Papers

We propose a random forest estimator for the intensity of spatial point processes, applicable with or without covariates. It retains the well-known advantages of a random forest approach, including the ability to handle a large number of covariates, out-of-bag cross-validation, and variable importance assessment. Importantly, even in the absence of covariates, it requires no border correction and adapts naturally to irregularly shaped domains and manifolds. Consistency and convergence rates are established under various asymptotic regimes, revealing the benefit of using covariates when available. Numerical experiments illustrate the methodology and demonstrate that it performs competitively with state-of-the-art methods.

A crucial step in fitting a regression model to data is determining the model's structure, i.e., the subset of explanatory variables to be included. However, the uncertainty in this step is often overlooked due to a lack of satisfactory methods. Frequentists have no broadly applicable confidence set constructions for a model's structure, and Bayesian posterior credible sets do not achieve the desired finite-sample coverage. In this paper, we propose an extension of the possibility-theoretic inferential model (IM) framework that offers reliable, data-driven uncertainty quantification about the unknown model structure. This particular extension allows for the inclusion of incomplete prior information about the unknown structure that facilitates regularization. We prove that this new, regularized, possibilistic IM's uncertainty quantification is suitably calibrated relative to the set of joint distributions compatible with the data-generating process and assumed partial prior knowledge about the structure. This implies, among other things, that the derived confidence sets for the unknown model structure attain the nominal coverage probability in finite samples. We provide background and guidance on quantifying prior knowledge in this new context and analyze two benchmark data sets, comparing our results to those obtained by existing methods.

This paper develops robust inference methods for predictive regressions that address key challenges posed by endogenously persistent or heavy-tailed regressors, as well as persistent volatility in errors. Building on the Cauchy estimation framework, we propose two novel tests: one based on $t$-statistic group inference and the other employing a hybrid approach that combines Cauchy and OLS estimation. These methods effectively mitigate size distortions that commonly arise in standard inference procedures under endogeneity, near nonstationarity, heavy tails, and persistent volatility. The proposed tests are simple to implement and applicable to both continuous- and discrete-time models. Extensive simulation experiments demonstrate favorable finite-sample performance across a range of realistic settings. An empirical application examines the predictability of excess stock returns using the dividend-price and earnings-price ratios as predictors. The results suggest that the dividend-price ratio possesses predictive power, whereas the earnings-price ratio does not significantly forecast returns.

Digital carbon incentives are increasingly used to promote low-carbon travel, but city-scale evidence on their behavioral and carbon-accounting implications remains limited. We evaluated a carbon-incentive program on a Beijing Mobility-as-a-Service platform using 4.82 billion trips from 2.96 million users over 13 months, with a matched panel of enrolled and non-enrolled users. Enrollment was associated with a 20.3 percentage-point increase in the monthly low-carbon travel share, with pre-enrollment trends remaining near zero across event-study tests. A random-forest accounting scenario trained on pre-enrollment data implied a 1.8% citywide decline in gasoline-car trips and annual reductions of 94,353 tonnes of CO2, equivalent to 5.7% of the certified reductions traded in Beijing's carbon market in 2023. This estimate is model-dependent rather than a directly observed or causally identified program effect. Larger program-associated responses were concentrated in areas with greater transit access. These results show that carbon-market-financed digital incentives can support measurable low-carbon travel responses at the city scale.

Proteins underpin most biological function, and the ability to design them with tailored structures and properties is central to advances in biotechnology. Diffusion-based generative models have emerged as powerful tools for protein design, but steering them toward proteins with specified properties remains challenging. The Feynman-Kac (FK) framework provides a principled way to guide diffusion models using user-defined rewards. In this paper, we enable FK-based steering of RFdiffusion through the development of guiding potentials that leverage ProteinMPNN and structural relaxation to guide the diffusion process towards desired properties. We show that steering can be used to consistently improve predicted interface energetics and increase binder designability by $89.5\%$. Together, these results establish that diffusion-based protein design can be effectively steered toward arbitrary, non-differentiable objectives, providing a model-independent framework for controllable protein generation.

