Papers

Adaptive behavior in volatile environments requires agents to switch among value-control regimes across latent contexts, but maintaining separate preferences, policy biases, and action-confidence parameters for every situation is intractable. We introduce value profiles: a small set of reusable bundles of value-related parameters (outcome preferences, policy priors, and policy precision) assigned to hidden states in a generative model. As posterior beliefs over states evolve trial by trial, effective control parameters arise via belief-weighted mixing, enabling state-conditional strategy recruitment without requiring independent parameters for each context. We evaluate this framework in probabilistic reversal learning, comparing static-precision, entropy-coupled dynamic-precision, and profile-based models using cross-validated log-likelihood and information criteria. Model comparison favors the profile-based model over simpler alternatives (about 100-point AIC differences), and parameter-recovery analyses support structural identifiability even when context must be inferred from noisy observations. Model-based inference further suggests that adaptive control in this task is driven primarily by modulation of policy priors rather than policy precision, with gradual belief-dependent profile recruitment consistent with state-conditional (not purely uncertainty-driven) control. Overall, reusable value profiles provide a tractable computational account of belief-conditioned value control in volatile environments and yield testable signatures of belief-dependent control and behavioral flexibility.

Spectral gradient methods, such as the recently popularized Muon optimizer, are a promising alternative to standard Euclidean gradient descent for training deep neural networks and transformers, but it is still unclear in which regimes they are expected to perform better. We propose a simple layerwise condition that predicts when a spectral update yields a larger decrease in the loss than a Euclidean gradient step. This condition compares, for each parameter block, the squared nuclear-to-Frobenius ratio of the gradient to the stable rank of the incoming activations. To understand when this condition may be satisfied, we first prove that post-activation matrices have low stable rank at Gaussian initialization in random feature regression, feedforward networks, and transformer blocks. In spiked random feature models we then show that, after a short burn-in, the Euclidean gradient's nuclear-to-Frobenius ratio grows with the data dimension while the stable rank of the activations remains bounded, so the predicted advantage of spectral updates scales with dimension. We validate these predictions in synthetic regression experiments and in NanoGPT-scale language model training, where we find that intermediate activations have low-stable-rank throughout training and the corresponding gradients maintain large nuclear-to-Frobenius ratios. Together, these results identify conditions for spectral gradient methods, such as Muon, to be effective in training deep networks and transformers.

Compositional observations arise when measurements are recorded as parts of a whole, so that only relative information is meaningful and the natural sample space is the simplex equipped with Aitchison geometry. Despite extensive development of compositional methods, a direct analogue of Moran's \(I\) for assessing spatial autocorrelation in areal compositional data has been lacking. We propose Reyes's \(I\), a Moran type statistic defined through the Aitchison inner product and norm, which is invariant to scale, to permutations of the parts, and to the choice of the \(\operatorname{ilr}\) contrast matrix. Under the randomization assumption, we derive an upper bound, the expected value, and the noncentral second moment, and we describe exact and Monte Carlo permutation procedures for inference. Through simulations covering identical, independent, and spatially correlated compositions under multiple covariance structures and neighborhood definitions, we show that Reyes's \(I\) provides stable behavior, competitive calibration, and improved efficiency relative to a naive alternative based on averaging componentwise Moran statistics. We illustrate practical utility by studying the spatial dependence of a composition measuring COVID-19 severity across Colombian departments during January 2021, documenting significant positive autocorrelation early in the month that attenuates over time.

Benchmarks are the primary tool for assessing progress in artificial intelligence (AI), yet current practice evaluates models on isolated test suites and provides little guidance for reasoning about generality or autonomous self-improvement. Here we introduce a geometric framework in which all psychometric batteries for AI agents are treated as points in a structured moduli space, and agent performance is described by capability functionals over this space. First, we define an Autonomous AI (AAI) Scale, a Kardashev-style hierarchy of autonomy grounded in measurable performance on batteries spanning families of tasks (for example reasoning, planning, tool use and long-horizon control). Second, we construct a moduli space of batteries, identifying equivalence classes of benchmarks that are indistinguishable at the level of agent orderings and capability inferences. This geometry yields determinacy results: dense families of batteries suffice to certify performance on entire regions of task space. Third, we introduce a general Generator-Verifier-Updater (GVU) operator that subsumes reinforcement learning, self-play, debate and verifier-based fine-tuning as special cases, and we define a self-improvement coefficient $\kappa$ as the Lie derivative of a capability functional along the induced flow. A variance inequality on the combined noise of generation and verification provides sufficient conditions for $\kappa > 0$. Our results suggest that progress toward artificial general intelligence (AGI) is best understood as a flow on moduli of benchmarks, driven by GVU dynamics rather than by scores on individual leaderboards.

