While gradient-based discrete samplers are effective in sampling from complex distributions, they are susceptible to getting trapped in local minima, particularly in high-dimensional, multimodal discrete distributions, owing to the discontinuities inherent in these landscapes. To circumvent this issue, we combine parallel tempering, also known as replica exchange, with the discrete Langevin proposal and develop the Parallel Tempering enhanced Discrete Langevin Proposal (PTDLP), which are simulated at a series of temperatures. Significant energy differences prompt sample swaps, which are governed by a Metropolis criterion specifically designed for discrete sampling to ensure detailed balance is maintained. Additionally, we introduce an automatic scheme to determine the optimal temperature schedule and the number of chains, ensuring adaptability across diverse tasks with minimal tuning. Theoretically, we establish that our algorithm converges non-asymptotically to the target energy and exhibits faster mixing compared to a single chain. Empirical results further emphasize the superiority of our method in sampling from complex, multimodal discrete distributions, including synthetic problems, restricted Boltzmann machines, and deep energy-based models.

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable information that can be integrated into a decision pipeline. Rather than seeing the lack of certitude and inherent randomness of GAI as a problem, we view it as an opportunity. Indeed, variable answers to given prompts can be leveraged to construct a prior distribution which reflects assuredness of AI predictions. This prior distribution may be combined with tailored datasets for a fully Bayesian analysis with an AI-driven prior. In this paper, we explore such a possibility within a non-parametric Bayesian framework. The basic idea consists of assigning a Dirichlet process prior distribution on the data-generating distribution with AI generative model as its baseline. Hyper-parameters of the prior can be tuned out-of-sample to assess the informativeness of the AI prior. Posterior simulation is achieved by computing a suitably randomized functional on an augmented data that consists of observed (labeled) data as well as fake data whose labels have been imputed using AI. This strategy can be parallelized and rapidly produces iid samples from the posterior by optimization as opposed to sampling from conditionals. Our method enables (predictive) inference and uncertainty quantification leveraging AI predictions in a coherent probabilistic manner.

We propose a scalable inference algorithm for Bayes posteriors defined on a reproducing kernel Hilbert space (RKHS). Given a likelihood function and a Gaussian random element representing the prior, the corresponding Bayes posterior measure $\Pi_{\text{B}}$ can be obtained as the stationary distribution of an RKHS-valued Langevin diffusion. We approximate the infinite-dimensional Langevin diffusion via a projection onto the first $M$ components of the Kosambi-Karhunen-Lo\`eve expansion. Exploiting the thus obtained approximate posterior for these $M$ components, we perform inference for $\Pi_{\text{B}}$ by relying on the law of total probability and a sufficiency assumption. The resulting method scales as $O(M^3+JM^2)$, where $J$ is the number of samples produced from the posterior measure $\Pi_{\text{B}}$. Interestingly, the algorithm recovers the posterior arising from the sparse variational Gaussian process (SVGP) (see Titsias, 2009) as a special case, owed to the fact that the sufficiency assumption underlies both methods. However, whereas the SVGP is parametrically constrained to be a Gaussian process, our method is based on a non-parametric variational family $\mathcal{P}(\mathbb{R}^M)$ consisting of all probability measures on $\mathbb{R}^M$. As a result, our method is provably close to the optimal $M$-dimensional variational approximation of the Bayes posterior $\Pi_{\text{B}}$ in $\mathcal{P}(\mathbb{R}^M)$ for convex and Lipschitz continuous negative log likelihoods, and coincides with SVGP for the special case of a Gaussian error likelihood.

We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let $\mathrm{OPT}:=\max_{\sigma_1,\cdots,\sigma_n}\mathbb{E}\left[\sum_{j=1}^{m}\max_{i\in S_j} X_i\right]$, where $X_i$ are Gaussian, $S_j\subset[n]$ and $\sum_i\sigma_i^2=1$, then our theoretical results include: - We characterize the optimal variance allocation -- it concentrates on a small subset of variables as $|S_j|$ increases, - A polynomial time approximation scheme (PTAS) for computing $\mathrm{OPT}$ when $m=1$, and - An $O(\log n)$ approximation algorithm for computing $\mathrm{OPT}$ for general $m>1$. Such expectation maximization problems occur in diverse applications, ranging from utility maximization in auctions markets to learning mixture models in quantitative genetics.

The widespread distribution of microplastics (MPs) in the environment presents significant challenges for their detection and identification. Fluorescence imaging has emerged as a promising technique for enhancing plastic particle detectability and enabling accurate classification based on fluorescence behavior. However, conventional segmentation techniques face limitations, including poor signal-to-noise ratio, inconsistent illumination, thresholding difficulties, and false positives from natural organic matter (NOM). To address these challenges, this study introduces the Fluorescence Imaging Microplastic Analysis Platform (FIMAP), a retrofitted multispectral camera with four optical filters and five excitation wavelengths. FIMAP enables comprehensive characterization of the fluorescence behavior of ten Nile Red-stained MPs: HDPE, LDPE, PP, PS, EPS, ABS, PVC, PC, PET, and PA, while effectively excluding NOM. Using K-means clustering for robust segmentation (Intersection over Union = 0.877) and a 20-dimensional color coordinate multivariate nearest neighbor approach for MP classification (>3.14 mm), FIMAP achieves 90% precision, 90% accuracy, 100% recall, and an F1 score of 94.7%. Only PS was occasionally misclassified as EPS. For smaller MPs (35-104 microns), classification accuracy declined, likely due to reduced stain sorption, fewer detectable pixels, and camera instability. Integrating FIMAP with higher-magnification instruments, such as a microscope, may enhance MP identification. This study presents FIMAP as an automated, high-throughput framework for detecting and classifying MPs across large environmental sample volumes.