Crossover designs randomly assign each unit to receive a sequence of treatments. By comparing outcomes within the same unit, these designs can effectively eliminate between-unit variation and facilitate the identification of both instantaneous effects of current treatments and carryover effects from past treatments. They are widely used in traditional biomedical studies and are increasingly adopted in modern digital platforms. However, standard analyses of crossover designs often rely on strong parametric models, making inference vulnerable to model misspecification. This paper adopts a design-based framework to analyze general crossover designs. We make two main contributions. First, we use potential outcomes to formally define the causal estimands and assumptions on the data-generating process. For any given type of crossover design and assumptions on potential outcomes, we outline a procedure for identification and estimation, emphasizing the central role of the treatment assignment mechanism in design-based inference. Second, we unify the analysis of crossover designs using least squares, with restrictions on the coefficients and weights on the units. Based on the theory, we recommend the specification of the regression function, weighting scheme, and coefficient restrictions to assess identifiability, construct efficient estimators, and estimate variances in a unified fashion. Crucially, the least squares procedure is simple to implement, and yields not only consistent and efficient point estimates but also valid variance estimates even when the working regression model is misspecified.

Prompt learning has become a key method for adapting large language models to specific tasks with limited data. However, traditional gradient-based optimization methods for tuning prompts are computationally intensive, posing challenges for efficiency. We introduce ZOSA (Zero-Order Sharpness-Aware Minimization), a novel optimization framework that integrates zero-order optimization with sharpness-aware minimization to enhance prompt tuning. ZOSA employs Rademacher perturbation vectors to estimate gradients without requiring backpropagation. By incorporating sharpness-aware principles, it targets flat minima in the loss landscape, improving generalization. An adaptive learning rate, guided by loss variability, further ensures stable convergence. Experiments on few-shot learning tasks, such as text classification and natural language inference, show that ZOSA significantly outperforms existing methods. With its theoretical foundation and computational efficiency, ZOSA offers a practical solution for prompt-based learning in resource-limited settings.

Generative models are increasingly central to scientific workflows, yet their systematic use and interpretation require a proper understanding of their limitations through rigorous validation. Classic approaches struggle with scalability, statistical power, or interpretability when applied to high-dimensional data, making it difficult to certify the reliability of these models in realistic, high-dimensional scientific settings. Here, we propose the use of the New Physics Learning Machine (NPLM), a learning-based approach to goodness-of-fit testing inspired by the Neyman–Pearson construction, to test generative networks trained on high-dimensional scientific data. We demonstrate the performance of NPLM for validation in two benchmark cases: generative models trained on mixtures of Gaussian models with increasing dimensionality, and a public end-to-end model, known as FlowSim, developed to generate high-energy physics collision events. We demonstrate that the NPLM can serve as a powerful validation method while also providing a means to diagnose sub-optimally modeled regions of the data.

Instrumental variables (eliminate the bias that afflicts least-squares identification of dynamical systems through noisy data, yet traditionally relies on external instruments that are seldom available for nonlinear time series data. We propose an IV estimator that synthesizes instruments from the data. We establish finite-sample $L^{p}$ consistency for all $p \ge 1$ in both discrete- and continuous-time models, recovering a nonparametric $\sqrt{n}$-convergence rate. On a forced Lorenz system our estimator reduces parameter bias by 200x (continuous-time) and 500x (discrete-time) relative to least squares and reduces RMSE by up to tenfold. Because the method only assumes that the model is linear in the unknown parameters, it is broadly applicable to modern sparsity-promoting dynamics learning models.

Intra-tumor heterogeneity driving disease progression is characterized by distinct growth and spatial proliferation patterns of cells and their nuclei within tumor and non-tumor tissues. A widely accepted hypothesis is that these spatial patterns are correlated with morphology of the cells and their nuclei. Nevertheless, tools to quantify the correlation, with uncertainty, are scarce, and the state-of-the-art is based on low-dimensional numerical summaries of the shapes that are inadequate to fully encode shape information. To this end, we propose a marked point process framework to assess spatial correlation among shapes of planar closed curves, which represent cell or nuclei outlines. With shapes of curves as marks, the framework is based on a mark-weighted $K$ function, a second-order spatial statistic that accounts for the marks' variation by using test functions that capture only the shapes of cells and their nuclei. We then develop local and global hypothesis tests for spatial dependence between the marks using the $K$ function. The framework is brought to bear on the cell nuclei extracted from histopathology images of breast cancer, where we uncover distinct correlation patterns that are consistent with clinical expectations.