The probability density function (PDF) plays a central role in statistical and machine learning modeling. Real-world data often deviates from Gaussian assumptions, exhibiting skewness and exponential decay. To evaluate how well different density estimation methods capture such irregularities, we generated six unimodal datasets from diverse distributions that reflect real-world anomalies. These were compared using parametric methods (Pearson Type I and Normal distribution) as well as non-parametric approaches, including histograms, kernel density estimation (KDE), and our proposed method. To accelerate computation, we implemented GPU-based versions of KDE (tKDE) and histogram estimation (tHDE) in TensorFlow, both of which outperform Python SciPy's KDE. Prior work demonstrated the use of piecewise modeling for density estimation, such as local polynomial regression; however, these methods are computationally intensive. Based on the concept of piecewise modeling, we developed a computationally efficient model, the Dual Polynomial Regression (DPR) method, which leverages tKDE or tHDE for training. DPR employs the piecewise strategy to split the PDF at its mode and fit polynomial regressions to the left and right halves independently, enabling better capture of the asymmetric shape of the unimodal distribution. We used the Mean Squared Error (MSE), Jensen-Shannon Divergence (JSD), and Pearson's correlation coefficient, with reference to the baseline PDF, to validate accuracy. We verified normalization using Area Under the Curve (AUC) and computational overhead via execution time. Validation on real-world systolic and diastolic data from 300,000 unique patients shows that the DPR of order 4, trained with tKDE, offers the best balance between accuracy and computational overhead.

The atmospheric boundary layer (ABL) plays a critical role in governing turbulent exchanges of momentum, heat moisture, and trace gases between the Earth's surface and the free atmosphere, thereby influencing meteorological phenomena, air quality, and climate processes. Accurate and temporally continuous characterization of the ABL structure and height evolution is crucial for both scientific understanding and practical applications. High-resolution retrievals of the ABL height from vertical velocity measurements is challenging because it is often estimated using empirical thresholds applied to profiles of vertical velocity variance or related turbulence diagnostics at each measurement altitude, which can suffer from limited sampling and sensitivity to noise. To address these limitations, this work employs nonstationary Gaussian process (GP) modeling to more effectively capture the spatio-temporal dependence structure in the data, enabling high-quality – and, if desired, high-resolution – estimates of the ABL height without reliance on ad-hoc parameter tuning. By leveraging Vecchia approximations, the proposed method can be applied to large-scale datasets, and example applications using full-day vertical velocity profiles comprising approximately $5$M measurements are presented.

Two pressing topics in the theory of deep learning are the interpretation of feature learning (FL) mechanisms and the determination of implicit bias of networks in the rich regime. Current theories of rich FL often appear in the form of high-dimensional non-linear equations, which require computationally intensive numerical solutions. Given the many details that go into defining a deep learning problem, this analytical complexity is a significant and often unavoidable challenge. Here, we propose a powerful heuristic route for predicting the data and width scales at which various patterns of FL emerge. This form of scale analysis is considerably simpler than such exact theories and reproduces the scaling exponents of various known results. In addition, we make novel predictions on complex toy architectures, such as three-layer non-linear networks and attention heads, thus extending the scope of first-principle theories of deep learning.

Peak inference concerns the use of local maxima ("peaks") of a noisy random field to detect and localize regions where underlying signal is present. We propose a peak inference method that first subjects observed peaks to a significance test of the null hypothesis that no signal is present, and then uses the peaks that are declared significant to construct post-selectively valid confidence regions for the location and height of nearby true peaks. We analyze the performance of this method in a smooth signal plus constant variance noise model under a high-curvature asymptotic assumption, and prove that it asymptotically controls both the number of false discoveries, and the number of confidence regions that do not contain a true peak, relative to the number of points at which inference is conducted. An important intermediate theoretical result uses the Kac-Rice formula to derive a novel approximation to the intensity function of a point process that counts local maxima, which is second-order accurate under the alternative, nearby high-curvature true peaks.

