Anguished family of teenager murdered at New Year's Eve party in 1982 reveal killer's final act of cruelty as he takes crucial detail to the grave after being executed in Florida Trump outlines plan to destroy Iran's power plants and bridges next week as he warns bombing will continue until he says'enough' DR PHIL: I've reviewed hundreds of secret government UFO videos and files that have been actively hidden from the public... what I can now reveal about non-human life and this psyop cover-up could spark a national crisis Heiress' $2m Aspen wedding was'horrific nightmare' that sparked the mother of all lawsuits before a bombshell divorce... Now she'll try again with new hunk Truth about Alix Earle's revolving door of famous men: Friends insist it's just a'hot girl summer' of one-time flings... but now insiders blow lid on her desperate secret and jaw-dropping ulterior motive Matt Damon reveals'new phase of life' as he brings wife and rarely seen daughter, 20, to The Odyssey ...

I'd Rather Risk Cancer Than See AI Move This Fast I'd benefit if AI cured cancer. And I still want AI progress to slow down. On a fall afternoon 15 years ago, I met an idealistic researcher outside a Stanford coffee shop to discuss our shared dream: using AI to detect cancer. He had wiry hair, a penchant for talking with his hands, and a reputation for brilliance. He worked at a research lab that developed early screens for cancer; I, at 20, had just learned that I carried a mutation that conferred a very high risk of breast, ovarian, and other cancers.

No feature ranking can be simultaneously faithful, stable, and complete when features are collinear. For collinear pairs, ranking reduces to a coin flip. We prove this impossibility, quantify it for four model classes, resolve it via ensemble averaging (DASH), and machine-verify it with 305 Lean 4 theorems. We characterize the complete attribution design space: exactly two families of methods exist -- faithful-complete methods (unstable, with rankings that flip up to 50% of the time) and ensemble methods like DASH (stable, reporting ties for symmetric features) -- and no method lies outside this dichotomy. The impossibility is quantitative: the attribution ratio diverges as 1/(1-rho^2) for gradient boosting, is infinite for Lasso, and converges for random forests. DASH (Diversified Aggregation of SHAP) is provably Pareto-optimal among unbiased aggregations, achieving the Cramer-Rao variance bound with a tight ensemble size formula. In a survey of 77 public datasets, 68% exhibit attribution instability. Switching to conditional SHAP does not escape the impossibility when features have equal causal effects. The framework includes practical diagnostics -- a Z-test workflow and single-model screening tool -- and has direct consequences for fairness auditing: SHAP-based proxy discrimination audits are provably unreliable under collinearity. The design space theorem, diagnostics, and impossibility are mechanically verified in Lean 4 (305 theorems from 16 axioms, 0 sorry) -- to our knowledge, the first formally verified impossibility in explainable AI.

Dna demethylation is associated with malignant progression oflower-grade gliomas.Scientific reports,9(1):1-12, 2019.

Existing methods typically rely on either interpretable but inflexible models or highly flexible black-box approaches that sacrifice interpretability; moreover, most impose a single global decision rule across patients. We introduce the Locally Interpretable Individualized Treatment Rule (LI-ITR) method, which combines flexible machine learning models to accurately learn complex treatment outcomes with locally interpretable approximations to construct subject-specific treatment rules. LI-ITR employs variational autoencoders to generate realistic local synthetic samples and learns individualized decision rules through a mixture of interpretable experts. Simulation studies show that LI-ITR accurately recovers true subject-specific local coefficients and optimal treatment strategies. An application to precision side-effect management in breast cancer illustrates the necessity of flexible predictive modeling and highlights the practical utility of LI-ITR in estimating optimal treatment rules while providing transparent, clinically interpretable explanations.

Many important datasets contain samples that are missing one or more feature values. Maintaining the interpretability of machine learning models in the presence of such missing data is challenging. Singly or multiply imputing missing values complicates the model's mapping from features to labels. On the other hand, reasoning on indicator variables that represent missingness introduces a potentially largenumber ofadditional terms, sacrificing sparsity.

Risk-based breast cancer screening matches individual genetics to mammogram frequency, showing safety compared to annual screening in a 28,000-woman study.

Abstract--Tree-based ensemble methods consistently outperform single models on tabular classification tasks, yet the conditions under which ensembles provide clear advantages--and prevent overfitting despite using high-variance base learners--are not always well understood by practitioners. We study four real-world classification problems (Breast Cancer diagnosis, Heart Disease prediction, Pima Indians Diabetes, and Credit Card Fraud detection) comparing classical single models against nine ensemble methods using five-seed repeated stratified cross-validation with statistical significance testing. Our results reveal three distinct regimes: (i) On nearly linearly separable data (Breast Cancer), well-regularized linear models achieve 97% accuracy with <2% generalization gaps; ensembles match but do not substantially exceed this performance. We systematically quantify dataset complexity through linearity scores, feature correlation, class separability, and noise estimates, explaining why different data regimes favor different model families. Cross-validated train/test accuracy and generalization-gap plots provide simple visual diagnostics for practitioners to assess when ensemble complexity is warranted. Statistical testing confirms that ensemble gains are significant on nonlinear tasks (p < 0.01) but not on near-linear data (p > 0.15). The study provides actionable guidelines for ensemble model selection in high-stakes tabular applications, with full code and reproducible experiments publicly available. A model that almost perfectly fits its training data can still fail badly on new cases. This gap between training performance and real-world behaviour is the essence of overfitting, and it is particularly problematic in domains such as medical diagnosis and financial fraud detection, where mistakes are costly: missed tumours delay treatment, and undetected fraud translates directly into monetary loss.

Recent advances in large language models (LLMs) have shown strong reasoning capabilities through large-scale pretraining and post-training reinforcement learning, demonstrated by DeepSeek-R1. However, current post-training methods, such as Grouped Relative Policy Optimization (GRPO), mainly reward correctness, which is not aligned with the multi-dimensional objectives required in high-stakes fields such as medicine, where reasoning must also be faithful and comprehensive. We introduce Clinical-Objective Relative Policy Optimization (CRPO), a scalable, multi-objective, verifiable reinforcement learning method designed to align LLM post-training with clinical reasoning principles. CRPO integrates rule-based and verifiable reward signals that jointly optimize accuracy, faithfulness, and comprehensiveness without relying on human annotation. To demonstrate its effectiveness, we train Clinical-R1-3B, a 3B-parameter model for clinical reasoning. The experiments on three benchmarks demonstrate that our CRPO substantially improves reasoning on truthfulness and completeness over standard GRPO while maintaining comfortable accuracy enhancements. This framework provides a scalable pathway to align LLM reasoning with clinical objectives, enabling safer and more collaborative AI systems for healthcare while also highlighting the potential of multi-objective, verifiable RL methods in post-training scaling of LLMs for medical domains.