Text clustering holds significant value across various domains due to its ability to identify patterns and group related information. Current approaches which rely heavily on a computed similarity measure between documents are often limited in accuracy and interpretability. We present a novel approach to the problem based on a set of evolved search queries. Clusters are formed as the set of documents matched by a single search query in the set of queries. The queries are optimized to maximize the number of documents returned and to minimize the overlap between clusters (documents returned by more than one query). Where queries contain more than one word they are interpreted disjunctively. We have found it useful to assign one word to be the root and constrain the query construction such that the set of documents returned by any additional query words intersect with the set returned by the root word. Not all documents in a collection are returned by any of the search queries in a set, so once the search query evolution is completed a second stage is performed whereby a KNN algorithm is applied to assign all unassigned documents to their nearest cluster. We describe the method and present results using 8 text datasets comparing effectiveness with well-known existing algorithms. We note that as well as achieving the highest accuracy on these datasets the search query format provides the qualitative benefits of being interpretable and modifiable whilst providing a causal explanation of cluster construction.

Cancer remains one of the leading causes of mortality worldwide, necessitating accurate diagnosis and prognosis. Whole Slide Imaging (WSI) has become an integral part of clinical workflows with advancements in digital pathology. While various studies have utilized WSIs, their extracted features may not fully capture the most relevant pathological information, and their lack of interpretability limits clinical adoption. In this paper, we propose PATH-X, a framework that integrates Vision Transformers (ViT) and Autoencoders with SHAP (Shapley Additive Explanations) to enhance model explainability for patient stratification and risk prediction using WSIs from The Cancer Genome Atlas (TCGA). A representative image slice is selected from each WSI, and numerical feature embeddings are extracted using Google's pre-trained ViT. These features are then compressed via an autoencoder and used for unsupervised clustering and classification tasks. Kaplan-Meier survival analysis is applied to evaluate stratification into two and three risk groups. SHAP is used to identify key contributing features, which are mapped onto histopathological slices to provide spatial context. PATH-X demonstrates strong performance in breast and glioma cancers, where a sufficient number of WSIs enabled robust stratification. However, performance in lung cancer was limited due to data availability, emphasizing the need for larger datasets to enhance model reliability and clinical applicability.

Addressing the inherent low acquisition frequency limitation of 3D LiDAR to achieve high-frequency output has become a critical research focus in the LiDAR-Inertial Odometry (LIO) domain. To ensure real-time performance, frequency-enhanced LIO systems must process each sweep within significantly reduced timeframe, which presents substantial challenges for deployment on low-computational-power platforms. To address these limitations, we introduce SR-LIO++, an innovative LIO system capable of achieving doubled output frequency relative to input frequency on resource-constrained hardware platforms, including the Raspberry Pi 4B. Our system employs a sweep reconstruction methodology to enhance LiDAR sweep frequency, generating high-frequency reconstructed sweeps. Building upon this foundation, we propose a caching mechanism for intermediate results (i.e., surface parameters) of the most recent segments, effectively minimizing redundant processing of common segments in adjacent reconstructed sweeps. This method decouples processing time from the traditionally linear dependence on reconstructed sweep frequency. Furthermore, we present a quantized map point management based on index table mapping, significantly reducing memory usage by converting global 3D point storage from 64-bit double precision to 8-bit char representation. This method also converts the computationally intensive Euclidean distance calculations in nearest neighbor searches from 64-bit double precision to 16-bit short and 32-bit integer formats, significantly reducing both memory and computational cost. Extensive experimental evaluations across three distinct computing platforms and four public datasets demonstrate that SR-LIO++ maintains state-of-the-art accuracy while substantially enhancing efficiency. Notably, our system successfully achieves 20Hz state output on Raspberry Pi 4B hardware.

Sparsified Learning is ubiquitous in many machine learning tasks. It aims to regularize the objective function by adding a penalization term that considers the constraints made on the learned parameters. This paper considers the problem of learning heavy-tailed LSP. We develop a flexible and robust sparse learning framework capable of handling heavy-tailed data with locally stationary behavior and propose concentration inequalities. We further provide non-asymptotic oracle inequalities for different types of sparsity, including $\ell_1$-norm and total variation penalization for the least square loss.

