The rapid diffusion of autonomous pricing algorithms has reshaped competitive dynamics in digital marketplaces, raising important economic and policy questions about their potential for collusive behavior. A substantial body of research demonstrates that reinforcement-learning (RL) agents can autonomously coordinate on supracompetitive outcomes even in the absence of explicit communication. Foundational contributions--including the work in [1]--show that algorithmic agents may systematically learn tacitly collusive strategies across multiple market structures, with Q-learning in particular generating prices above competitive levels in Logit, Hotelling, and linear demand environments. These concerns are reinforced by seminal work such as [2], which demonstrates that simple Q-learning agents reliably sustain collusion through structured punishment and reward cycles in repeated pricing games, as well as by [3], who document how algorithmic systems may generate sudden price spikes in response to high-impact, low-probability events (HILP), unintentionally coordinating on elevated prices. The study of [4] establishes a robust empirical and computational foundation demonstrating that pricing algorithms may autonomously learn to collude. A complementary line of research focuses specifically on Q-learning's capacity to learn collusive equilibria, as documented in papers [2], [5], and [6]. These findings are consistent with the theoretical properties of Q-learning established by [7], who show that the algorithm incrementally learns long-run discounted value-maximizing strategies in sequential decision problems. More recent studies further reveal that deep reinforcement-learning (deep RL) algorithms--including DDQN and SAC--may also display collusive tendencies. For instance, [8] documents that modern RL systems can coordinate on higher-than-competitive prices under a variety of market configurations.

Two-photon lithography (TPL) is a sophisticated additive manufacturing technology for creating three-dimensional (3D) micro- and nano-structures. Maintaining the health of TPL systems is critical for ensuring consistent fabrication quality. Current maintenance practices often rely on experience rather than informed monitoring of machine health, resulting in either untimely maintenance that causes machine downtime and poor-quality fabrication, or unnecessary maintenance that leads to inefficiencies and avoidable downtime. To address this gap, this paper presents three methods for accurate and timely monitoring of TPL machine health. Through integrating physics-informed data-driven predictive models for structure dimensions with statistical approaches, the proposed methods are able to handle increasingly complex scenarios featuring different levels of generalizability. A comprehensive experimental dataset that encompasses six process parameter combinations and six structure dimensions under two machine health conditions was collected to evaluate the effectiveness of the proposed approaches. Across all test scenarios, the approaches are shown to achieve high accuracies, demonstrating excellent effectiveness, robustness, and generalizability. These results represent a significant step toward condition-based maintenance for TPL systems.

Change-point detection has garnered significant attention due to its broad range of applications, including epidemic disease outbreaks, social network evolution, image analysis, and wireless communications. In an online setting, where new data samples arrive sequentially, it is crucial to continuously test whether these samples originate from a different distribution. Ideally, the detection algorithm should be distribution-free to ensure robustness in real-world applications. In this paper, we reproduce a recently proposed online change-point detection algorithm based on an efficient kernel-based scan B-statistic, and compare its performance with two commonly used parametric statistics. Our numerical experiments demonstrate that the scan B-statistic consistently delivers superior performance. In more challenging scenarios, parametric methods may fail to detect changes, whereas the scan B-statistic successfully identifies them in a timely manner. Additionally, the use of subsampling techniques offers a modest improvement to the original algorithm.

There are synergies of research interests and industrial efforts in modeling fairness and correcting algorithmic bias in machine learning. In this paper, we present a scalable algorithm for spectral clustering (SC) with group fairness constraints. Group fairness is also known as statistical parity where in each cluster, each protected group is represented with the same proportion as in the entirety. While FairSC algorithm (Kleindessner et al., 2019) is able to find the fairer clustering, it is compromised by high costs due to the kernels of computing nullspaces and the square roots of dense matrices explicitly. We present a new formulation of underlying spectral computation by incorporating nullspace projection and Hotelling's deflation such that the resulting algorithm, called s-FairSC, only involves the sparse matrix-vector products and is able to fully exploit the sparsity of the fair SC model. The experimental results on the modified stochastic block model demonstrate that s-FairSC is comparable with FairSC in recovering fair clustering. Meanwhile, it is sped up by a factor of 12 for moderate model sizes. s-FairSC is further demonstrated to be scalable in the sense that the computational costs of s-FairSC only increase marginally compared to the SC without fairness constraints.

