In longitudinal observational studies with a time-to-event outcome, a common objective in causal analysis is to estimate the causal survival curve under hypothetical intervention scenarios within the study cohort. The g-formula is a particularly useful tool for this analysis. To enhance the traditional parametric g-formula approach, we developed a more adaptable Bayesian g-formula estimator. This estimator facilitates both longitudinal predictive and causal inference. It incorporates Bayesian additive regression trees in the modeling of the time-evolving generative components, aiming to mitigate bias due to model misspecification. Specifically, we introduce a more general class of g-formulas for discrete survival data. These formulas can incorporate the longitudinal balancing scores, which serve as an effective method for dimension reduction and are vital when dealing with an expanding array of time-varying confounders. The minimum sufficient formulation of these longitudinal balancing scores is linked to the nature of treatment regimes, whether static or dynamic. For each type of treatment regime, we provide posterior sampling algorithms, which are grounded in the Bayesian additive regression trees framework. We have conducted simulation studies to illustrate the empirical performance of our proposed Bayesian g-formula estimators, and to compare them with existing parametric estimators. We further demonstrate the practical utility of our methods in real-world scenarios using data from the Yale New Haven Health System's electronic health records.

In this paper, we find that ubiquitous time series (TS) forecasting models are prone to severe overfitting. To cope with this problem, we embrace a de-redundancy approach to progressively reinstate the intrinsic values of TS for future intervals. Specifically, we renovate the vanilla Transformer by reorienting the information aggregation mechanism from addition to subtraction. Then, we incorporate an auxiliary output branch into each block of the original model to construct a highway leading to the ultimate prediction. The output of subsequent modules in this branch will subtract the previously learned results, enabling the model to learn the residuals of the supervision signal, layer by layer. This designing facilitates the learning-driven implicit progressive decomposition of the input and output streams, empowering the model with heightened versatility, interpretability, and resilience against overfitting. Since all aggregations in the model are minus signs, which is called Minusformer. Extensive experiments demonstrate the proposed method outperform existing state-of-the-art methods, yielding an average performance improvement of 11.9% across various datasets.

Although convergence analyses of SGD with momentum for nonconvex functions have been provided While stochastic gradient descent (SGD) with momentum [11, 16, 39], none of them explain why convergence has fast convergence and excellent generalizability, a is faster than with SGD. The generalizability of SGD with theoretical explanation for this is lacking. In this paper, momentum has been well studied, and various experimental we show that SGD with momentum smooths the objective findings have been reported. While it has been suggested function, the degree of which is determined by the learning that momentum plays a role in reducing stochastic noise rate, the batch size, the momentum factor, the variance of [8, 11], stochastic noise has been shown to increase generalizability the stochastic gradient, and the upper bound of the gradient [18, 37, 59], and it has been claimed that stochastic norm. This theoretical finding reveals why momentum improves noise can help an algorithm escape from local solutions generalizability and provides new insights into the with poor generalizability [10, 15, 20, 28, 32].

Graph Neural Networks (GNNs) have seen significant success in tasks such as node classification, largely contingent upon the availability of sufficient labeled nodes. Yet, the excessive cost of labeling large-scale graphs led to a focus on active learning on graphs, which aims for effective data selection to maximize downstream model performance. Notably, most existing methods assume reliable graph topology, while real-world scenarios often present noisy graphs. Given this, designing a successful active learning framework for noisy graphs is highly needed but challenging, as selecting data for labeling and obtaining a clean graph are two tasks naturally interdependent: selecting high-quality data requires clean graph structure while cleaning noisy graph structure requires sufficient labeled data. Considering the complexity mentioned above, we propose an active learning framework, GALClean, which has been specifically designed to adopt an iterative approach for conducting both data selection and graph purification simultaneously with best information learned from the prior iteration. Importantly, we summarize GALClean as an instance of the Expectation-Maximization algorithm, which provides a theoretical understanding of its design and mechanisms. This theory naturally leads to an enhanced version, GALClean+. Extensive experiments have demonstrated the effectiveness and robustness of our proposed method across various types and levels of noisy graphs.

