Classification

Many prediction tasks can admit multiple models that can perform almost equally well. This phenomenon can undermine interpretability and safety when competing models assign conflicting predictions to individuals. In this work, we study how arbitrariness can arise in probabilistic classification tasks as a result of an effect that we call \emph{observational multiplicity}. We discuss how this effect arises in a broad class of practical applications where we learn a classifier to predict probabilities $p_i \in [0,1]$ but are given a dataset of observations $y_i \in \{0,1\}$. We propose to evaluate the arbitrariness of individual probability predictions through the lens of \emph{regret}. We introduce a measure of regret for probabilistic classification tasks, which measures how the predictions of a model could change as a result of different training labels. We present a general-purpose method to estimate the regret in a probabilistic classification task. We use our measure to show that regret is often higher for certain groups in the dataset and discuss potential applications of regret. We demonstrate how estimating regret can be used to promote safety in real-world applications by abstention and data collection.

Despite growing empirical evidence of bias amplification in machine learning, its theoretical foundations remain poorly understood. We develop a formal framework for majority-minority learning tasks, showing how standard training can favor majority groups and produce stereotypical predictors that neglect minority-specific features. Assuming population and variance imbalance, our analysis reveals three key findings: (i) the close proximity between ``full-data'' and stereotypical predictors, (ii) the dominance of a region where training the entire model tends to merely learn the majority traits, and (iii) a lower bound on the additional training required. Our results are illustrated through experiments in deep learning for tabular and image classification tasks.

We ask: Can focusing on likely classes of a single, in-domain sample improve accuracy? Prior work argued "no", we answer "yes" on average. Standard entropy minimization yields largest gains, and we further dissect why by looking at its two core mechanisms: increasing likely and decreasing unlikely class predictions. Simply maximizing logits of the two most likely classes explains most of its benefits and, in some cases, even outperforms entropy minimization. Thus, decreasing classes is a secondary concern. Our controlled experiment and theory investigate the most puzzling case, why simply optimizing the logits of the two most likely classes leads to accuracy gains. Our small scale networks suggest that the degree of uncertainty of a prediction, followed by model choice, and to a lesser extent dataset choice moderate the success chances of the optimization. We show that the true class tends to have larger gradients independent of whether the prediction is correct or not. Our theory thoroughly investigates one of multiple possible explanations from the angle of shared features. Our evaluation focuses on 26 large language models and 12 text datasets, and 18 image recognition models trained on ImageNet. It demonstrates gains of 0.6 percent on average for entropy minimization on uncertain samples using no extra data aside from the given test sample using a fixed learning rate. We also suggest gradient-ray ensembling. When traversing input/embedding space by applying the same gradient with differing learning rates and aggregating probabilities for the same sample further improves accuracy significantly to 0.75 percent relying on a coarse range for learning rates, thus improving accuracy and eliminating the need to find a precise learning rate at the expense of computation.

The practical success of deep learning has led to the discovery of several surprising phenomena. One of these phenomena, that has spurred intense theoretical research, is ``benign overfitting'': deep neural networks seem to generalize well in the over-parametrized regime even though the networks show a perfect fit to noisy training data. It is now known that benign overfitting also occurs in various classical statistical models. For linear maximum margin classifiers, benign overfitting has been established theoretically in a class of mixture models with very strong assumptions on the covariate distribution. However, even in this simple setting, many questions remain open. For instance, most of the existing literature focuses on the noiseless case where all true class labels are observed without errors, whereas the more interesting noisy case remains poorly understood. We provide a comprehensive study of benign overfitting for linear maximum margin classifiers. We discover a phase transition in test error bounds for the noisy model which was previously unknown and provide some geometric intuition behind it. We further considerably relax the required covariate assumptions in both the noisy and noiseless cases. Our results demonstrate that benign overfitting of maximum margin classifiers holds in a much wider range of scenarios than was previously known and provide new insights into the underlying mechanisms.

Rule set learning has recently been frequently revisited because of its interpretability. Existing methods have several shortcomings though. First, most existing methods impose orders among rules, either explicitly or implicitly, which makes the models less comprehensible. Second, due to the difficulty of handling conflicts caused by overlaps (i.e., instances covered by multiple rules), existing methods often do not consider probabilistic rules. Third, learning classification rules for multi-class target is understudied, as most existing methods focus on binary classification or multi-class classification via the one-versus-rest" approach. To address these shortcomings, we propose TURS, for Truly Unordered Rule Sets. To resolve conflicts caused by overlapping rules, we propose a novel model that exploits the probabilistic properties of our rule sets, with the intuition of only allowing rules to overlap if they have similar probabilistic outputs. We next formalize the problem of learning a TURS model based on the MDL principle and develop a carefully designed heuristic algorithm. We benchmark against a wide range of rule-based methods and demonstrate that our method learns rule sets that have lower model complexity and highly competitive predictive performance. In addition, we empirically show that rules in our model are empirically independent" and hence truly unordered.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fréchet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

Open-set recognition refers to the problem in which classes that were not seen during training appear at inference time. This requires the ability to identify instances of novel classes while maintaining discriminative capability for closed-set classification. OpenMax was the first deep neural network-based approach to address open-set recognition by calibrating the predictive scores of a standard closed-set classification network. In this paper we present MetaMax, a more effective post-processing technique that improves upon contemporary methods by directly modeling class activation vectors. MetaMax removes the need for computing class mean activation vectors (MAVs) and distances between a query image and a class MAV as required in OpenMax. Experimental results show that MetaMax outperforms OpenMax and is comparable in performance to other state-of-the-art approaches.