We present a novel scheme to boost detection power for kernel maximum mean discrepancy based sequential change-point detection procedures. Our proposed scheme features an optimal sub-sampling of the history data before the detection procedure, in order to tackle the power loss incurred by the random sub-sample from the enormous history data. We apply our proposed scheme to both Scan $B$ and Kernel Cumulative Sum (CUSUM) procedures, and improved performance is observed from extensive numerical experiments.

The ongoing transition from a linear (produce-use-dispose) to a circular economy poses significant challenges to current state-of-the-art information and communication technologies. In particular, the derivation of integrated, high-level views on material, process, and product streams from (real-time) data produced along value chains is challenging for several reasons. Most importantly, sufficiently rich data is often available yet not shared across company borders because of privacy concerns which make it impossible to build integrated process models that capture the interrelations between input materials, process parameters, and key performance indicators along value chains. In the current contribution, we propose a privacy-preserving, federated multivariate statistical process control (FedMSPC) framework based on Federated Principal Component Analysis (PCA) and Secure Multiparty Computation to foster the incentive for closer collaboration of stakeholders along value chains. We tested our approach on two industrial benchmark data sets - SECOM and ST-AWFD. Our empirical results demonstrate the superior fault detection capability of the proposed approach compared to standard, single-party (multiway) PCA. Furthermore, we showcase the possibility of our framework to provide privacy-preserving fault diagnosis to each data holder in the value chain to underpin the benefits of secure data sharing and federated process modeling.

In contrast to classical techniques for exploratory analysis of high-dimensional data sets, such as principal component analysis (PCA), neighbor embedding (NE) techniques tend to better preserve the local structure/topology of high-dimensional data. However, the ability to preserve local structure comes at the expense of interpretability: Techniques such as t-Distributed Stochastic Neighbor Embedding (t-SNE) or Uniform Manifold Approximation and Projection (UMAP) do not give insights into which input variables underlie the topological (cluster) structure seen in the corresponding embedding. We here propose different "tricks" from the chemometrics field based on PCA, Q-residuals and Hotelling's T2 contributions in combination with novel visualization approaches to derive local and global explanations of neighbor embedding. We show how our approach is capable of identifying discriminatory features between groups of data points that remain unnoticed when exploring NEs using standard univariate or multivariate approaches.

Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a wide range of applications, including signal processing, neuroscience and network analysis. In these applications, the online detection of changes is of crucial importance, but this can be highly challenging since such changes often occur in a low-dimensional embedding within high-dimensional data streams. We thus propose a new method, called PERsistence diagram-based ChangE-PoinT detection (PERCEPT), which leverages the learned topological structure from TDA to sequentially detect changes. PERCEPT follows two key steps: it first learns the embedded topology as a point cloud via persistence diagrams, then applies a non-parametric monitoring approach for detecting changes in the resulting point cloud distributions. This yields a non-parametric, topology-aware framework which can efficiently detect online changes from high-dimensional data streams. We investigate the effectiveness of PERCEPT over existing methods in a suite of numerical experiments where the data streams have an embedded topological structure. We then demonstrate the usefulness of PERCEPT in two applications in solar flare monitoring and human gesture detection.

We present a novel method for controlling extrapolation in the prediction profiler in the JMP software. The prediction profiler is a graphical tool for exploring high dimensional prediction surfaces for statistical and machine learning models. The profiler contains interactive cross-sectional views, or profile traces, of the prediction surface of a model. Our method helps users avoid exploring predictions that should be considered extrapolation. It also performs optimization over a constrained factor region that avoids extrapolation using a genetic algorithm. In simulations and real world examples, we demonstrate how optimal factor settings without constraint in the profiler are frequently extrapolated, and how extrapolation control helps avoid these solutions with invalid factor settings that may not be useful to the user.

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal components simultaneously using manifold optimization techniques to enforce orthogonality constraints. While effective, this approach is computationally burdensome so we also consider iterative deflation approaches which take advantage of efficient algorithms for rank-one SFPCA. We show that alternative deflation schemes can more efficiently extract signal from the data, in turn improving estimation of subsequent components. Finally, we compare the performance of our manifold optimization and deflation techniques in a scenario where orthogonality does not hold and find that they still lead to significantly improved performance.