algorithmic fairness community; finally, we investigate analytical properties of cross-model fairness and its ramifications in a broader context. Our findings suggest that such unfairness can be readily found in real life and it may be difficult to mitigate by technical means alone as doing so is likely to degrade predictive performance.

Markus Kängsepp, Meelis Kull

In driving scenarios with poor visibility or occlusions, it is important that the autonomous vehicle would take into account all the uncertainties when making driving decisions, including choice of a safe speed. The grid-based perception outputs, such as occupancy grids, and object-based outputs, such as lists of detected objects, must then be accompanied by well-calibrated uncertainty estimates. We highlight limitations in the state-of-the-art and propose a more complete set of uncertainties to be reported, particularly including undetected-object-ahead probabilities. We suggest a novel way to get these probabilistic outputs from bird's-eye-view probabilistic semantic segmentation, in the example of the FIERY model. We demonstrate that the obtained probabilities are not calibrated out-of-the-box and propose methods to achieve well-calibrated uncertainties.

Markus Kängsepp, Kaspar Valk, Meelis Kull

Every uncalibrated classifier has a corresponding true calibration map that calibrates its confidence. Deviations of this idealistic map from the identity map reveal miscalibration. Such calibration errors can be reduced with many post-hoc calibration methods which fit some family of calibration maps on a validation dataset. In contrast, evaluation of calibration with the expected calibration error (ECE) on the test set does not explicitly involve fitting. However, as we demonstrate, ECE can still be viewed as if fitting a family of functions on the test data. This motivates the fit-on-the-test view on evaluation: first, approximate a calibration map on the test data, and second, quantify its distance from the identity. Exploiting this view allows us to unlock missed opportunities: (1) use the plethora of post-hoc calibration methods for evaluating calibration; (2) tune the number of bins in ECE with cross-validation. Furthermore, we introduce: (3) benchmarking on pseudo-real data where the true calibration map can be estimated very precisely; and (4) novel calibration and evaluation methods using new calibration map families PL and PL3.

Maksym Del, Markus Kängsepp, Marharyta Domnich et al.

Uncertainty estimation is critical for deploying reasoning language models, yet remains poorly understood under extended chain-of-thought reasoning. We study parallel sampling as a fully black-box approach using verbalized confidence and self-consistency. Across three reasoning models and 17 tasks spanning mathematics, STEM, and humanities, we characterize how these signals scale. Both self-consistency and verbalized confidence scale in reasoning models, but self-consistency exhibits lower initial discrimination and lags behind verbalized confidence under moderate sampling. Most uncertainty gains, however, arise from signal combination: with just two samples, a hybrid estimator improves AUROC by up to $+12$ on average and already outperforms either signal alone even when scaled to much larger budgets, after which returns diminish. These effects are domain-dependent: in mathematics, the native domain of RLVR-style post-training, reasoning models achieve higher uncertainty quality and exhibit both stronger complementarity and faster scaling than in STEM or humanities.

Viacheslav Komisarenko, Meelis Kull

Proper losses such as cross-entropy incentivize classifiers to produce class probabilities that are well-calibrated on the training data. Due to the generalization gap, these classifiers tend to become overconfident on the test data, mandating calibration methods such as temperature scaling. The focal loss is not proper, but training with it has been shown to often result in classifiers that are better calibrated on test data. Our first contribution is a simple explanation about why focal loss training often leads to better calibration than cross-entropy training. For this, we prove that focal loss can be decomposed into a confidence-raising transformation and a proper loss. This is why focal loss pushes the model to provide under-confident predictions on the training data, resulting in being better calibrated on the test data, due to the generalization gap. Secondly, we reveal a strong connection between temperature scaling and focal loss through its confidence-raising transformation, which we refer to as the focal calibration map. Thirdly, we propose focal temperature scaling - a new post-hoc calibration method combining focal calibration and temperature scaling. Our experiments on three image classification datasets demonstrate that focal temperature scaling outperforms standard temperature scaling.

Tom Diethe, Meelis Kull, Niall Twomey et al.

This paper describes HyperStream, a large-scale, flexible and robust software package, written in the Python language, for processing streaming data with workflow creation capabilities. HyperStream overcomes the limitations of other computational engines and provides high-level interfaces to execute complex nesting, fusion, and prediction both in online and offline forms in streaming environments. HyperStream is a general purpose tool that is well-suited for the design, development, and deployment of Machine Learning algorithms and predictive models in a wide space of sequential predictive problems. Source code, installation instructions, examples, and documentation can be found at: https://github.com/IRC-SPHERE/HyperStream.