Classification outperforms regression across matched machine learning models in portfolio construction. A stacking ensemble of gradient boosted tree, random forest, and neural network yields a value-weighted annualized Sharpe ratio of 1.83 for classification and 1.11 for regression. This outperformance persists in multiclass settings, across subsamples, and after transaction costs. Spanning tests show that classification retains economically large alphas after we control for regression, whereas regression alphas shrink substantially once we control for classification. These results indicate that classification extracts more return information than matched regression. Our diagnostics trace classification's advantage to sharper and more precise separation of return deciles.

Selecting an appropriate classification algorithm for a given data set remains a challenging problem in data mining and machine learning. Existing algorithm recommendation models are typically trained with individual learners and rely on only one type of meta-feature, which may limit their ability to capture the diverse characteristics of classification problems. This paper proposes a multi-view ensemble meta-learning framework for classification algorithm recommendation. The framework constructs base recommendation models from different combinations of heterogeneous meta-feature groups and combines them through an accuracy- and diversity-aware ensemble strategy. The main focus of this work is empirical: we evaluate the proposed method on 1,090 benchmark classification problems derived from 84 public data sets, using 13 widely used candidate classification algorithms and five types of meta-features. The experimental results show that the proposed ensemble recommendation method consistently improves ranking loss, average precision, and top-ranked recommendation precision over individual recommendation models. These results suggest that combining complementary meta-feature views is an effective strategy for robust classification algorithm recommendation.

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases, there exist no general analytical expressions, standard numerical methods or software for these integrals. Here we present mathematical results and open-source software that provide (i) the probability in any domain of a normal in any dimensions with any parameters, (ii) the probability density, cumulative distribution, and inverse cumulative distribution of any function of a normal vector, (iii) the classification errors among any number of normal distributions, the Bayes-optimal discriminability index and relation to the operating characteristic, (iv) ways to scale the discriminability of two distributions, (v) dimension reduction and visualizations for such problems, and (vi) tests for how reliably these methods may be used on given data. We demonstrate these tools with vision research applications of detecting occluding objects in natural scenes, and detecting camouflage.

We introduce a class of random polytopes which simultaneously generalizes several known constructions. While being fairly general, these polytopes are also computationally exceptionally benign. We indicate how these properties can be exploited for classification and clustering tasks in data analysis. Crucially, our construction lets users smoothly trade off between a tighter description of the data and faster computation.

This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and multiple classes. The estimation of parameters in LDA and QDA are also covered. Then, we explain how LDA and QDA are related to metric learning, kernel principal component analysis, Mahalanobis distance, logistic regression, Bayes optimal classifier, Gaussian naive Bayes, and likelihood ratio test. We also prove that LDA and Fisher discriminant analysis are equivalent. We finally clarify some of the theoretical concepts with simulations we provide.

Home-based physiotherapy is performed without supervision, which leads to incorrect execution and motivates systems that assess movement automatically from inertial measurement units (IMUs). Such systems assign each repetition to a category, yet a relevant share of repetitions falls near a class boundary, where even trained raters disagree. Classifiers trained with one-hot labels collapse these borderline repetitions onto a single class and discard this ambiguity. We address this with a method that automatically generates a label distribution per repetition without a large rater pool. We train a network to reproduce the full distribution with a Kullback-Leibler objective, the ambiguity approach, and compare it against a one-hot cross-entropy baseline on four IMU exercise datasets. From the network output we further determine whether a repetition is ambiguous and which classes are relevant to it. The ambiguity approach matched or exceeded the baseline classification on all four datasets, and detected ambiguity and the relevant classes more reliably. Representing the label distribution in the training target therefore adds information about ambiguity at no cost to classification.

We introduce Video2Reaction, a multimodal dataset that maps short movie segments to the induced emotional reactions of viewers in the wild, as expressed through social media comments. Video2Reaction captures the natural diversity of emotional responses by aggregating reactions from online comments at scale, modeling labels as distributions over categorical emotions to better reflect the subjective and ambiguous nature of emotional perception. We benchmark two vision-language models (VLMs) finetuned with LoRA, showing that VLMs learn effectively from Video2Reaction and outperform specialized baselines on dominant reaction prediction. We further demonstrate that VLMs pre-finetuned on Video2Reaction transfer effectively to VCE, another induced emotion dataset with a different taxonomy and video domain. Notably, LLaVA-NeXT-Video-7B pre-finetuned on Video2Reaction and adapted on only 1% of VCE training data achieves a top-3 accuracy of 0.682, on par with the best reported VCE performance trained on the full dataset. The dataset is available at https://huggingface.co/datasets/infofusionlab/Video2Reaction