The discovery of Bell that there exist quantum correlations that cannot be reproduced classically is one of the most important in the foundations of quantum mechanics, as well as having practical implications. Bell's result was originally proven in a simple bipartite causal structure, but analogous results have also been shown in further causal structures. Here we study the only causal structure with six or fewer nodes in which the question of whether or not there exist quantum correlations that cannot be achieved classically was open. In this causal structure we show that such quantum correlations exist using a method that involves imposing additional restrictions on the correlations. This hence completes the picture of which causal structures of up to six nodes support non-classical quantum correlations. We also provide further illustrations of our method using other causal structures.

Cross-entropy (CE) training loss dominates deep learning practice, yet existing theory often relies on simplifications, either replacing it with squared loss or restricting to convex models, that miss essential behavior. CE and squared loss generate fundamentally different dynamics, and convex linear models cannot capture the complexities of non-convex optimization. We provide an in-depth characterization of multi-class CE optimization dynamics beyond the convex regime by analyzing a canonical two-layer linear neural network with standard-basis vectors as inputs: the simplest non-convex extension for which the implicit bias remained unknown. This model coincides with the unconstrained features model used to study neural collapse, making our work the first to prove that gradient flow on CE converges to the neural collapse geometry. We construct an explicit Lyapunov function that establishes global convergence, despite the presence of spurious critical points in the non-convex landscape. A key insight underlying our analysis is an inconspicuous finding: Hadamard Initialization diagonalizes the softmax operator, freezing the singular vectors of the weight matrices and reducing the dynamics entirely to their singular values. This technique opens a pathway for analyzing CE training dynamics well beyond our specific setting considered here.

With the emergence of dynamic multiplex networks, corresponding to graphs where multiple types of edges evolve over time, a key inferential task is to determine whether the layers associated with different edge types differ in their connectivity. In this work, we introduce a hypothesis testing framework, under a latent space network model, for assessing whether the layers share a common latent representation. The method we propose extends previous literature related to the problem of pairwise testing for random graphs and enables global testing of differences between layers in multiplex graphs. While we introduce the method as a test for differences between layers, it can easily be adapted to test for differences between time points. We construct a test statistic based on a spectral embedding of an unfolded representation of the graph adjacency matrices and demonstrate its ability to detect differences across layers in the asymptotic regime where the number of nodes in each graph tends to infinity. The finite-sample properties of the test are empirically demonstrated by assessing its performance on both simulated data and a biological dataset describing the neural activity of larval Drosophila.

Estimating the health impacts of exposure to a mixture of chemicals poses many statistical challenges: multiple correlated exposure variables, moderate to high dimensionality, and possible nonlinear and interactive health effects of mixture components. Reviews of chemical mixture methods aim to help researchers select a statistical method suited to their goals and data, but examinations of empirical performance have emphasized novel methods purpose-built for analyzing complex chemical mixtures, or other more advanced methods, over more general methods which are widely used in many application domains. We conducted a broad experimental comparison, across simulated scenarios, of both more general methods (such as generalized linear models) and novel methods (such as Bayesian Kernel Machine Regression) designed to study chemical mixtures. We assessed methods based on their ability to control Type I error rate, maximize power, provide interpretable results, and make accurate predictions. We find that when there is moderate correlation between mixture components and the exposure-response function does not have complicated interactions, or when mixture components have opposite effects, general methods are preferred over novel ones. With highly interactive exposure-response functions or highly correlated exposures, novel methods provide important benefits. We provide a comprehensive summary of when different methods are most suitable.

Functional connectivity (FC) derived from functional magnetic resonance imaging (fMRI) data offers vital insights for understanding brain function and neurological and psychiatric disorders. Unsupervised clustering methods are desired to group individuals based on shared features, facilitating clinical diagnosis. In this study, a parsimonious clustering model is proposed, which integrates the Mixture-of-Experts (MoE) and covariance regression framework, to cluster individuals based on FC captured by data covariance matrices in resting-state fMRI studies. The model assumes common linear projections across covariance matrices and a generalized linear model with covariates, allowing for flexible yet interpretable projection-specific clustering solutions. To evaluate the performance of the proposed framework, extensive simulation studies are conducted to assess clustering accuracy and robustness. The approach is applied to resting-state fMRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Subgroups are identified based on brain coherence and simultaneously uncover the association with demographic factors and cognitive functions.