Self-consuming generative models have received significant attention over the last few years. In this paper, we study a self-consuming generative model with heterogeneous preferences that is a generalization of the model in Ferbach et al. (2024). The model is retrained round by round using real data and its previous-round synthetic outputs. The asymptotic behavior of the retraining dynamics is investigated across four regimes using different techniques including the nonlinear Perron–Frobenius theory. Our analyses improve upon that of Ferbach et al. (2024) and provide convergence results in settings where the well-known Banach contraction mapping arguments do not apply. Stability and non-stability results regarding the retraining dynamics are also given.

Background: Accurate prediction of surgical case duration underpins operating room (OR) scheduling, yet existing models often depend on site- or surgeon-specific inputs and rarely undergo external validation, limiting generalisability. Methods: We undertook a retrospective multicentre study using routinely collected perioperative data from two general hospitals in Japan (development: 1 January 2021-31 December 2023; temporal test: 1 January-31 December 2024). Elective weekday procedures with American Society of Anesthesiologists (ASA) Physical Status 1-4 were included. Pre-specified preoperative predictors comprised surgical context (year, month, weekday, scheduled duration, general anaesthesia indicator, body position) and patient factors (sex, age, body mass index, allergy, infection, comorbidity, ASA). Missing data were addressed by multiple imputation by chained equations. Four learners (elastic-net, generalised additive models, random forest, gradient-boosted trees) were tuned within internal-external cross-validation (IECV; leave-one-cluster-out by centre-year) and combined by stacked generalisation to predict log-transformed duration. Results: We analysed 63,206 procedures (development 45,647; temporal test 17,559). Cluster-specific and pooled errors and calibrations from IECV are provided with consistent performance across centres and years. In the 2024 temporal test cohort, calibration was good (intercept 0.423, 95%CI 0.372 to 0.474; slope 0.921, 95%CI 0.911 to 0.932). Conclusions: A stacked machine-learning model using only widely available preoperative variables achieved accurate, well-calibrated predictions in temporal external validation, supporting transportability across sites and over time. Such general-purpose tools may improve OR scheduling without relying on idiosyncratic inputs.

Active statistical inference is a new method for inference with AI-assisted data collection. Given a budget on the number of labeled data points that can be collected and assuming access to an AI predictive model, the basic idea is to improve estimation accuracy by prioritizing the collection of labels where the model is most uncertain. The drawback, however, is that inaccurate uncertainty estimates can make active sampling produce highly noisy results, potentially worse than those from naive uniform sampling. In this work, we present robust sampling strategies for active statistical inference. Robust sampling ensures that the resulting estimator is never worse than the estimator using uniform sampling. Furthermore, with reliable uncertainty estimates, the estimator usually outperforms standard active inference. This is achieved by optimally interpolating between uniform and active sampling, depending on the quality of the uncertainty scores, and by using ideas from robust optimization. We demonstrate the utility of the method on a series of real datasets from computational social science and survey research.

Randomized controlled trials (RCTs) are indispensable for establishing the clinical value of medical artificial-intelligence (AI) tools, yet their high cost and long timelines hinder timely validation as new models emerge rapidly. Here, we propose BRIDGE, a data-reuse RCT design for AI-based risk models. AI risk models support a broad range of interventions, including screening, treatment selection, and clinical alerts. BRIDGE trials recycle participant-level data from completed trials of AI models when legacy and updated models make concordant predictions, thereby reducing the enrollment requirement for subsequent trials. We provide a practical checklist for investigators to assess whether reusing data from previous trials allows for valid causal inference and preserves type I error. Using real-world datasets across breast cancer, cardiovascular disease, and sepsis, we demonstrate concordance between successive AI models, with up to 64.8% overlap in top 5% high-risk cohorts. We then simulate a series of breast cancer screening studies, where our design reduced required enrollment by 46.6%–saving over US$2.8 million–while maintaining 80% power. By transforming trials into adaptive, modular studies, our proposed design makes Level I evidence generation feasible for every model iteration, thereby accelerating cost-effective translation of AI into routine care.

