Class-Conditioned Gaussian Mixture Modeling for Imbalanced Time Series Quantification

Time series data is very common in many real-world applications and in numerous domains, with increasing interest for automated information extraction using machine learning. One of these subfields is time series classification, which consists in assigning a label to each new, unseen time series. Many algorithms have been developed over the past decades, with the trade-off between predictive performance and computational cost being consistently discussed. Quant, an interval-based algorithm extracting quantiles from recursive, fixed, dyadic intervals, was shown to achieve high accuracy, while being very fast. We propose two changes to make this algorithm even faster. The first one is a better optimized implementation of the exact same algorithm. The second one is to derive approximate quantiles, using the Cornish-Fisher expansion, instead of exact quantiles. This change removes the necessity to sort the time series, leading to a smaller computational complexity. We call this novel algorithm MomentQuant. We provide evidence that our implementation of Quant is faster than the original one, and that MomentQuant is even faster than our implementation of Quant, at the cost of a tiny decrease in predictive performance. These improvements are especially relevant for real-life applications, where inference is performed much more often than training.

Time series classification (TSC) is dominated by a two-stage paradigm: train a feature encoder -- either from scratch on the target dataset or via pretraining on large corpora -- and then fit a task-specific classifier on top. While effective, this decoupling optimizes representation learning independently of the classification objective, requires per-dataset training, and prevents the model from exploiting label information during inference. We introduce TimEE, a 4.5M-parameter foundation model for end-to-end TSC via in-context learning. Given a labeled support set and a query time series, TimEE directly outputs a predicted class distribution in a single forward pass with no per-dataset training required. Following the prior-data fitted network (PFN) framework, TimEE is meta-trained exclusively on synthetic TSC tasks, where each task contains time series with distinct class identities arising from structured distributional shifts in the generative process. Despite seeing no real time series during pre-training, TimEE ranks first in ROC AUC (and third on accuracy) on the UCR benchmark among all compared methods, which include both foundation models and supervised deep learning baselines. To our knowledge, TimEE is the first purely synthetic-pretrained model to reach state-of-the-art performance on the UCR benchmark. These results establish end-to-end ICL with synthetic priors as a compelling, largely unexplored direction for TSC, with scaling, prior design, and richer generation mechanisms as natural avenues for improvement. Code is publicly available at http://github.com/automl/timee.

Real-world time-series classification tasks often exhibit class imbalance, which can be extremely severe in some applications. To avoid training biased classifiers on imbalanced data, sampling is one of the most popular data pre-processing techniques because of its classifier-agnostic nature. However, due to the complex temporal dependencies in original time-series data and the scarcity of minority-class samples, existing sampling methods, including interpolation-based oversampling methods and deep learning-based generative models, usually suffer from limited generalization and poor diversity when generating new time-series samples. This paper proposes a Frequency-domain representation-guided Multi-tree Genetic Programming-based oversampling approach (FreMGP) to imbalanced time-series classification, where each individual represents a set of synthetic samples for the minority class. A frequency-domain class-discriminative representation module based on contrastive learning is also developed, guiding the evolutionary search toward high-quality synthetic time-series samples. Experiments on imbalanced time-series datasets demonstrate that FreMGP outperforms existing oversampling methods and consistently improves the performance of different classifiers, including both general machine learning and deep learning models.