Spatio-temporal point processes (STPPs) model discrete events distributed in time and space, with important applications in areas such as criminology, seismology, epidemiology, and social networks. Traditional models often rely on parametric kernels, limiting their ability to capture heterogeneous, nonstationary dynamics. Recent innovations integrate deep neural architectures -- either by modeling the conditional intensity function directly or by learning flexible, data-driven influence kernels, substantially broadening their expressive power. This article reviews the development of the deep influence kernel approach, which enjoys statistical explainability, since the influence kernel remains in the model to capture the spatiotemporal propagation of event influence and its impact on future events, while also possessing strong expressive power, thereby benefiting from both worlds. We explain the main components in developing deep kernel point processes, leveraging tools such as functional basis decomposition and graph neural networks to encode complex spatial or network structures, as well as estimation using both likelihood-based and likelihood-free methods, and address computational scalability for large-scale data. We also discuss the theoretical foundation of kernel identifiability. Simulated and real-data examples highlight applications to crime analysis, earthquake aftershock prediction, and sepsis prediction modeling, and we conclude by discussing promising directions for the field.

Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified robustness and empirical robustness accuracy. This paper introduces a new framework that bridges this gap by leveraging Lipschitz continuity for certification and proposing a novel, less conservative method for computing confidence intervals in randomized smoothing. Our approach tightens the bounds of certified robustness, offering a more accurate reflection of model robustness in practice. Through rigorous experimentation we show that our method improves the robust accuracy, compressing the gap between empirical findings and previous theoretical results. We argue that investigating local Lipschitz constants and designing ad-hoc confidence intervals can further enhance the performance of randomized smoothing. These results pave the way for a deeper understanding of the relationship between Lipschitz continuity and certified robustness.

Functional time series (FTS) extend traditional methodologies to accommodate data observed as functions/curves. A significant challenge in FTS consists of accurately capturing the time-dependence structure, especially with the presence of time-varying covariates. When analyzing time series with time-varying statistical properties, locally stationary time series (LSTS) provide a robust framework that allows smooth changes in mean and variance over time. This work investigates Nadaraya-Watson (NW) estimation procedure for the conditional distribution of locally stationary functional time series (LSFTS), where the covariates reside in a semi-metric space endowed with a semi-metric. Under small ball probability and mixing condition, we establish convergence rates of NW estimator for LSFTS with respect to Wasserstein distance. The finite-sample performances of the model and the estimation method are illustrated through extensive numerical experiments both on functional simulated and real data.

Variational Bayesian Monte Carlo (VBMC) is a sample-efficient method for approximate Bayesian inference with computationally expensive likelihoods. While VBMC's local surrogate approach provides stable approximations, its conservative exploration strategy and limited evaluation budget can cause it to miss regions of complex posteriors. In this work, we introduce Stacking Variational Bayesian Monte Carlo (S-VBMC), a method that constructs global posterior approximations by merging independent VBMC runs through a principled and inexpensive post-processing step. Our approach leverages VBMC's mixture posterior representation and per-component evidence estimates, requiring no additional likelihood evaluations while being naturally parallelizable. We demonstrate S-VBMC's effectiveness on two synthetic problems designed to challenge VBMC's exploration capabilities and two real-world applications from computational neuroscience, showing substantial improvements in posterior approximation quality across all cases.

Diffusion wavelets extract information from graph signals at different scales of resolution by utilizing graph diffusion operators raised to various powers, known as diffusion scales. Traditionally, the diffusion scales are chosen to be dyadic integers, $\mathbf{2^j}$. Here, we propose a novel, unsupervised method for selecting the diffusion scales based on ideas from information theory. We then show that our method can be incorporated into wavelet-based GNNs via graph classification experiments.

Co-clustering exploits the duality of instances and features to simultaneously uncover meaningful groups in both dimensions, often outperforming traditional clustering in high-dimensional or sparse data settings. Although recent deep learning approaches successfully integrate feature learning and cluster assignment, they remain susceptible to noise and can suffer from posterior collapse within standard autoencoders. In this paper, we present the first fully variational Co-clustering framework that directly learns row and column clusters in the latent space, leveraging a doubly reparameterized ELBO to improve gradient signal-to-noise separation. Our unsupervised model integrates a Variational Deep Embedding with a Gaussian Mixture Model (GMM) prior for both instances and features, providing a built-in clustering mechanism that naturally aligns latent modes with row and column clusters. Furthermore, our regularized end-to-end noise learning Compositional ELBO architecture jointly reconstructs the data while regularizing against noise through the KL divergence, thus gracefully handling corrupted or missing inputs in a single training pipeline. To counteract posterior collapse, we introduce a scale modification that increases the encoder's latent means only in the reconstruction pathway, preserving richer latent representations without inflating the KL term. Finally, a mutual information-based cross-loss ensures coherent co-clustering of rows and columns. Empirical results on diverse real-world datasets from multiple modalities, numerical, textual, and image-based, demonstrate that our method not only preserves the advantages of prior Co-clustering approaches but also exceeds them in accuracy and robustness, particularly in high-dimensional or noisy settings.