Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of equivariance or conditional invariance are absent from the literature. This work initiates the study of nonparametric randomization tests for symmetry (invariance or equivariance) of a conditional distribution under the action of a specified locally compact group. We develop a general framework for randomization tests with finite-sample Type I error control and, using kernel methods, implement tests with finite-sample power lower bounds. We also describe and implement approximate versions of the tests, which are asymptotically consistent. We study their properties empirically on synthetic examples, and on applications to testing for symmetry in two problems from high-energy particle physics.

We study a censored variant of the data-driven newsvendor problem, where the decision-maker must select an ordering quantity that minimizes expected overage and underage costs based only on offline censored sales data, rather than historical demand realizations. Our goal is to understand how the degree of historical demand censoring affects the performance of any learning algorithm for this problem. To isolate this impact, we adopt a distributionally robust optimization framework, evaluating policies according to their worst-case regret over an ambiguity set of distributions. This set is defined by the largest historical order quantity (the observable boundary of the dataset), and contains all distributions matching the true demand distribution up to this boundary, while allowing them to be arbitrary afterwards. We demonstrate a spectrum of achievability under demand censoring by deriving a natural necessary and sufficient condition under which vanishing regret is an achievable goal. In regimes in which it is not, we exactly characterize the information loss due to censoring: an insurmountable lower bound on the performance of any policy, even when the decision-maker has access to infinitely many demand samples. We then leverage these sharp characterizations to propose a natural robust algorithm that adapts to the historical level of demand censoring. We derive finite-sample guarantees for this algorithm across all possible censoring regimes and show its near-optimality with matching lower bounds (up to polylogarithmic factors). We moreover demonstrate its robust performance via extensive numerical experiments on both synthetic and real-world datasets.

In recent years, Artificial Intelligence (AI) and Machine Learning (ML) have grown tremendously in popularity across various industries. From healthcare and finance to retail and automotive, adopting machine learning models has led to significant advancements[1]. However, building machine learning models traditionally requires deep knowledge in multiple areas, such as data preprocessing, feature engineering, model selection, hyperparameter tuning, and evaluation[2]. For many beginners and even experienced practitioners, this process can be time-consuming and technically challenging. This is where AutoML (Automated Machine Learning) comes in. AutoML simplifies the process of building machine learning models by automating many of the steps that would otherwise require manual intervention [3]. AutoML tools can automatically preprocess data, select the most suitable algorithms, and fine-tune hyperparameters to produce highly accurate models [4]. This automation not only speeds up the model development cycle but also allows users without deep knowledge of machine learning to create models with comparable performance to those made by experienced data scientists.

The frequency or volume estimation of unending data streams is a concern in many domains, starting with telecommunications but spreading to social networks, finance, and learning-augmented streaming algorithms [10-15] is receiving website engine. In network fields, for example, professionals significant attention due to the powerful potential of machine want to keep track of the activity frequency to identify overall learning (ML) to relieve or eliminate the binding of data network health and potential anomalies or changes in behavior, characteristics and the sketch design. Their typical workflow which, however, is often challenging because the amount of involves training a heavy hitter oracle, which receives a key information may be too large to store in an embedded device and returns a prediction of whether it will be heavy or not, then or to keep conveniently in fast storage [1]. As a consequence, inserts the most frequent keys into unique buckets and applies sketch, which is a set of counters or bitmaps associated with a sketch to the remaining keys. Although filtering heavy items hash functions, and a set of simple operations that record has been proven to improve the overall sketch performance on approximate information [2], has grown in popularity in the heavy-tailed distribution [4, 10], these offline and supervised context of high-velocity data streams and limited computational methods could hardly work in real-world applications.

Clustering the nodes of a graph is a cornerstone of graph analysis and has been extensively studied. However, some popular methods are not suitable for very large graphs: e.g., spectral clustering requires the computation of the spectral decomposition of the Laplacian matrix, which is not applicable for large graphs with a large number of communities. This work introduces PASCO, an overlay that accelerates clustering algorithms. Our method consists of three steps: 1-We compute several independent small graphs representing the input graph by applying an efficient and structure-preserving coarsening algorithm. 2-A clustering algorithm is run in parallel onto each small graph and provides several partitions of the initial graph. 3-These partitions are aligned and combined with an optimal transport method to output the final partition. The PASCO framework is based on two key contributions: a novel global algorithm structure designed to enable parallelization and a fast, empirically validated graph coarsening algorithm that preserves structural properties. We demonstrate the strong performance of 1 PASCO in terms of computational efficiency, structural preservation, and output partition quality, evaluated on both synthetic and real-world graph datasets.

