Rare-Event Prediction

Forecasting rare, high-cost events in multivariate time-series systems is hard because their precursors are seldom observed, so a purely data-driven model has little to learn from. The engineers who run these systems, however, hold knowledge that precedes such events, information absent from the scarce labels. We call this a semantic prior and inject it into a self-supervised event forecaster through two switchable mechanisms, a covariate mechanism and an attention-bias mechanism, each the identity at its null, so one architecture serves every prior type with no per-dataset architecture search. A prior helps when it supplies information the observed window does not already contain: in a short context an informative prior beats no prior in-domain (pooled h-AUROC over the no-prior baseline: a periodicity clock +14%, p<0.001; a conservation residual +47% at a 0.25 label fraction), and a working prior transfers out-of-domain (+53%), substituting for feature transfer, while priors the window already recovers stay inert and the attention-bias mechanism shows no measurable gain. KITE is a switchable, attributable route to contextual conditioning, and a substrate for scaling toward cross-domain, pretrained time-series foundation world models that carry their governing structure explicitly.

Diffusion models are increasingly used as surrogates for expensive simulators in weather prediction, molecular dynamics, and materials design. In these models, computing the probability $p_0[E]$ of an event $E$ is difficult, especially when the event of interest is rare. A stable estimate using Monte Carlo becomes computationally intractable, requiring a growing sample size $\propto\!1/p_0[E]$ to compensate for an increasing rarity. In this paper, we present Diffusion rare event sampling with Sequential Monte Carlo (DireSMC), a sequential Monte Carlo scheme that guides a population of weighted samples towards the rare event, giving access not only to samples but also to a calibrated estimate of its probability. We set up our guidance using an analytical relaxation of the event set, allowing the method to easily extend to a wide range of user-defined rare events. We validate our method on a toy problem with analytical solutions and on a score-based climate emulator, where we obtain accurate rare-event probabilities on a range of rarities from $10^{-3}$ to $10^{-5}$, achieving net speed-ups of $9\times$ to $1413\times$ over Monte Carlo.

As agents are deployed with increased autonomy, even extremely rare events along their stochastic output trajectories can occur and prove catastrophic. Safe deployment therefore does not depend on whether these events can occur, but on how often they might. We study the problem of estimating the probability of rare events that arise from stochastic variation in the agent's own actions. Estimating this type of risk requires searching over the combinatorially vast space of trajectories. Naive Monte Carlo is computationally prohibitive in this regime, and constructing effective importance sampling (IS) proposals requires coordinated changes to a context-dependent chain of conditional distributions. We develop a new IS method that perturbs the original model's weights to construct the proposal. The proposal is itself a differentiably parameterized language model, enabling gradient-based search over weight space. We formulate an objective that combines a differentiable surrogate for event amplification and an adaptive regularization scheme that dynamically balances amplification against estimator stability. We evaluate our approach on $\sim$120M and $\sim$2.6B models across three event families spanning 300+ rare events as rare as $10^{-9}$, with reference probabilities computed with $<10\%$ relative standard error. In our most verifiable settings, we observe that our IS estimator achieves over $800\times$ compute-weighted efficiency gains over naive Monte Carlo for events with probabilities lower than $10^{-7}$. Our implementation is available at https://github.com/namkoong-lab/iterative-unalignment.

Multi-horizon rare-event forecasting is hard under long macroeconomic series' data constraints: labeled events are scarce, and standard uncertainty quantification assumes an exchangeability that autocorrelation violates. A controlled ablation shows an apparent rare-event threshold for Adaptive Conformal Inference instead reflects calibration-set size. Across 200 random calibration sets, support width of the nonconformity-score distribution explains up to 85% of coverage variance versus 2% for rare-event count; the same, not the same magnitude, replicates across synthetic conditions and five countries (five-country Spearman $ρ$ 0.45-0.66 vs. 0.02-0.23). A diversity-maximizing selector built on this is the only strategy tested that improves long-horizon coverage (67.8% to 81.4% at six months); Mondrian, shift-robust, and extreme-value alternatives fail to close it. Mondrian even worsens coverage under oracle labels. A compact proposition explains why: coverage deficit reflects how closely the calibration set's upper quantile reaches the test distribution's. Diversity is necessary, not sufficient. Demonstrated on a two-stage U.S. recession-forecasting framework with RegressorChain, whether six-month coverage reaches 90% under honest scoring remains open, a question this paper quantifies rather than resolves.