Mari-Liis Allikivi, Joonas Järve, Meelis Kull

Being cautious is crucial for enhancing the trustworthiness of machine learning systems integrated into decision-making pipelines. Although calibrated probabilities help in optimal decision-making, perfect calibration remains unattainable, leading to estimates that fluctuate between under- and overconfidence. This becomes a critical issue in high-risk scenarios, where even occasional overestimation can lead to extreme expected costs. In these scenarios, it is important for each predicted probability to lean towards underconfidence, rather than just achieving an average balance. In this study, we introduce the novel concept of cautious calibration in binary classification. This approach aims to produce probability estimates that are intentionally underconfident for each predicted probability. We highlight the importance of this approach in a high-risk scenario and propose a theoretically grounded method for learning cautious calibration maps. Through experiments, we explore and compare our method to various approaches, including methods originally not devised for cautious calibration but applicable in this context. We show that our approach is the most consistent in providing cautious estimates. Our work establishes a strong baseline for further developments in this novel framework.

Daniel Urda, Branly Martínez, Nuño Basurto et al.

Websites, as essential digital assets, are highly vulnerable to cyberattacks because of their high traffic volume and the significant impact of breaches. This study aims to enhance the identification of web traffic attacks by leveraging machine learning techniques. A methodology was proposed to extract relevant features from HTTP traces using the CSIC2010 v2 dataset, which simulates e-commerce web traffic. Ensemble methods, such as Random Forest and Extreme Gradient Boosting, were employed and compared against baseline classifiers, including k-nearest Neighbor, LASSO, and Support Vector Machines. The results demonstrate that the ensemble methods outperform baseline classifiers by approximately 20% in predictive accuracy, achieving an Area Under the ROC Curve (AUC) of 0.989. Feature selection methods such as Information Gain, LASSO, and Random Forest further enhance the robustness of these models. This study highlights the efficacy of ensemble models in improving attack detection while minimizing performance variability, offering a practical framework for securing web traffic in diverse application contexts.

Novin Shahroudi, Viacheslav Komisarenko, Meelis Kull

Every prediction is ultimately used in a downstream task. Consequently, evaluating prediction quality is more meaningful when considered in the context of its downstream use. Metrics based solely on predictive performance often diverge from measures of real-world downstream impact. Existing approaches incorporate the downstream view by relying on multiple task-specific metrics, which can be burdensome to analyze, or by formulating cost-sensitive evaluations that require an explicit cost structure, typically assumed to be known a priori. We frame this mismatch as an evaluation alignment problem and propose a data-driven method to learn a proxy evaluation function aligned with the downstream evaluation. Building on the theory of proper scoring rules, we explore transformations of scoring rules that ensure the preservation of propriety. Our approach leverages weighted scoring rules parametrized by a neural network, where weighting is learned to align with the performance in the downstream task. This enables fast and scalable evaluation cycles across tasks where the weighting is complex or unknown a priori. We showcase our framework through synthetic and real-data experiments for regression tasks, demonstrating its potential to bridge the gap between predictive evaluation and downstream utility in modular prediction systems.

Joonas Järve, Karl Kaspar Haavel, Meelis Kull

Despite rapid advances in AI, safety remains the main bottleneck to deploying machine-learning systems. A critical safety component is out-of-distribution detection: given an input, decide whether it comes from the same distribution as the training data. In generative models, the most natural OOD score is the data likelihood. Actually, under the assumption of uniformly distributed OOD data, the likelihood is even the optimal OOD detector, as we show in this work. However, earlier work reported that likelihood often fails in practice, raising doubts about its usefulness. We explore whether, in practice, the representation space also suffers from the inability to learn good density estimation for OOD detection, or if it is merely a problem of the pixel space typically used in generative models. To test this, we trained a Variational Diffusion Model not on images, but on the representation space of a pre-trained ResNet-18 to assess the performance of our likelihood-based detector in comparison to state-of-the-art methods from the OpenOOD suite.

Telmo Silva Filho, Hao Song, Miquel Perello-Nieto et al.

This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its instance-wise predictions. This is essential for critical applications, optimal decision making, cost-sensitive classification, and for some types of context change. Calibration research has a rich history which predates the birth of machine learning as an academic field by decades. However, a recent increase in the interest on calibration has led to new methods and the extension from binary to the multiclass setting. The space of options and issues to consider is large, and navigating it requires the right set of concepts and tools. We provide both introductory material and up-to-date technical details of the main concepts and methods, including proper scoring rules and other evaluation metrics, visualisation approaches, a comprehensive account of post-hoc calibration methods for binary and multiclass classification, and several advanced topics.

Theodore James Thibault Heiser, Mari-Liis Allikivi, Meelis Kull

Minimizing expected loss measured by a proper scoring rule, such as Brier score or log-loss (cross-entropy), is a common objective while training a probabilistic classifier. If the data have experienced dataset shift where the class distributions change post-training, then often the model's performance will decrease, over-estimating the probabilities of some classes while under-estimating the others on average. We propose unbounded and bounded general adjustment (UGA and BGA) methods that transform all predictions to (re-)equalize the average prediction and the class distribution. These methods act differently depending on which proper scoring rule is to be minimized, and we have a theoretical guarantee of reducing loss on test data, if the exact class distribution is known. We also demonstrate experimentally that, when in practice the class distribution is known only approximately, there is often still a reduction in loss depending on the amount of shift and the precision to which the class distribution is known.

