Dataset condensation is a newborn technique that generates a small dataset
that can be used in training deep neural networks to lower training costs. The
objective of dataset condensation is to ensure that the model trained with the
synthetic dataset can perform comparably to the model trained with full
datasets. However, existing methods predominantly concentrate on classification
tasks, posing challenges in their adaptation to time series forecasting
(TS-forecasting). This challenge arises from disparities in the evaluation of
synthetic data. In classification, the synthetic data is considered
well-distilled if the model trained with the full dataset and the model trained
with the synthetic dataset yield identical labels for the same input,
regardless of variations in output logits distribution. Conversely, in
TS-forecasting, the effectiveness of synthetic data distillation is determined
by the distance between predictions of the two models. The synthetic data is
deemed well-distilled only when all data points within the predictions are
similar. Consequently, TS-forecasting has a more rigorous evaluation
methodology compared to classification. To mitigate this gap, we theoretically
analyze the optimization objective of dataset condensation for TS-forecasting
and propose a new one-line plugin of dataset condensation designated as Dataset
Condensation for Time Series Forecasting (CondTSF) based on our analysis.
Plugging CondTSF into previous dataset condensation methods facilitates a
reduction in the distance between the predictions of the model trained with the
full dataset and the model trained with the synthetic dataset, thereby
enhancing performance. We conduct extensive experiments on eight commonly used
time series datasets. CondTSF consistently improves the performance of all
previous dataset condensation methods across all datasets, particularly at low
condensing ratios.

基于对时间序列预测数据集的理论分析，我们提出了一种针对时间序列预测的数据集精简方法 CondTSF，通过将 CondTSF 插入到先前的数据集精简方法中，减小了使用全数据集和使用合成数据集训练的模型之间的预测差距，从而提高了性能。我们在八个常用时间序列数据集上进行了大量实验，CondTSF 在所有数据集上持续改进了所有先前的数据集精简方法的性能，尤其是在精简比例低的情况下。

CondTSF：时间序列预测数据集简化的一行插件

CondTSF: One-line Plugin of Dataset Condensation for Time Series  Forecasting

Recent technological advancements have given rise to the ability of
collecting vast amounts of data, that often exceed the capacity of commonly
used machine learning algorithms. Approaches such as coresets and synthetic
data distillation have emerged as frameworks to generate a smaller, yet
representative, set of samples for downstream training. As machine learning is
increasingly applied to decision-making processes, it becomes imperative for
modelers to consider and address biases in the data concerning subgroups
defined by factors like race, gender, or other sensitive attributes. Current
approaches focus on creating fair synthetic representative samples by
optimizing local properties relative to the original samples. These methods,
however, are not guaranteed to positively affect the performance or fairness of
downstream learning processes. In this work, we present Fair Wasserstein
Coresets (FWC), a novel coreset approach which generates fair synthetic
representative samples along with sample-level weights to be used in downstream
learning tasks. FWC aims to minimize the Wasserstein distance between the
original datasets and the weighted synthetic samples while enforcing (an
empirical version of) demographic parity, a prominent criterion for algorithmic
fairness, via a linear constraint. We show that FWC can be thought of as a
constrained version of Lloyd's algorithm for k-medians or k-means clustering.
Our experiments, conducted on both synthetic and real datasets, demonstrate the
scalability of our approach and highlight the competitive performance of FWC
compared to existing fair clustering approaches, even when attempting to
enhance the fairness of the latter through fair pre-processing techniques.

通过生成公平的合成代表样本及样本级权重来最小化原始数据集与加权合成样本之间的 Wasserstein 距离，并通过线性约束实施（实证版本的）人口平等，从而在下游学习任务中提供公平的聚类算法，其竞争性能优于现有的公平聚类方法，即使通过公平预处理技术来增强后者的公平性。