William Toner

William Toner, Amos Storkey

Training neural network classifiers on datasets contaminated with noisy labels significantly increases the risk of overfitting. Thus, effectively implementing Early Stopping in noisy label environments is crucial. Under ideal circumstances, Early Stopping utilises a validation set uncorrupted by label noise to effectively monitor generalisation during training. However, obtaining a noise-free validation dataset can be costly and challenging to obtain. This study establishes that, in many typical learning environments, a noise-free validation set is not necessary for effective Early Stopping. Instead, near-optimal results can be achieved by monitoring accuracy on a noisy dataset - drawn from the same distribution as the noisy training set. Referred to as `Noisy Early Stopping' (NES), this method simplifies and reduces the cost of implementing Early Stopping. We provide theoretical insights into the conditions under which this method is effective and empirically demonstrate its robust performance across standard benchmarks using common loss functions.

William Toner, Amos Storkey

Training neural network classifiers on datasets with label noise poses a risk of overfitting them to the noisy labels. To address this issue, researchers have explored alternative loss functions that aim to be more robust. The `forward-correction' is a popular approach wherein the model outputs are noised before being evaluated against noisy data. When the true noise model is known, applying the forward-correction guarantees consistency of the learning algorithm. While providing some benefit, the correction is insufficient to prevent overfitting to finite noisy datasets. In this work, we propose an approach to tackling overfitting caused by label noise. We observe that the presence of label noise implies a lower bound on the noisy generalised risk. Motivated by this observation, we propose imposing a lower bound on the training loss to mitigate overfitting. Our main contribution is providing theoretical insights that allow us to approximate the lower bound given only an estimate of the average noise rate. We empirically demonstrate that using this bound significantly enhances robustness in various settings, with virtually no additional computational cost.

William Toner, Luke Darlow

Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature normalisation that improves model generalisation. In this paper we analyse the sets of functions expressible using these linear model architectures. In so doing we show that several popular variants of linear models for time series forecasting are equivalent and functionally indistinguishable from standard, unconstrained linear regression. We characterise the model classes for each linear variant. We demonstrate that each model can be reinterpreted as unconstrained linear regression over a suitably augmented feature set, and therefore admit closed-form solutions when using a mean-squared loss function. We provide experimental evidence that the models under inspection learn nearly identical solutions, and finally demonstrate that the simpler closed form solutions are superior forecasters across 72% of test settings.

William Toner, Thomas L. Lee, Artjom Joosen et al.

Time series foundation models (FMs) have emerged as a popular paradigm for zero-shot multi-domain forecasting. FMs are trained on numerous diverse datasets and claim to be effective forecasters across multiple different time series domains, including cloud data. In this work we investigate this claim, exploring the effectiveness of FMs on cloud data. We demonstrate that many well-known FMs fail to generate meaningful or accurate zero-shot forecasts in this setting. We support this claim empirically, showing that FMs are outperformed consistently by simple linear baselines. We also illustrate a number of interesting pathologies, including instances where FMs suddenly output seemingly erratic, random-looking forecasts. Our results suggest a widespread failure of FMs to model cloud data.

Thomas L. Lee, William Toner, Rajkarn Singh et al.

Foundation models (FMs) have emerged as a promising approach for time series forecasting. While effective, FMs typically remain fixed during deployment due to the high computational costs of learning them online. Consequently, deployed FMs fail to adapt their forecasts to current data characteristics, despite the availability of online feedback from newly arriving data. This raises the question of whether FM performance can be enhanced by the efficient usage of this feedback. We propose ELF to answer this question. ELF is a lightweight mechanism for the online adaption of FM forecasts in response to online feedback. ELF consists of two parts: a) the ELF-Forecaster which is used to learn the current data distribution; and b) the ELF-Weighter which is used to combine the forecasts of the FM and the ELF-Forecaster. We evaluate the performance of ELF in conjunction with several recent FMs across a suite of standard time series datasets. In all of our experiments we find that using ELF improves performance. This work demonstrates how efficient usage of online feedback can be used to improve FM forecasts.