This paper presents a novel data-driven approach to mitigating employee attrition using machine learning and data engineering techniques. The proposed framework integrates data from various human resources systems and leverages advanced feature engineering to capture a comprehensive set of factors influencing attrition. The study outlines a robust modeling approach that addresses challenges such as imbalanced datasets, categorical data handling, and model interpretation. The methodology includes careful consideration of training and testing strategies, baseline model establishment, and the development of calibrated predictive models. The research emphasizes the importance of model interpretation using techniques like SHAP values to provide actionable insights for organizations. Key design choices in algorithm selection, hyperparameter tuning, and probability calibration are discussed. This approach enables organizations to proactively identify attrition risks and develop targeted retention strategies, ultimately redu

Data classification techniques partition the data or feature space into smaller sub-spaces, each corresponding to a specific class. To classify into subspaces, physical features e.g., distance and distributions are utilized. This approach is challenging for the characterization of complex patterns that are embedded in the dataset. However, complex networks remain a powerful technique for capturing internal relationships and class structures, enabling High-Level Classification. Although several complex network-based classification techniques have been proposed, high-level classification by leveraging pattern formation to classify data has not been utilized. In this work, we present two network-based classification techniques utilizing unique measures derived from the Minimum Spanning Tree and Single Source Shortest Path. These network measures are evaluated from the data patterns represented by the inherent network constructed from each class. We have applied our proposed techniques to several data classification scenarios including synthetic and real-world datasets. Compared to the existing classic high-level and machine-learning classification techniques, we have observed promising numerical results for our proposed approaches. Furthermore, the proposed models demonstrate the following distinguished features in comparison to the previous high-level classification techniques: (1) A single network measure is introduced to characterize the data pattern, eliminating the need to determine weight parameters among network measures. Therefore, the model is largely simplified, while obtaining better classification results. (2) The metrics proposed are sensitive and used for classification with competitive results.

We introduce a novel mathematical framework that unifies neural population dynamics, hippocampal sharp wave-ripple (SpWR) generation, and cognitive consistency constraints inspired by Heider's theory. Our model leverages low-dimensional manifold representations to capture structured neural drift and incorporates a balance energy function to enforce coherent synaptic interactions, effectively simulating the memory consolidation processes observed in biological systems. Simulation results demonstrate that our approach not only reproduces key features of SpWR events but also enhances network interpretability. This work paves the way for scalable neuromorphic architectures that bridge neuroscience and artificial intelligence, offering more robust and adaptive learning mechanisms for future intelligent systems.

Glioma, the prevalent primary brain tumor, exhibits diverse aggressiveness levels and prognoses. Precise classification of glioma is paramount for treatment planning and predicting prognosis. This study aims to develop an algorithm to fuse the MRI images from T1, T2, T1ce, and fluid-attenuated inversion recovery (FLAIR) sequences to enhance the efficacy of glioma subclass classification as no tumor, necrotic core, peritumoral edema, and enhancing tumor. The MRI images from BraTS datasets were used in this work. The images were pre-processed using max-min normalization to ensure consistency in pixel intensity values across different images. The segmentation of the necrotic core, peritumoral edema, and enhancing tumor was performed on 2D and 3D images separately using UNET architecture. Further, the segmented regions from multimodal MRI images were fused using the weighted averaging technique. Integrating 2D and 3D segmented outputs enhances classification accuracy by capturing detailed features like tumor shape, boundaries, and intensity distribution in slices, while also providing a comprehensive view of spatial extent, shape, texture, and localization within the brain volume. The fused images were used as input to the pre-trained ResNet50 model for glioma subclass classification. The network is trained on 80% and validated on 20% of the data. The proposed method achieved a classification of accuracy of 99.25%, precision of 99.30%, recall of 99.10, F1 score of 99.19%, Intersection Over Union of 84.49%, and specificity of 99.76, which showed a significantly higher performance than existing techniques. These findings emphasize the significance of glioma segmentation and classification in aiding accurate diagnosis.

Object-Centric Motion Generation (OCMG) plays a key role in a variety of industrial applications$\unicode{x2014}$such as robotic spray painting and welding$\unicode{x2014}$requiring efficient, scalable, and generalizable algorithms to plan multiple long-horizon trajectories over free-form 3D objects. However, existing solutions rely on specialized heuristics, expensive optimization routines, or restrictive geometry assumptions that limit their adaptability to real-world scenarios. In this work, we introduce a novel, fully data-driven framework that tackles OCMG directly from 3D point clouds, learning to generalize expert path patterns across free-form surfaces. We propose MaskPlanner, a deep learning method that predicts local path segments for a given object while simultaneously inferring "path masks" to group these segments into distinct paths. This design induces the network to capture both local geometric patterns and global task requirements in a single forward pass. Extensive experimentation on a realistic robotic spray painting scenario shows that our approach attains near-complete coverage (above 99%) for unseen objects, while it remains task-agnostic and does not explicitly optimize for paint deposition. Moreover, our real-world validation on a 6-DoF specialized painting robot demonstrates that the generated trajectories are directly executable and yield expert-level painting quality. Our findings crucially highlight the potential of the proposed learning method for OCMG to reduce engineering overhead and seamlessly adapt to several industrial use cases.