As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a particular label (e.g. approve a bank loan), and manipulate their features accordingly. Work in strategic classification and decision-dependent distributions seeks to characterize the closed-loop behavior of deploying learning algorithms by explicitly considering the effect of the classifier on the underlying data distribution. More recently, works in performative prediction seek to classify the closed-loop behavior by considering general properties of the mapping from classifier to data distribution, rather than an explicit form. Building on this notion, we analyze repeated risk minimization as the perturbed trajectories of the gradient flows of performative risk minimization. We consider the case where there may be multiple local minimizers of performative risk, motivated by situations where the initial conditions may have significant impact on the long-term behavior of the system. We provide sufficient conditions to characterize the region of attraction for the various equilibria in this settings. Additionally, we introduce the notion of performative alignment, which provides a geometric condition on the convergence of repeated risk minimization to performative risk minimizers.

Unlocking the potential of deep learning in Peak-Hour Series Forecasting (PHSF) remains a critical yet underexplored task in various domains. While state-of-the-art deep learning models excel in regular Time Series Forecasting (TSF), they struggle to achieve comparable results in PHSF. This can be attributed to the challenges posed by the high degree of non-stationarity in peak-hour series, which makes direct forecasting more difficult than standard TSF. Additionally, manually extracting the maximum value from regular forecasting results leads to suboptimal performance due to models minimizing the mean deficit. To address these issues, this paper presents Seq2Peak, a novel framework designed specifically for PHSF tasks, bridging the performance gap observed in TSF models. Seq2Peak offers two key components: the CyclicNorm pipeline to mitigate the non-stationarity issue and a simple yet effective trainable-parameter-free peak-hour decoder with a hybrid loss function that utilizes both the original series and peak-hour series as supervised signals. Extensive experimentation on publicly available time series datasets demonstrates the effectiveness of the proposed framework, yielding a remarkable average relative improvement of 37.7% across four real-world datasets for both transformer- and non-transformer-based TSF models.

Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invariances called the twelvefold way in enumerative combinatorics and develop a method to characterize lossless compression limits. Explicit computations for all twelve settings are carried out for i.i.d. uniform and Bernoulli distributions. Comparisons among settings provide quantitative insight.

Graph convolutional networks (GCNs), aiming to obtain node embeddings by integrating high-order neighborhood information through stacked graph convolution layers, have demonstrated great power in many network analysis tasks such as node classification and link prediction. However, a fundamental weakness of GCNs, that is, topological limitations, including over-smoothing and local homophily of topology, limits their ability to represent networks. Existing studies for solving these topological limitations typically focus only on the convolution of features on network topology, which inevitably relies heavily on network structure. Moreover, most networks are text-rich, so it is important to integrate not only document-level information, but also the local text information which is particularly significant while often ignored by the existing methods. To solve these limitations, we propose BiTe-GCN, a novel GCN architecture modeling via bidirectional convolution of topology and features on text-rich networks. Specifically, we first transform the original text-rich network into an augmented bi-typed heterogeneous network, capturing both the global document-level information and the local text-sequence information from texts. We then introduce discriminative convolution mechanisms, which performs convolution on this augmented bi-typed network, realizing the convolutions of topology and features altogether in the same system, and learning different contributions of these two parts (i.e., network part and text part), automatically for the given learning objectives. Extensive experiments on text-rich networks demonstrate that our new architecture outperforms the state-of-the-arts by a breakout improvement. Moreover, this architecture can also be applied to several e-commerce search scenes such as JD searching, and experiments on JD dataset show the superiority of the proposed architecture over the related methods.