Fuzzy simplicial sets have become an object of interest in dimensionality reduction and manifold learning, most prominently through their role in UMAP. However, their definition through tools from algebraic topology without a clear probabilistic interpretation detaches them from commonly used theoretical frameworks in those areas. In this work we introduce a framework that explains fuzzy simplicial sets as marginals of probability measures on simplicial sets. In particular, this perspective shows that the fuzzy weights of UMAP arise from a generative model that samples Vietoris-Rips filtrations at random scales, yielding cumulative distribution functions of pairwise distances. More generally, the framework connects fuzzy simplicial sets to probabilistic models on the face poset, clarifies the relation between Kullback-Leibler divergence and fuzzy cross-entropy in this setting, and recovers standard t-norms and t-conorms via Boolean operations on the underlying simplicial sets. We then show how new embedding methods may be derived from this framework and illustrate this on an example where we generalize UMAP using Čech filtrations with triplet sampling. In summary, this probabilistic viewpoint provides a unified probabilistic theoretical foundation for fuzzy simplicial sets, clarifies the role of UMAP within this framework, and enables the systematic derivation of new dimensionality reduction methods.

Multiple testing is widely applied across scientific fields, particularly in genomic and health data analysis, where protecting sensitive personal information is imperative. However, developing private multiple testing algorithms for super uniform $p$-values remains an open question, as privacy mechanisms introduce intricate dependence among the peeled $p$-values and disrupt their super uniformity, complicating post-selection inference. To address this, we introduce a general Super Uniform Private (SUP) multiple testing framework with three key components. First, we develop a novel \( p \)-value transformation that is compatible with diverse privacy regimes while retaining the super uniformity. Next, a reversed peeling algorithm is designed to reduce privacy budgets while facilitating inference. Then, we provide diverse rejection thresholds that are privacy-parameter-free and tailored for different Type-I errors, including the family-wise error rate (FWER) and the false discovery rate (FDR). Building upon these, we advance adaptive techniques to determine the peeling number and boost thresholds. Theoretically, we propose a technique overcoming the post-selection obstacle to Type-I error control, quantify the privacy-induced power loss of SUP relative to its non-private counterpart, and demonstrate that SUP surpasses existing private methods in terms of power. The results of extensive simulations and a real data application validate our theories.

Neural networks have become a widely adopted tool for modeling nonlinear dynamical systems from data. However, the choice of training strategy remains a key design decision, particularly for simulation tasks. This paper compares two predominant strategies: parallel and series-parallel training. The conducted empirical analysis spans five neural network architectures and two examples: a pneumatic valve test bench and an industrial robot benchmark. The study reveals that, even though series-parallel training dominates current practice, parallel training consistently yields better long-term prediction accuracy. Additionally, this work clarifies the often inconsistent terminology in the literature and relate both strategies to concepts from system identification. The findings suggest that parallel training should be considered the default training strategy for neural network-based simulation of dynamical systems.

Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the matrix product, which improves interpretability and reduces the approximation error. It is also used in role mining and computer vision. In this paper, we first propose algorithms for BMF that perform alternating optimization (AO) of the factor matrices, where each subproblem is solved via integer programming (IP). We then design different approaches to further enhance AO-based algorithms by selecting an optimal subset of rank-one factors from multiple runs. To address the scalability limits of IP-based methods, we introduce new greedy and local-search heuristics. We also construct a new C++ data structure for Boolean vectors and matrices that is significantly faster than existing ones and is of independent interest, allowing our heuristics to scale to large datasets. We illustrate the performance of all our proposed methods and compare them with the state of the art on various real datasets, both with and without missing data, including applications in topic modeling and imaging.