This article proposes an improved version of the Spearman rank correlation based on using Wilcoxon rank score function. A smoothed empirical cumulative distribution function (ecdf)computes the smoothed ranks and replaces the regular ranks in the Wilcoxon rank score function. The smoothed Wilcoxon rank scores are then used for estimation of the Spearman's correlation. The proposed approach is similar to the Spearman's rho estimator which uses ranks of the random samples of X and Y but the proposed method improves Spearman's approach such as handling ties and gaining higher efficiency under monotone associations. A Wald type hypothesis test has been proposed for the new estimator and the asymptotic properties are shown.

Time series prediction is challenging due to our limited understanding of the underlying dynamics. Conventional models such as ARIMA and Holt's linear trend model experience difficulty in identifying nonlinear patterns in time series. In contrast, machine learning models excel at learning complex patterns and handling high-dimensional data; however, they are unable to quantify the uncertainty associated with their predictions, as statistical models do. To overcome these drawbacks, we propose Random Feature Bayesian Lasso Takens (rfBLT) for forecasting time series data. This non-parametric model captures the underlying system via the Takens' theorem and measures the degree of uncertainty with credible intervals. This is achieved by projecting delay embeddings into a higher-dimensional space via random features and applying regularization within the Bayesian framework to identify relevant terms. Our results demonstrate that the rfBLT method is comparable to traditional statistical models on simulated data, while significantly outperforming both conventional and machine learning models when evaluated on real-world data. The proposed algorithm is implemented in an R package, rfBLT.

We need to collect data in any science and reliability is a fundamental problem for measurement in all of science. Reliability means calculation the variance ratio. Reliability was defined as the fraction of an observed score variance that was not error. here are a lot of methods to estimated reliability. All of these indicators of dependability and stability are in contradiction to the long held belief that a problem with test-retest reliability is that it introduces memory effects of learning and practice. As a result, Kuder and Richardson developed a method named KR20 before advances in computational speed made it trivial to find the factor structure of tests, and were based upon test and item variances. These procedures were essentially short cuts for estimating reliability. Exploratory factor analysis is also a Traditional method to calculate the reliability. It focus on only one variable in the liner model, a statistical method that can be used to collect an important type of validity evidence. but in reality, we need to focus on many more variables. So we will introduce a novel method following.

Machine learning and data processing techniques relying on covariance information are widespread as they identify meaningful patterns in unsupervised and unlabeled settings. As a prominent example, Principal Component Analysis (PCA) projects data points onto the eigenvectors of their covariance matrix, capturing the directions of maximum variance. This mapping, however, falls short in two directions: it fails to capture information in low-variance directions, relevant when, e.g., the data contains high-variance noise; and it provides unstable results in low-sample regimes, especially when covariance eigenvalues are close. CoVariance Neural Networks (VNNs), i.e., graph neural networks using the covariance matrix as a graph, show improved stability to estimation errors and learn more expressive functions in the covariance spectrum than PCA, but require training and operate in a labeled setup. To get the benefits of both worlds, we propose Covariance Scattering Transforms (CSTs), deep untrained networks that sequentially apply filters localized in the covariance spectrum to the input data and produce expressive hierarchical representations via nonlinearities. We define the filters as covariance wavelets that capture specific and detailed covariance spectral patterns. We improve CSTs' computational and memory efficiency via a pruning mechanism, and we prove that their error due to finite-sample covariance estimations is less sensitive to close covariance eigenvalues compared to PCA, improving their stability. Our experiments on age prediction from cortical thickness measurements on 4 datasets collecting patients with neurodegenerative diseases show that CSTs produce stable representations in low-data settings, as VNNs but without any training, and lead to comparable or better predictions w.r.t. more complex learning models.

We develop Gaussian approximations for high-dimensional vectors formed by second-order $U$-and $V$-statistics whose kernels depend on sample size. To accommodate weighted and two-sample $U$-and $V$-statistics within a unified framework, we establish our results under independent but not identically distributed (i.n.i.d.) sampling. The resulting theorems apply to a broad range of problems, including estimation in linear regression models with many covariates or many-weak instruments, variance component analysis, smoothed two-sample testing, and inference for separately exchangeable arrays, among others. Our results do not require either component of the Hoeffding decomposition to dominate, thereby covering both non-degenerate and degenerate regimes. In addition, we develop maximal inequalities for high-dimensional $U$-statistics with size-dependent kernels under the i.n.i.d.~setting, in a form that remains sharp across a broad range of applications, which may be of independent interest. Finally, applications to estimation and testing with many weak instrumental variables demonstrate that, our results are sharp enough to recover the corresponding fixed-dimensional rate conditions up to logarithmic factors.