In the realm of gradient-based optimization, Nesterov's accelerated gradient method (NAG) is a landmark advancement, achieving an accelerated convergence rate that outperforms the vanilla gradient descent method for convex function. However, for strongly convex functions, whether NAG converges linearly remains an open question, as noted in the comprehensive review by Chambolle and Pock [2016]. This issue, aside from the critical step size, was addressed by Li et al. [2024a] using a high-resolution differential equation framework. Furthermore, Beck [2017, Section 10.7.4] introduced a monotonically convergent variant of NAG, referred to as M-NAG. Despite these developments, the Lyapunov analysis presented in [Li et al., 2024a] cannot be directly extended to M-NAG. In this paper, we propose a modification to the iterative relation by introducing a gradient term, leading to a new gradient-based iterative relation. This adjustment allows for the construction of a novel Lyapunov function that excludes kinetic energy. The linear convergence derived from this Lyapunov function is independent of both the parameters of the strongly convex functions and the step size, yielding a more general and robust result. Notably, we observe that the gradient iterative relation derived from M-NAG is equivalent to that from NAG when the position-velocity relation is applied. However, the Lyapunov analysis does not rely on the position-velocity relation, allowing us to extend the linear convergence to M-NAG. Finally, by utilizing two proximal inequalities, which serve as the proximal counterparts of strongly convex inequalities, we extend the linear convergence to both the fast iterative shrinkage-thresholding algorithm (FISTA) and its monotonic counterpart (M-FISTA).

We address the challenge of incorporating document-level metadata into topic modeling to improve topic mixture estimation. To overcome the computational complexity and lack of theoretical guarantees in existing Bayesian methods, we extend probabilistic latent semantic indexing (pLSI), a frequentist framework for topic modeling, by incorporating document-level covariates or known similarities between documents through a graph formalism. Modeling documents as nodes and edges denoting similarities, we propose a new estimator based on a fast graph-regularized iterative singular value decomposition (SVD) that encourages similar documents to share similar topic mixture proportions. We characterize the estimation error of our proposed method by deriving high-probability bounds and develop a specialized cross-validation method to optimize our regularization parameters. We validate our model through comprehensive experiments on synthetic datasets and three real-world corpora, demonstrating improved performance and faster inference compared to existing Bayesian methods.

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.

Log-based anomaly detection (LogAD) is the main component of Artificial Intelligence for IT Operations (AIOps), which can detect anomalous that occur during the system on-the-fly. Existing methods commonly extract log sequence features using classical machine learning techniques to identify whether a new sequence is an anomaly or not. However, these classical approaches often require trade-offs between efficiency and accuracy. The advent of quantum machine learning (QML) offers a promising alternative. By transforming parts of classical machine learning computations into parameterized quantum circuits (PQCs), QML can significantly reduce the number of trainable parameters while maintaining accuracy comparable to classical counterparts. In this work, we introduce a unified framework, \ourframework{}, for evaluating QML models in the context of LogAD. This framework incorporates diverse log data, integrated QML models, and comprehensive evaluation metrics. State-of-the-art methods such as DeepLog, LogAnomaly, and LogRobust, along with their quantum-transformed counterparts, are included in our framework.Beyond standard metrics like F1 score, precision, and recall, our evaluation extends to factors critical to QML performance, such as specificity, the number of circuits, circuit design, and quantum state encoding. Using \ourframework{}, we conduct extensive experiments to assess the performance of these models and their quantum counterparts, uncovering valuable insights and paving the way for future research in QML model selection and design for LogAD.

Humans distill complex experiences into fundamental abstractions that enable rapid learning and adaptation. Similarly, autoregressive transformers exhibit adaptive learning through in-context learning (ICL), which begs the question of how. In this paper, we propose concept encoding-decoding mechanism to explain ICL by studying how transformers form and use internal abstractions in their representations. On synthetic ICL tasks, we analyze the training dynamics of a small transformer and report the coupled emergence of concept encoding and decoding. As the model learns to encode different latent concepts (e.g., ``Finding the first noun in a sentence.") into distinct, separable representations, it concureently builds conditional decoding algorithms and improve its ICL performance. We validate the existence of this mechanism across pretrained models of varying scales (Gemma-2 2B/9B/27B, Llama-3.1 8B/70B). Further, through mechanistic interventions and controlled finetuning, we demonstrate that the quality of concept encoding is causally related and predictive of ICL performance. Our empirical insights shed light into better understanding the success and failure modes of large language models via their representations.