Infinite hidden Markov models provide a flexible framework for modeling time-series with structural changes and complex dynamics, without requiring the number of latent states to be specified in advance. This flexibility is achieved through the hierarchical Dirichlet process prior, while efficient Bayesian inference is enabled by the beam sampler, which combines dynamic programming with slice sampling to truncate the infinite state space adaptively. Despite extensive methodological developments, the role of initialization in this framework has received limited attention. This gap is addressed by systematically evaluating initialization strategies commonly used for finite hidden Markov models and assessing their suitability in the infinite setting. Results from both simulated and real datasets show that distance-based clustering initializations consistently outperform model-based and uniform alternatives, the latter being the most widely adopted in the existing literature.

We revisit macroeconomic time-varying parameter vector autoregressions (TVP-VARs), whose persistent coefficients may adapt too slowly to large, abrupt shifts such as those during major crises. We explore the performance of an adaptively-varying parameter (AVP) VAR that incorporates deterministic adjustments driven by observable exogenous variables, replacing latent state innovations with linear combinations of macroeconomic and financial indicators. This reformulation collapses the state equation into the measurement equation, enabling simple linear estimation of the model. Simulations show that adaptive parameters are substantially more parsimonious than conventional TVPs, effectively disciplining parameter dynamics without sacrificing flexibility. Using macroeconomic datasets for both the U.S. and the euro area, we demonstrate that AVP-VAR consistently improves out-of-sample forecasts, especially during periods of heightened volatility.

The adequate use of information measured in a continuous manner along a period of time represents a methodological challenge. In the last decades, most of traditional statistical procedures have been extended for accommodating these functional data. The binary classification problem, which aims to correctly identify units as positive or negative based on marker values, is not aside of this scenario. The crucial point for making binary classifications based on a marker is to establish an order in the marker values, which is not immediate when these values are presented as functions. Here, we argue that if the marker is related to the characteristic under study, a trajectory from a positive participant should be more similar to trajectories from the positive population than to those drawn from the negative. With this criterion, a classification procedure based on the distance between the involved functions is proposed. Besides, we propose a fully non-parametric estimator for this so-called probability-based criterion, PBC. We explore its asymptotic properties, and its finite-sample behavior from an extensive Monte Carlo study. The observed results suggest that the proposed methodology works adequately, and frequently better than its competitors, for a wide variety of situations when the sample size in both the training and the testing cohorts is adequate. The practical use of the proposal is illustrated from real-world dataset. As online supplementary material, the manuscript includes a document with further simulations and additional comments. An R function which wraps up the implemented routines is also provided.

Prevalence surveys are routinely used to monitor the effectiveness of mass drug administration (MDA) programmes for controlling neglected tropical diseases (NTDs). We propose a decay-adjusted spatio-temporal (DAST) model that explicitly accounts for the time-varying impact of MDA on NTD prevalence, providing a flexible and interpretable framework for estimating intervention effects from sparse survey data. Using case studies on soil-transmitted helminths and lymphatic filariasis, we show that DAST offers a practical alternative to standard geostatistical models when the objective includes quantifying MDA impact and supporting short-term programmatic forecasting. We also discuss extensions and identifiability challenges, advocating for data-driven parsimony over complexity in settings where the available data are too sparse to support the estimation of highly parameterised models.

Reliable uncertainty quantification is essential in survival prediction, particularly in clinical settings where erroneous decisions carry high risk. Conformal prediction has attracted substantial attention as it offers a model-agnostic framework with finite-sample coverage guarantees. Extending it to right-censored outcomes poses nontrivial challenges. Several adaptations of conformal approaches for survival outcomes have been developed, but they either rely on restrictive censoring settings or substantial computation. A recent conformal approach for right-censored data constructs censoring-adjusted p-values and enables prediction intervals in general survival settings. However, the empirical coverage depends sensitively on heuristic tuning choices and its validity is limited to scenarios without covariate shift. In this paper, we establish theoretical justification for its prediction-set construction, providing a principled basis for defining prediction-set bounds, and extend the approach to covariate-shift settings. Simulation studies and a real data application demonstrate that the proposed method achieves robust coverage and coherent interval structure across varying censoring levels and covariate-shift settings.

Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs well-suited for analyzing complex systems and supporting decision-making. Recent advances in topological signal processing highlight the importance of variables defined on topological spaces in several application domains. In such cases, the underlying topology shapes statistical relationships, limiting the expressiveness of canonical PGMs. To overcome this limitation, we introduce Colored Markov Random Fields (CMRFs), which model both conditional and marginal dependencies among Gaussian edge variables on topological spaces, with a theoretical foundation in Hodge theory. CMRFs extend classical Gaussian Markov Random Fields by including link coloring: connectivity encodes conditional independence, while color encodes marginal independence. We quantify the benefits of CMRFs through a distributed estimation case study over a physical network, comparing it with baselines with different levels of topological prior.

Transformer-based audio self-supervised learning (SSL) models commonly use spectrograms, vision-style Transformers, and masked modeling objectives. However, convolutional patchification with temporal downsampling lowers the effective Nyquist frequency and introduces aliasing, while naïve low-pass filtering may remove task-relevant high-frequency cues. We present AaSP, an aliasing-aware self-supervised pre-training framework for audio spectrogram transformers. AaSP combines an aliasing-aware patch representation, teacher-student masked modeling, a cross-attention predictor, and multi-mask contrastive regularization to learn representations that integrate features from alias-prone modulation bands while remaining stable across masked views. Its patch-embedding module, Aliasing-aware Patch Embedding (AaPE), augments standard patch tokens with features from alias-prone modulation bands using a band-limited complex sinusoidal kernel with a two-sided exponential window. The kernel's frequency and decay parameters are estimated from the input, enabling adaptive subband analysis whose outputs are fused with standard patch tokens. We pre-train on AudioSet and evaluate the learned representations by fine-tuning and linear evaluation on acoustic/environmental, speech, and music recognition benchmarks. Under fine-tuning, the full AaSP framework achieves state-of-the-art results on AS-20K, ESC-50, and NSynth among compared self-supervised baselines, while remaining competitive elsewhere. Linear evaluation shows a similar trend, including gains on US8K and NSynth. Overall, AaSP learns representations that are more stable under aliasing-sensitive temporal perturbations and competitive for downstream transfer.

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets—tasks ubiquitous in data science and machine learning. Because these frameworks are computationally expensive, large-scale applications often rely on closed-form solutions for Gaussian distributions under quadratic cost. This work provides a comprehensive treatment of Gaussian, quadratic cost OT and inner product GW (IGW) alignment, closing several gaps in the literature to broaden applicability. First, we treat the open problem of IGW alignment between uncentered Gaussians on separable Hilbert spaces by giving an exact variational characterization through a quadratic optimization over isometries and co-isometries (orthogonal matrices in finite dimensions), for which we derive tight analytic upper and lower bounds. If at least one Gaussian measure is centered, the solution reduces to a fully closed-form expression, which we further extend to an analytic solution for the IGW barycenter between centered Gaussians. We also present a reduction of Gaussian multimarginal OT with pairwise quadratic costs to a tractable optimization problem and prove that every second-order stationary point of this problem is globally optimal. To demonstrate utility, we compare embedding distributions of already-trained language-model distillations and cluster synthetic users using covariance spectra of their text embeddings.

Modelling multivariate extreme events is essential when extrapolating beyond the range of observed data. Parametric models that are suitable for real-world extremes must be flexible – particularly in their ability to capture asymmetric dependence structures – while also remaining parsimonious for interpretability and computationally scalable in high dimensions. Although many models have been proposed, it is rare for any single construction to satisfy all of these requirements. For instance, the popular Hüsler-Reiss model is limited to symmetric dependence structures. In this manuscript, we introduce a class of additive factor models and derive their extreme-value limits. This leads to a broad and tractable family of models characterised by a manageable number of parameters. These models naturally accommodate asymmetric tail dependence and allow for non-stationary behaviour. We present the limiting models from both the componentwise-maxima and Peaks-over-Thresholds perspectives, via the multivariate extreme value and multivariate generalized Pareto distributions, respectively. Simulation studies illustrate identifiability properties based on existing inference methodologies. Finally, applications to summer temperature maxima in Melbourne, Australia, and to weekly negative returns from four major UK banks demonstrate improved fit compared with the Hüsler-Reiss model.