We introduce the QuadratiK package that incorporates innovative data analysis methodologies. The presented software, implemented in both R and Python, offers a comprehensive set of goodness-of-fit tests and clustering techniques using kernel-based quadratic distances, thereby bridging the gap between the statistical and machine learning literatures. Our software implements one, two and k-sample tests for goodness of fit, providing an efficient and mathematically sound way to assess the fit of probability distributions. Expanded capabilities of our software include supporting tests for uniformity on the $d$-dimensional Sphere based on Poisson kernel densities, and algorithms for generating random samples from Poisson kernel densities. Particularly noteworthy is the incorporation of a unique clustering algorithm specifically tailored for spherical data that leverages a mixture of Poisson-kernel-based densities on the sphere. Alongside this, our software includes additional graphical functions, aiding the users in validating, as well as visualizing and representing clustering results. This enhances interpretability and usability of the analysis. In summary, our R and Python packages serve as a powerful suite of tools, offering researchers and practitioners the means to delve deeper into their data, draw robust inference, and conduct potentially impactful analyses and inference across a wide array of disciplines.

Initial weighting is significant in deep neural networks because the random selection of weights produces different outputs and increases the probability of overfitting and underfitting. On the other hand, vector-based approaches to extract vector features need rich vectors for more accurate classification. The InceptionCapsule approach is presented to alleviate these two problems. This approach uses transfer learning and the Inception-ResNet model to avoid random selection of weights, which takes initial weights from ImageNet. It also uses the output of Inception middle layers to generate rich vectors. Extracted vectors are given to a capsule network for learning, which is equipped with an attention technique. Kvasir data and BUSI with the GT dataset were used to evaluate this approach. This model was able to achieve 97.62 accuracies in 5-class classification and also achieved 94.30 accuracies in 8-class classification on Kvasir. In the BUSI with GT dataset, the proposed approach achieved accuracy=98.88, Precision=95.34, and F1-score=93.74, which are acceptable results compared to other approaches in the literature.

Event prediction aims to forecast the time and type of a future event based on a historical event sequence. Despite its significance, several challenges exist, including the irregularity of time intervals between consecutive events, the existence of cycles, periodicity, and multi-scale event interactions, as well as the high computational costs for long event sequences. Existing neural temporal point processes (TPPs) methods do not capture the multi-scale nature of event interactions, which is common in many real-world applications such as clinical event data. To address these issues, we propose the cross-temporal-scale transformer (XTSFormer), designed specifically for irregularly timed event data. Our model comprises two vital components: a novel Feature-based Cycle-aware Time Positional Encoding (FCPE) that adeptly captures the cyclical nature of time, and a hierarchical multi-scale temporal attention mechanism. These scales are determined by a bottom-up clustering algorithm. Extensive experiments on several real-world datasets show that our XTSFormer outperforms several baseline methods in prediction performance.

Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction methods to project data onto interpretable spaces or organizing points into meaningful clusters. In practice, these methods are used sequentially, without guaranteeing that the clustering aligns well with the conducted dimensionality reduction. In this work, we offer a fresh perspective: that of distributions. Leveraging tools from optimal transport, particularly the Gromov-Wasserstein distance, we unify clustering and dimensionality reduction into a single framework called distributional reduction. This allows us to jointly address clustering and dimensionality reduction with a single optimization problem. Through comprehensive experiments, we highlight the versatility and interpretability of our method and show that it outperforms existing approaches across a variety of image and genomics datasets.

Considering a graph with unknown weights, can we find the shortest path for a pair of nodes if we know the minimal Steiner trees associated with some subset of nodes? That is, with respect to a fixed latent decision-making system (e.g., a weighted graph), we seek to solve one optimization problem (e.g., the shortest path problem) by leveraging information associated with another optimization problem (e.g., the minimal Steiner tree problem). In this paper, we study such a prototype problem called \textit{query-decision regression with task shifts}, focusing on the shortest path problem and the minimum Steiner tree problem. We provide theoretical insights regarding the design of realizable hypothesis spaces for building scoring models, and present two principled learning frameworks. Our experimental studies show that such problems can be solved to a decent extent with statistical significance.

We propose novel "clustering and conquer" procedures for the parallel large-scale ranking and selection (R&S) problem, which leverage correlation information for clustering to break the bottleneck of sample efficiency. In parallel computing environments, correlation-based clustering can achieve an $\mathcal{O}(p)$ sample complexity reduction rate, which is the optimal reduction rate theoretically attainable. Our proposed framework is versatile, allowing for seamless integration of various prevalent R&S methods under both fixed-budget and fixed-precision paradigms. It can achieve improvements without the necessity of highly accurate correlation estimation and precise clustering. In large-scale AI applications such as neural architecture search, a screening-free version of our procedure surprisingly surpasses fully-sequential benchmarks in terms of sample efficiency. This suggests that leveraging valuable structural information, such as correlation, is a viable path to bypassing the traditional need for screening via pairwise comparison--a step previously deemed essential for high sample efficiency but problematic for parallelization. Additionally, we propose a parallel few-shot clustering algorithm tailored for large-scale problems.