Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack interpretability and formal guarantees, or impose restrictive assumptions like linearity, continuous-only observations, and strong structural priors. These limitations particularly challenge applications with a large number of discrete latent variables and mixed-type observations. To address these challenges, we propose discrete causal representation learning (DCRL), a generative framework that models a directed acyclic graph among discrete latent variables, along with a sparse bipartite graph linking latent and observed layers. This design accommodates continuous, count, and binary responses through flexible measurement models while maintaining interpretability. Under mild conditions, we prove that both the bipartite measurement graph and the latent causal graph are identifiable from the observed data distribution alone. We further propose a three-stage estimate-resample-discovery pipeline: penalized estimation of the generative model parameters, resampling of latent configurations from the fitted model, and score-based causal discovery on the resampled latents. We establish the consistency of this procedure, ensuring reliable recovery of the latent causal structure. Empirical studies on educational assessment and synthetic image data demonstrate that DCRL recovers sparse and interpretable latent causal structures.

Deploying neural networks on microcontrollers is constrained by kilobytes of flash and SRAM, where 1x1 pointwise (PW) mixers often dominate memory even after INT8 quantization across vision, audio, and wearable sensing. We present HYPER-TINYPW, a compression-as-generation approach that replaces most stored PW weights with generated weights: a shared micro-MLP synthesizes PW kernels once at load time from tiny per-layer codes, caches them, and executes them with standard integer operators. This preserves commodity MCU runtimes and adds only a one-off synthesis cost; steady-state latency and energy match INT8 separable CNN baselines. Enforcing a shared latent basis across layers removes cross-layer redundancy, while keeping PW1 in INT8 stabilizes early, morphology-sensitive mixing. We contribute (i) TinyML-faithful packed-byte accounting covering generator, heads/factorization, codes, kept PW1, and backbone; (ii) a unified evaluation with validation-tuned t* and bootstrap confidence intervals; and (iii) a deployability analysis covering integer-only inference and boot versus lazy synthesis. On three ECG benchmarks (Apnea-ECG, PTB-XL, MIT-BIH), HYPER-TINYPW shifts the macro-F1 versus flash Pareto frontier: at about 225 kB it matches a roughly 1.4 MB CNN while being 6.31x smaller (84.15% fewer bytes), retaining at least 95% of large-model macro-F1. Under 32-64 kB budgets it sustains balanced detection where compact baselines degrade. The mechanism applies broadly to other 1D biosignals, on-device speech, and embedded sensing tasks where per-layer redundancy dominates, indicating a wider role for compression-as-generation in resource-constrained ML systems. Beyond ECG, HYPER-TINYPW transfers to TinyML audio: on Speech Commands it reaches 96.2% test accuracy (98.2% best validation), supporting broader applicability to embedded sensing workloads where repeated linear mixers dominate memory.

A key capability of modern neural networks is their capacity to simultaneously learn underlying rules and memorize specific facts or exceptions. Yet, theoretical understanding of this dual capability remains limited. We introduce the Rules-and-Facts (RAF) model, a minimal solvable setting that enables precise characterization of this phenomenon by bridging two classical lines of work in the statistical physics of learning: the teacher-student framework for generalization and Gardner-style capacity analysis for memorization. In the RAF model, a fraction $1 - \varepsilon$ of training labels is generated by a structured teacher rule, while a fraction $\varepsilon$ consists of unstructured facts with random labels. We characterize when the learner can simultaneously recover the underlying rule - allowing generalization to new data - and memorize the unstructured examples. Our results quantify how overparameterization enables the simultaneous realization of these two objectives: sufficient excess capacity supports memorization, while regularization and the choice of kernel or nonlinearity control the allocation of capacity between rule learning and memorization. The RAF model provides a theoretical foundation for understanding how modern neural networks can infer structure while storing rare or non-compressible information.

There remain theoretical gaps in deep neural network estimators for the nonparametric Cox proportional hazards model. In particular, it is unclear how gradient-based optimization error propagates to population risk under partial likelihood, how pointwise bias can be controlled to permit valid inference, and how ensemble-based uncertainty quantification behaves under realistic variance decay regimes. We develop an asymptotic distribution theory for deep Cox estimators that addresses these issues. First, we establish nonasymptotic oracle inequalities for general trained networks that link in-sample optimization error to population risk without requiring the exact empirical risk optimizer. We then construct a structured neural parameterization that achieves infinity-norm approximation rates compatible with the oracle bound, yielding control of the pointwise bias. Under these conditions and using the Hajek--Hoeffding projection, we prove pointwise and multivariate asymptotic normality for subsampled ensemble estimators. We derive a range of subsample sizes that balances bias correction with the requirement that the Hajek--Hoeffding projection remain dominant. This range accommodates decay conditions on the single-overlap covariance, which measures how strongly a single shared observation influences the estimator, and is weaker than those imposed in the subsampling literature. An infinitesimal jackknife representation provides analytic covariance estimation and valid Wald-type inference for relative risk contrasts such as log-hazard ratios. Finally, we illustrate the finite-sample implications of the theory through simulations and a real data application.

