biomedical data analysts

Abstract: Many supervised dimensionality reduction methods promote intra-class compactness and inter-class separation but do not explicitly constrain class geometry, leading to variability in the relative arrangement of classes across independent runs. Such variability limits the reproducibility and interpretability of low-dimensional embeddings. We propose the Isometric Centroid-Encoder (ICE), a supervised dimensionality reduction framework in which class centroids are learned directly in the latent space while preserving a prescribed pairwise class-centroid geometry. Unlike existing centroid- or prototype-based methods that primarily encourage intra-class compactness, ICE explicitly regularizes the relative arrangement of latent class centroids. Unlike multidimensional scaling and many metric-learning approaches that preserve sample-level relationships, ICE operates on class centroids, preserving inter-class geometry without requiring large numbers of sample-pair or triplet constraints. We further show that the intrinsic dimensionality required to represent the centroid-distance configuration of $M$ classes is at most $M-1$, explaining the observed saturation of distance-preservation measures as the latent dimensionality increases. To quantify embedding reproducibility, we introduce the Centroid Neighborhood Stability (CNS) metric, which measures the consistency of class-level neighborhood topology across independent runs and complements existing embedding quality measures. Experiments on image and biological datasets demonstrate that ICE produces stable embeddings with improved preservation of class-centroid geometry while remaining computationally efficient. Additional analyses of optimization dynamics, sensitivity, and preprocessing further provide practical insights into latent dimensionality and explicit geometry modeling for supervised dimensionality reduction.

Abstract: We introduce two new methods for boundary detection in high-dimensional point cloud data, intended to work in situations with non-uniform density, high ambient dimension, and substantial noise. Our first method fits a separating hyperplane on local neighborhoods after doing local dimension reduction---this method works best when one can reliably estimate the intrinsic dimension of the data. Our second method measures the directional uniformity of local neighborhoods, and has the best overall performance on synthetic data. In addition to pointwise numerical boundary scores, our algorithms yield an estimated normal vector at each boundary point. We validate our methodology on synthetic data as well as two real examples: we analyze spatial transcriptomics data, where we show that we can detect the boundary of a tumor, and we also study LLM activation geometry.

Abstract: Tabular foundation models based on prior-data fitted networks (PFNs) predict on a new data set in a single forward pass, but they cannot report which inputs their predictions depend on. We propose SelectPFN, a PFN that performs Bayesian variable selection and prediction jointly for sparse nonlinear regression. In one forward pass it returns posterior inclusion probabilities for every variable, and its predictions are computed from sampled subsets only, so excluded variables provably cannot affect them; we show this is exactly what the Bayesian model prescribes. The network is pretrained once on synthetic tasks from a meta-prior built around a group spike-and-slab sparse-input neural network. Column-permutation equivariance combined with random interleaving of original and knockoff columns yields knockoff statistics with exact finite-sample false discovery rate control, even when the meta-prior is wrong. We develop theory for amortized selection: a Bayes-regret bound for the amortized median probability model, a characterization showing that the information needed to detect a variable grows like $(2/λ)\log(1/ω)$ in the prior weight $ω$ of structures that can use it, where $λ\le1$ is an efficiency, and a negative result showing that average-case training does not transfer to frequentist guarantees at a fixed truth. On out-of-prior nonlinear designs with p up to 500, SelectPFN improves the area under the precision-recall curve by 0.23-0.28 over the lasso, BART, DART, LassoNet and a group-penalized sparse neural network, at a false discovery proportion of about 0.07 and 0.04 seconds per data set. The advantage persists on real covariate matrices, and, as the theory predicts, detection of interaction-only variables rises monotonically with their prior weight.

Abstract: We develop a model-free, noise-aware Bayesian clustering framework that constructs a martingale posterior over clusterings from a predictive Bayesian perspective. This avoids explicit likelihood-prior model specification, expensive MCMC sampling, and mode-seeking variational approximations, while accommodating irregular cluster shapes and enabling parallel generation of posterior draws. To interpret the posterior over high-dimensional, noise-aware clusterings, we introduce a Wasserstein-type summarization method. Using a novel noise-aware loss, this approach compresses the large collection of posterior draws into a small set of weighted representatives, capturing distinct cluster structures and noise assignments. Further, we marginalise the uncertainty in the density level, avoiding reliance on a specific choice. We establish theoretical properties of the proposed loss and guarantees for the level-marginal posterior approximation. Results demonstrate the framework's effectiveness in capturing clustering and noise uncertainty.