Continual learning requires models to learn continuously while preserving prior knowledge under evolving data streams. Distillation-based methods are appealing for retaining past knowledge in a shared single-model framework with low storage overhead. However, they remain constrained by the stability-plasticity dilemma: knowledge acquisition and preservation are still optimized through coupled objectives, and existing enhancement methods do not alter this underlying bottleneck. To address this issue, we propose a plugin extension paradigm termed Distillation-aware Lightweight Components (DLC) for distillation-based CL. DLC deploys lightweight residual plugins into the base feature extractor's classifier-proximal layer, enabling semantic-level residual correction for better classification accuracy while minimizing disruption to the overall feature extraction process. During inference, plugin-enhanced representations are aggregated to produce classification predictions. To mitigate interference from non-target plugins, we further introduce a lightweight weighting unit that learns to assign importance scores to different plugin-enhanced representations. DLC could deliver a significant 8% accuracy gain on large-scale benchmarks while introducing only a 4% increase in backbone parameters, highlighting its exceptional efficiency. Moreover, DLC is compatible with other plug-and-play CL enhancements and delivers additional gains when combined with them.

Most climate trend studies analyze long-term trends as a proxy for climate dynamics. However, when examining seasonal data, it is unrealistic to assume that long-term trends remain consistent across all seasons. Instead, each season likely experiences distinct trends. Additionally, seasonal climate time series, such as seasonal maximum precipitation, often exhibit nonstationarities, including periodicities and location shifts. Failure to rigorously account for these features in modeling may lead to inaccurate trend estimates. This study quantifies seasonal trends in the contiguous United States' seasonal maximum precipitation series while addressing these nonstationarities. To ensure accurate trend estimation, we identify changepoints where the seasonal maximum precipitation shifts due to factors like measurement device changes, observer differences, or location moves. We employ a penalized likelihood method to estimate multiple changepoints, incorporating a generalized extreme value distribution with periodic features. A genetic algorithm based search algorithm efficiently explores the vast space of potential changepoints in both number and timing. Additionally, we compute seasonal return levels for extreme precipitation. Our methods are illustrated using two selected stations, and the results for the US are summarized through maps. We find that seasonal trends vary more when changepoints are considered than in studies that ignore them. Our findings also reveal distinct regional and seasonal patterns, with increasing trends more prevalent during fall in the South and along the East Coast when changepoints are accounted for.

Event-based models (EBMs) infer disease progression from cross-sectional data, and standard EBMs assume a single underlying disease per individual. In contrast, mixed pathologies are common in neurodegeneration. We introduce the Joint Progression Model (JPM), a probabilistic framework that treats single-disease trajectories as partial rankings and builds a prior over joint progressions. We study several JPM variants (Pairwise, Bradley-Terry, Plackett-Luce, and Mallows) and analyze three properties: (i) calibration – whether lower model energy predicts smaller distance to the ground truth ordering; (ii) separation – the degree to which sampled rankings are distinguishable from random permutations; and (iii) sharpness – the stability of sampled aggregate rankings. All variants are calibrated, and all achieve near-perfect separation; sharpness varies by variant and is well-predicted by simple features of the input partial rankings (number and length of rankings, conflict, and overlap). In synthetic experiments, JPM improves ordering accuracy by roughly 21 percent over a strong EBM baseline (SA-EBM) that treats the joint disease as a single condition. Finally, using NACC, we find that the Mallows variant of JPM and the baseline model (SA-EBM) have results that are more consistent with prior literature on the possible disease progression of the mixed pathology of AD and VaD.

Chronic diseases often progress differently across patients. Rather than randomly varying, there are typically a small number of subtypes for how a disease progresses across patients. To capture this structured heterogeneity, the Subtype and Stage Inference Event-Based Model (SuStaIn) estimates the number of subtypes, the order of disease progression for each subtype, and assigns each patient to a subtype from primarily cross-sectional data. It has been widely applied to uncover the subtypes of many diseases and inform our understanding of them. But how robust is its performance? In this paper, we develop a principled Bayesian subtype variant of the event-based model (BEBMS) and compare its performance to SuStaIn in a variety of synthetic data experiments with varied levels of model misspecification. BEBMS substantially outperforms SuStaIn across ordering, staging, and subtype assignment tasks. Further, we apply BEBMS and SuStaIn to a real-world Alzheimer's data set. We find BEBMS has results that are more consistent with the scientific consensus of Alzheimer's disease progression than SuStaIn.