Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most existing coarsening methods are training-dependent, leading to lower efficiency, and they all require a predefined coarsening rate, lacking an adaptive approach. In this paper, we employ granular-ball computing to effectively compress graph data. We construct a coarsened graph network by iteratively splitting the graph into granular-balls based on a purity threshold and using these granular-balls as super vertices. This granulation process significantly reduces the size of the original graph, thereby greatly enhancing the training efficiency and scalability of GNNs. Additionally, our algorithm can adaptively perform splitting without requiring a predefined coarsening rate. Experimental results demonstrate that our method achieves accuracy comparable to training on the original graph. Noise injection experiments further indicate that our method exhibits robust performance. Moreover, our approach can reduce the graph size by up to 20 times without compromising test accuracy, substantially enhancing the scalability of GNNs.

Open intent classification is critical for the development of dialogue systems, aiming to accurately classify known intents into their corresponding classes while identifying unknown intents. Prior boundary-based methods assumed known intents fit within compact spherical regions, focusing on coarse-grained representation and precise spherical decision boundaries. However, these assumptions are often violated in practical scenarios, making it difficult to distinguish known intent classes from unknowns using a single spherical boundary. To tackle these issues, we propose a Multi-granularity Open intent classification method via adaptive Granular-Ball decision boundary (MOGB). Our MOGB method consists of two modules: representation learning and decision boundary acquiring. To effectively represent the intent distribution, we design a hierarchical representation learning method. This involves iteratively alternating between adaptive granular-ball clustering and nearest sub-centroid classification to capture fine-grained semantic structures within known intent classes. Furthermore, multi-granularity decision boundaries are constructed for open intent classification by employing granular-balls with varying centroids and radii. Extensive experiments conducted on three public datasets demonstrate the effectiveness of our proposed method.

Bundle recommendation aims to recommend the user a bundle of items as a whole. Nevertheless, they usually neglect the diversity of the user's intents on adopting items and fail to disentangle the user's intents in representations. In the real scenario of bundle recommendation, a user's intent may be naturally distributed in the different bundles of that user (Global view), while a bundle may contain multiple intents of a user (Local view). Each view has its advantages for intent disentangling: 1) From the global view, more items are involved to present each intent, which can demonstrate the user's preference under each intent more clearly. 2) From the local view, it can reveal the association among items under each intent since items within the same bundle are highly correlated to each other. To this end, we propose a novel model named Multi-view Intent Disentangle Graph Networks (MIDGN), which is capable of precisely and comprehensively capturing the diversity of the user's intent and items' associations at the finer granularity. Specifically, MIDGN disentangles the user's intents from two different perspectives, respectively: 1) In the global level, MIDGN disentangles the user's intent coupled with inter-bundle items; 2) In the Local level, MIDGN disentangles the user's intent coupled with items within each bundle. Meanwhile, we compare the user's intents disentangled from different views under the contrast learning framework to improve the learned intents. Extensive experiments conducted on two benchmark datasets demonstrate that MIDGN outperforms the state-of-the-art methods by over 10.7% and 26.8%, respectively.

We propose Distribution Embedding Networks (DEN) for classification with small data using meta-learning techniques. Unlike existing meta-learning approaches that focus on image recognition tasks and require the training and target tasks to be similar, DEN is specifically designed to be trained on a diverse set of training tasks and applied on tasks whose number and distribution of covariates differ vastly from its training tasks. Such property of DEN is enabled by its three-block architecture: a covariate transformation block followed by a distribution embedding block and then a classification block. We provide theoretical insights to show that this architecture allows the embedding and classification blocks to be fixed after pre-training on a diverse set of tasks; only the covariate transformation block with relatively few parameters needs to be updated for each new task. To facilitate the training of DEN, we also propose an approach to synthesize binary classification training tasks, and demonstrate that DEN outperforms existing methods in a number of synthetic and real tasks in numerical studies.

We consider the problem of estimating a good maximizer of a black-box function given noisy examples. To solve such problems, we propose to fit a new type of function which we call a global optimization network (GON), defined as any composition of an invertible function and a unimodal function, whose unique global maximizer can be inferred in $\mathcal{O}(D)$ time. In this paper, we show how to construct invertible and unimodal functions by using linear inequality constraints on lattice models. We also extend to \emph{conditional} GONs that find a global maximizer conditioned on specified inputs of other dimensions. Experiments show the GON maximizers are statistically significantly better predictions than those produced by convex fits, GPR, or DNNs, and are more reasonable predictions for real-world problems.

Real-world machine learning applications often have complex test metrics, and may have training and test data that follow different distributions. We propose addressing these issues by using a weighted loss function with a standard convex loss, but with weights on the training examples that are learned to optimize the test metric of interest on the validation set. These metric-optimized example weights can be learned for any test metric, including black box losses and customized metrics for specific applications. We illustrate the performance of our proposal with public benchmark datasets and real-world applications with domain shift and custom loss functions that balance multiple objectives, impose fairness policies, and are non-convex and non-decomposable.

In recent years, a great deal of interest has focused on conducting inference on the parameters in a linear model in the high-dimensional setting. In this paper, we consider a simple and very na\"{i}ve two-step procedure for this task, in which we (i) fit a lasso model in order to obtain a subset of the variables; and (ii) fit a least squares model on the lasso-selected set. Conventional statistical wisdom tells us that we cannot make use of the standard statistical inference tools for the resulting least squares model (such as confidence intervals and $p$-values), since we peeked at the data twice: once in running the lasso, and again in fitting the least squares model. However, in this paper, we show that under a certain set of assumptions, with high probability, the set of variables selected by the lasso is deterministic. Consequently, the na\"{i}ve two-step approach can yield confidence intervals that have asymptotically correct coverage, as well as p-values with proper Type-I error control. Furthermore, this two-step approach unifies two existing camps of work on high-dimensional inference: one camp has focused on inference based on a sub-model selected by the lasso, and the other has focused on inference using a debiased version of the lasso estimator.