Abstract: Single-cell trajectory inference maps transcriptomic measurements onto developmental continua, yet configurations that fit the data equally well can assign conflicting cell fates. FateMultiplicity is a label-free framework that constructs a statistically admissible model set, or Rashomon set, without lineage labels, by evaluating model discrepancy on cross-fitted held-out genes under non-inferiority testing calibrated against random-seed variation. Multiplicity is large and depends more on the diversity of the model space than its size: twelve configurations of a second algorithm expose 20.0% of cells where twenty-four of the first expose 3.8%. Whether the per-cell certified fate margin FM yields more reliable assignments than the fitted model already provides is then tested, and it does not. On simulation ground truth, on the same cells, FM discriminates misassignment at AUC 0.682, against 0.965 for the baseline configuration's own decision margin (p = 0.003) and 0.854 for a seed-dispersion baseline. Informativeness is governed by the breadth of the admitted set, not its cardinality: at cardinality four, seed refits give 0.933 and hyperparameter-perturbed sets 0.701. Relaxing the infimum to a q-quantile recovers discrimination but converges toward the single model's own confidence; the supremum reaches 0.973 because theta*'s membership bounds it from below, while the infimum is unanchored. Multiplicity in trajectory inference is worth measuring and reporting, but per-cell certification over a label-free Rashomon set is not a route to more reliable fate calls. Two constructions survive: a margin-erosion ratio separates real from spurious branch points in simulation (AUC 0.890, untested on real data), and against clonally observed fate, uncertified cells disagree with their clone's outcome 16.4 percentage points more often than certified cells (p < 0.001).

Abstract: In this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings under a spiked model. The existing theory of the SVM in the HDLSS context relies on the geometric representation of HDLSS data, which requires that the eigenvalues of the covariance matrices are not dominant. We first show that the geometric representation does not hold under the spiked model. We show that the Gram matrix of HDLSS data converges in distribution to a random matrix, namely, the HDLSS data converge to a random configuration in a finite-dimensional space whose dimension is given by the number of the spikes. We show that the misclassification rates of the SVM do not tend to zero, that is, the SVM does not hold the consistency property. We also show that the bias-corrected SVM (BC-SVM) does not give preferable performance in this setting because the bias term itself should be modified. In order to overcome such difficulties, we propose a spike-corrected SVM (SC-SVM). We show that the SC-SVM holds the consistency property when the sample size goes to infinity, and that the growth of the sample size is essential in the sense that any projection-based procedure fails when the sample size is fixed. Finally, we check the performance of the classifiers by numerical simulations.

Abstract: We study spectral graph neural networks built from Hermite polynomials and propose HermNet, a simple model that combines a nodewise predictor with normalized Hermite propagation. Its sparse recurrence requires neither eigendecomposition nor a learned basis. We distinguish the basic model from optional coordinate calibration, response normalization and Gaussian derivative regularization. Hermite and other complete polynomial bases span the same degree-bounded filter space, but their coordinates can produce different optimization behavior under limited training budgets. We analyze this behavior through spectral signal energy, label sampling, changes in learned features and the bias--variance trade-off of regularization. Controlled synthetic experiments identify a regime in which plain HermNet outperforms matched polynomial-basis alternatives, including with a jointly trained nonlinear predictor. Curvature regularization further improves HermNet when the same functional penalty is available to every comparator. Fixed-predictor controls support the advantage under short training budgets, but longer training removes the plain-model lead. Matched real-data comparisons show accuracy deficits, and architectural and numerical studies identify further limits. Together, the analysis and experiments clarify when Hermite propagation is useful and how calibration and regularization affect its performance.

Abstract: This paper introduces a novel framework for Regularized Multivariate Functional Principal Component Analysis (ReMFPCA) via Functional Singular Value Decomposition (SVD). The proposed method extends existing MFPCA approaches by incorporating a generalized functional SVD within a Hilbert space framework, enabling simultaneous regularization of both functional principal components (PCs) and their associated PC scores. A key innovation of this framework is the inclusion of a sparsity penalty on the PC scores, which enhances interpretability by filtering out irrelevant subject-specific variations. This dual-penalization strategy represents a significant advancement beyond existing covariance-based eigen decomposition methods, which penalize only the functional PCs. Two power algorithm implementations, sequential and joint, are proposed, together with a cross-validation approach based on iterative regression for optimal smoothing parameter selection. Comprehensive simulation studies and real data applications demonstrate that the proposed framework substantially improves the extraction of informative and interpretable components, offering methodological and practical benefits for analyzing multivariate functional data across diverse domains.