Mohamed Maher, Meelis Kull

Label smoothing is widely used in deep neural networks for multi-class classification. While it enhances model generalization and reduces overconfidence by aiming to lower the probability for the predicted class, it distorts the predicted probabilities of other classes resulting in poor class-wise calibration. Another method for enhancing model generalization is self-distillation where the predictions of a teacher network trained with one-hot labels are used as the target for training a student network. We take inspiration from both label smoothing and self-distillation and propose two novel instance-based label smoothing approaches, where a teacher network trained with hard one-hot labels is used to determine the amount of per class smoothness applied to each instance. The assigned smoothing factor is non-uniformly distributed along with the classes according to their similarity with the actual class. Our methods show better generalization and calibration over standard label smoothing on various deep neural architectures and image classification datasets.

Anti Ingel, Novin Shahroudi, Markus Kängsepp et al.

We participated in the M4 competition for time series forecasting and describe here our methods for forecasting daily time series. We used an ensemble of five statistical forecasting methods and a method that we refer to as the correlator. Our retrospective analysis using the ground truth values published by the M4 organisers after the competition demonstrates that the correlator was responsible for most of our gains over the naive constant forecasting method. We identify data leakage as one reason for its success, partly due to test data selected from different time intervals, and partly due to quality issues in the original time series. We suggest that future forecasting competitions should provide actual dates for the time series so that some of those leakages could be avoided by the participants.

Meelis Kull, Miquel Perello-Nieto, Markus Kängsepp et al.

Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplicative factor for inputs to the last softmax layer. On non-neural models the existing methods apply binary calibration in a pairwise or one-vs-rest fashion. We propose a natively multiclass calibration method applicable to classifiers from any model class, derived from Dirichlet distributions and generalising the beta calibration method from binary classification. It is easily implemented with neural nets since it is equivalent to log-transforming the uncalibrated probabilities, followed by one linear layer and softmax. Experiments demonstrate improved probabilistic predictions according to multiple measures (confidence-ECE, classwise-ECE, log-loss, Brier score) across a wide range of datasets and classifiers. Parameters of the learned Dirichlet calibration map provide insights to the biases in the uncalibrated model.

Hao Song, Tom Diethe, Meelis Kull et al.

We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of distribution calibration, and demonstrate its advantages over the existing definition of quantile calibration. We further propose a post-hoc approach to improving the predictions from previously trained regression models, using multi-output Gaussian Processes with a novel Beta link function. The proposed method is experimentally verified on a set of common regression models and shows improvements for both distribution-level and quantile-level calibration.

Hao Song, Meelis Kull, Peter Flach

The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not yet been well-established for regression tasks. This paper considers the problem of calibrating a probabilistic regression model to improve the estimated probability densities over the real-valued targets. We propose to calibrate a regression model through the cumulative probability density, which can be derived from calibrating a multi-class classifier. We provide three non-parametric approaches to solve the problem, two of which provide empirical estimates and the third providing smooth density estimates. The proposed approaches are experimentally evaluated to show their ability to improve the performance of regression models on the predictive likelihood.

Tom Diethe, Niall Twomey, Meelis Kull et al.

There is a widely-accepted need to revise current forms of health-care provision, with particular interest in sensing systems in the home. Given a multiple-modality sensor platform with heterogeneous network connectivity, as is under development in the Sensor Platform for HEalthcare in Residential Environment (SPHERE) Interdisciplinary Research Collaboration (IRC), we face specific challenges relating to the fusion of the heterogeneous sensor modalities. We introduce Bayesian models for sensor fusion, which aims to address the challenges of fusion of heterogeneous sensor modalities. Using this approach we are able to identify the modalities that have most utility for each particular activity, and simultaneously identify which features within that activity are most relevant for a given activity. We further show how the two separate tasks of location prediction and activity recognition can be fused into a single model, which allows for simultaneous learning an prediction for both tasks. We analyse the performance of this model on data collected in the SPHERE house, and show its utility. We also compare against some benchmark models which do not have the full structure,and show how the proposed model compares favourably to these methods

Niall Twomey, Tom Diethe, Meelis Kull et al.

This paper outlines the Sensor Platform for HEalthcare in Residential Environment (SPHERE) project and details the SPHERE challenge that will take place in conjunction with European Conference on Machine Learning and Principles and Practice of Knowledge Discovery (ECML-PKDD) between March and July 2016. The SPHERE challenge is an activity recognition competition where predictions are made from video, accelerometer and environmental sensors. Monetary prizes will be awarded to the top three entrants, with Euro 1,000 being awarded to the winner, Euro 600 being awarded to the first runner up, and Euro 400 being awarded to the second runner up.