Extreme events (EEs) in chaotic dynamics are rare broad excursions whose forecastability can be altered by dynamical noise. We investigate how noise changes EE occurrence and prediction skill across forecast horizons in a third-order autonomous chaotic flow. A single clean-data threshold is frozen for all realizations, broad events are defined by one maximum per excursion, and a future window W=15 is predicted from a 15-time-unit history using HistGradientBoosting with chronological data separation. As the forecast gap G between the observed history and the future event window increases, the clean Matthews correlation coefficient (MCC) decreases from 0.641 at G=0 to 0.165 at G=15. Noise dependence is evaluated with ten paired realizations at eight amplitudes. The mean short-horizon score increases from 0.456 in clean data to 0.546 at sigma=0.007; the paired gain is 0.0895 (95% CI 0.0494-0.1295; Holm-adjusted p=0.0234). Noise strongly increases EE occurrence while event amplitude and width remain comparatively stable. Equalizing positive training counts across noise levels substantially attenuates the short-horizon gain, whereas strong noise reduces intermediate-horizon skill. We term this horizon-dependent, nonuniform change in forecast skill noise-induced predictability redistribution (NIPR).

Predicting failures before they occur remains a major challenge in predictive maintenance, particularly when failures are rare, when equipment of the same family differ in sensor configurations, and when the goal is anticipation rather than diagnosis of an already observed fault. This paper proposes a common-to-target probabilistic model that learns shared failure-related patterns across a family of heterogeneous equipment and adapts parsimoniously to target equipment. The model explicitly accounts for sensor heterogeneity, operating context, and degradation dynamics to produce calibrated failureprobability estimates suitable for maintenance planning. Its performance is evaluated on a synthetic refrigerator dataset comprising 27 simulated refrigerators with varying sensor configurations, operating conditions, and failure types, providing a controlle

Prediction of wildfire occurrence is a rare-event problem compounded by spatial heterogeneity and temporal distribution shift, as fire occurrences are vastly outnumbered by non-occurrences, and predictor--fire relationship varies across space and time. Models trained on historical fire data may perform poorly under new conditions and require adaptation to the target distribution before operational use. We propose PyroAdapt, a pretrain--retrieve--rank framework that adapts a pretrained model to target conditions by retrieving historical locations with similar conditions and fine-tuning on the retrievals through risk ranking. For spatial adaptation, we condition risk on terrain, ecoregion embeddings, and fire rates, accounting for spatial context in the retrieval, and learn risk ordering from same-day fire--nonfire cell pairs. We compare direct ranking, residual pairwise DPO (RDPO), and selective ranking through a unified score-gap formulation that characterizes their gradient allocation. Over California (discretized into 666 0.25x0.25 grid cells), these objectives raise daily average precision from 21.62% for continued focal fine-tuning to 24.35--24.57%, and Top5% recall from 18.70% to 22.11--22.79%. Under a fixed daily detection budget of 34 cells (5% area), selective ranking captures 344 additional positive cell--days. For fires in the top 5%/10%/20% of dry matter consumption, selective ranking raises recall by 39.70/28.18/20.50 percentage points, respectively. Furthermore, rolling evaluations over Yosemite show that the gains from ranking persist under temporal distribution shift. Together, these results show that PyroAdapt prioritizes the most fire-prone locations under a daily budget constraint and detects more extreme fire events.