Sentiment signals derived from sparse news are commonly used in financial analysis and technology monitoring, yet transforming raw article-level observations into reliable temporal series remains a largely unsolved engineering problem. Rather than treating this as a classification challenge, we propose to frame it as a causal signal reconstruction problem: given probabilistic sentiment outputs from a fixed classifier, recover a stable latent sentiment series that is robust to the structural pathologies of news data such as sparsity, redundancy, and classifier uncertainty. We present a modular three-stage pipeline that (i) aggregates article-level scores onto a regular temporal grid with uncertainty-aware and redundancy-aware weights, (ii) fills coverage gaps through strictly causal projection rules, and (iii) applies causal smoothing to reduce residual noise. Because ground-truth longitudinal sentiment labels are typically unavailable, we introduce a label-free evaluation framework based on signal stability diagnostics, information preservation lag proxies, and counterfactual tests for causality compliance and redundancy robustness. As a secondary external check, we evaluate the consistency of reconstructed signals against stock-price data for a multi-firm dataset of AI-related news titles (November 2024 to February 2026). The key empirical finding is a three-week lead lag pattern between reconstructed sentiment and price that persists across all tested pipeline configurations and aggregation regimes, a structural regularity more informative than any single correlation coefficient. Overall, the results support the view that stable, deployable sentiment indicators require careful reconstruction, not only better classifiers.

Understanding how biomarker distributions evolve over time is a central challenge in digital health and chronic disease monitoring. In diabetes, changes in the distribution of glucose measurements can reveal patterns of disease progression and treatment response that conventional summary measures miss. Motivated by a 26-week clinical trial comparing the closed-loop insulin delivery system t:slim X2 with standard therapy in children with type 1 diabetes, we propose a probabilistic framework to model the continuous-time evolution of time-indexed distributions using continuous glucose monitoring data (CGM) collected every five minutes. We represent the glucose distribution as a Gaussian mixture, with time-varying mixture weights governed by a neural ODE. We estimate the model parameter using a distribution-matching criterion based on the maximum mean discrepancy. The resulting framework is interpretable, computationally efficient, and sensitive to subtle temporal distributional changes. Applied to CGM trial data, the method detects treatment-related improvements in glucose dynamics that are difficult to capture with traditional analytical approaches.

Background: Determining an adequate sample size is essential for developing reliable and generalisable clinical prediction models, yet practical guidance on selecting appropriate methods remains limited. Existing analytical and simulation-based approaches often rely on restrictive assumptions and focus on mean-based criteria. We present and validate pmsims, an R package that uses Gaussian process surrogate modelling to provide a flexible and computationally efficient simulation-based framework for sample size determination across diverse prediction settings. Methods: We conducted a comprehensive simulation study with two aims. First, we compared three search engines implemented in pmsims: a Gaussian process-based adaptive method, a deterministic bisection method, and a hybrid approach, across binary, continuous, and survival outcomes. Second, we benchmarked the best-performing pmsims engine against existing analytical (pmsampsize) and simulation-based (samplesizedev) methods, evaluating recommended sample sizes, computational time, and achieved performance on large independent validation datasets. Results: The Gaussian process-based method consistently produced the most stable sample size estimates, particularly in low-signal, high-dimensional settings. In benchmarking, pmsims achieved performance close to prespecified targets across all outcome types, matching simulation-based approaches and outperforming analytical methods in more challenging scenarios. Conclusions: pmsims provides an efficient and flexible framework for principled sample size planning in clinical prediction modelling, requiring fewer model evaluations than non-adaptive simulation approaches.

Privacy and algorithmic fairness have become two central issues in modern machine learning. Although each has separately emerged as a rapidly growing research area, their joint effect remains comparatively under-explored. In this paper, we systematically study the joint impact of differential privacy and fairness on classification in a federated setting, where data are distributed across multiple servers. Targeting demographic disparity constrained classification under federated differential privacy, we propose a two-step algorithm, namely FDP-Fair. In the special case where there is only one server, we further propose a simple yet powerful algorithm, namely CDP-Fair, serving as a computationally-lightweight alternative. Under mild structural assumptions, theoretical guarantees on privacy, fairness and excess risk control are established. In particular, we disentangle the source of the private fairness-aware excess risk into a) intrinsic cost of classification, b) cost of private classification, c) non-private cost of fairness and d) private cost of fairness. Our theoretical findings are complemented by extensive numerical experiments on both synthetic and real datasets, highlighting the practicality of our designed algorithms.

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has emerged as a rapidly growing alternative framework that is particularly well suited to modern applications involving high-dimensional data and complex machine learning models. Its appeal stems from being both distribution-free -- relying mainly on symmetry assumptions such as exchangeability -- and model-agnostic, treating the learning algorithm as a black box. Even under such limited assumptions, conformal prediction provides exact finite-sample guarantees, though these are typically of a marginal nature that requires careful interpretation. This paper explains the core ideas of conformal prediction and reviews selected methods. Rather than offering an exhaustive survey, it aims to provide a clear conceptual entry point and a pedagogical overview of the field.

The company's sudden decision to pull the plug on Sora is a sign of deeper trouble. When I opened Sora this morning, I was met with a flood of strange and disturbing AI-generated videos. On OpenAI's video app, I scrolled through fabricated scenes of the Iran war and a barrage of fake Donald Trumps blabbering about Jeffrey Epstein. In my least favorite clip, I watched a man deep-fry an infant. The app lets users create fairly realistic-looking AI-generated clips--including of their own likeness--and then post them on a TikTok-like feed.