Pretrial risk assessment tools are used on over one million U.S. defendants each year, yet their use for predicting rare violent re-offense faces a basic statistical barrier. We derive a universal precision bound -- the Likelihood Ratio Wall -- showing that when violent re-arrest rates are low (2-5%), achieving even a 50% hit rate among people labeled "high risk" (positive predictive value, or PPV) would require tools far more discriminative than current instruments appear to be. For rare outcomes, a tool can have respectable-looking performance metrics and still be wrong most of the time it flags someone as "high risk for violence." We show that post-hoc score recalibration cannot solve this problem because it does not improve the tool's underlying ability to separate true positives from false positives. We further prove a Surveillance Ceiling: when over-policing inflates recorded "risk factors" among those who would not re-offend, the maximum achievable precision is structurally lower for over-policed groups, even at equal offense rates. We translate these results into the Number Needed to Detain (how many people must be detained to prevent one violent offense), and propose that risk reports should communicate this uncertainty explicitly. Our findings suggest that for rare violent outcomes, debates about fairness metrics alone are incomplete: under current data regimes, the available features may not support high-confidence individualized detention decisions.

Large language models (LLMs) are increasingly used for high-stakes decision-making, yet existing approaches struggle to reconcile scalability, interpretability, and reproducibility. Black-box models obscure their reasoning, while recent LLM-based rule systems rely on per-sample evaluation, causing costs to scale with dataset size and introducing stochastic, hallucination-prone outputs. We propose reframing LLMs as code generators rather than per-instance evaluators. A single LLM call generates executable, human-readable decision logic that runs deterministically over structured data, eliminating per-sample LLM queries while enabling reproducible and auditable predictions. We combine code generation with automated statistical validation using precision lift, binomial significance testing, and coverage filtering, and apply cluster-based gap analysis to iteratively refine decision logic without human annotation. We instantiate this framework in venture capital founder screening, a rare-event prediction task with strong interpretability requirements. On VCBench, a benchmark of 4,500 founders with a 9% base success rate, our approach achieves 37.5% precision and an F0.5 score of 25.0%, outperforming GPT-4o (at 30.0% precision and an F0.5 score of 25.7%) while maintaining full interpretability. Each prediction traces to executable rules over human-readable attributes, demonstrating verifiable and interpretable LLM-based decision-making in practice.

Rare-event prediction is critical in domains such as healthcare, finance, reliability engineering, customer support, aviation safety, where positive outcomes are infrequent yet potentially catastrophic. Extreme class imbalance biases conventional models toward majority-class predictions, limiting recall, calibration, and operational usefulness. We propose LPCORP (Low-Prevalence CORrector for Prediction)*, a two-stage framework that combines reasoning-enhanced prediction with confidence-based outcome correction. A reasoning model first produces enriched predictions from narrative inputs, after which a lightweight classifier evaluates and selectively corrects these outputs to mitigate prevalence-driven bias. In this study we used Logistic-Regression (LR) and a simple Multilayer Perceptron (MLP) classifiers for this purpose. We evaluate LPCORP on real-world datasets from medical and consumer service domains. The results show that this method transforms the original rare-event prediction problem into a more balanced supervised correction task without discarding or resampling observations. Test-set evaluation demonstrates substantially improved performance, particularly in precision, which is a known weakness in low-prevalence data. We further provide a cost-reduction analysis comparing the expenses associated with rare-event damage control without preventive measures to those incurred when low-cost, prediction-based preventive interventions are applied that showed up to 40+% reduction in some cases.

Many high-stakes screening tasks require predicting rare outcomes from unstructured text, where errors are costly and decisions must be auditable. We introduce Random Rule Forest (RRF), an interpretable ensemble that uses a large language model (LLM) not as an end-to-end predictor but as a generator of simple YES/NO questions. Each question acts as a weak learner, and their responses are combined by a plain unit-weight vote into an auditable ``green-flags'' scorecard: enough independent positive signals indicate a higher chance of success. We argue this deliberate simplicity is a robust default when positives are scarce and learned weights are hard to estimate. We evaluate RRF in two low-base-rate domains. On early-stage startup screening from founder profiles, RRF produces a transparent scorecard whose precision is several times the base rate (with light expert input raising it further) and, unlike direct prompting, its operating point can be controlled directly. On an established Phase~I clinical-trial benchmark, RRF outperforms published baselines on the threshold-independent metrics PR-AUC and ROC-AUC. Together these show that LLMs can serve as auditable feature generators for high-stakes text-based decisions, combining transparency with competitive predictive performance.