Various complex water management decisions are made in snow-dominant watersheds with the knowledge of Snow-Water Equivalent (SWE) – a key measure widely used to estimate the water content of a snowpack. However, forecasting SWE is challenging because SWE is influenced by various factors including topography and an array of environmental conditions, and has therefore been observed to be spatio-temporally variable. Classical approaches to SWE forecasting have not adequately utilized these spatial/temporal correlations, nor do they provide uncertainty estimates – which can be of significant value to the decision maker. In this paper, we present ForeSWE, a new probabilistic spatio-temporal forecasting model that integrates deep learning and classical probabilistic techniques. The resulting model features a combination of an attention mechanism to integrate spatiotemporal features and interactions, alongside a Gaussian process module that provides principled quantification of prediction uncertainty. We evaluate the model on data from 512 Snow Telemetry (SNOTEL) stations in the Western US. The results show significant improvements in both forecasting accuracy and prediction interval compared to existing approaches. The results also serve to highlight the efficacy in uncertainty estimates between different approaches. Collectively, these findings have provided a platform for deployment and feedback by the water management community.

Detecting chemical modifications on RNA molecules remains a key challenge in epitranscriptomics. Traditional reverse transcription-based sequencing methods introduce enzyme- and sequence-dependent biases and fragment RNA molecules, confounding the accurate mapping of modifications across the transcriptome. Nanopore direct RNA sequencing offers a powerful alternative by preserving native RNA molecules, enabling the detection of modifications at single-molecule resolution. However, current computational tools can identify only a limited subset of modification types within well-characterized sequence contexts for which ample training data exists. Here, we introduce a model-free computational method that reframes modification detection as an anomaly detection problem, requiring only canonical (unmodified) RNA reads without any other annotated data. For each nanopore read, our approach extracts robust, modification-sensitive features from the raw ionic current signal at a site using the signature transform, then computes an anomaly score by comparing the resulting feature vector to its nearest neighbors in an unmodified reference dataset. We convert anomaly scores into statistical p-values to enable anomaly detection at both individual read and site levels. Validation on densely-modified E. coli rRNA demonstrates that our approach detects known sites harboring diverse modification types, without prior training on these modifications. We further applyied this framework to dengue virus (DENV) transcripts and mammalian mRNAs. For DENV sfRNA, it led to revealing a novel 2'-O-methylated site, which we validate orthogonally by qRT-PCR assays. These results demonstrate that our model-free approach operates robustly across different types of RNAs and datasets generated with different nanopore sequencing chemistries.

Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the topological descriptors - the Euler characteristic (EC) and persistent homology (PH). In particular, we establish a complete characterization of the expressive power of EC on general color-based filtrations. We also show that the PH descriptors of (virtual) graph products contain strictly more information than the computation on individual graphs, whereas EC does not. Additionally, we provide algorithms to compute the PH diagrams of the product of vertex- and edge-level filtrations on the graph product. We also substantiate our theoretical analysis with empirical investigations on runtime analysis, expressivity, and graph classification performance. Overall, this work paves way for powerful graph persistent descriptors via product filtrations. Code is available at https://github.com/Aalto-QuML/tda_graph_product.

Bayesian neural networks (BNNs) require scalable sampling algorithms to approximate posterior distributions over parameters. Existing stochastic gradient Markov Chain Monte Carlo (SGMCMC) methods are highly sensitive to the choice of stepsize and adaptive variants such as pSGLD typically fail to sample the correct invariant measure without addition of a costly divergence correction term. In this work, we build on the recently proposed `SamAdams' framework for timestep adaptation (Leimkuhler, Lohmann, and Whalley 2025), introducing an adaptive scheme: SA-SGLD, which employs time rescaling to modulate the stepsize according to a monitored quantity (typically the local gradient norm). SA-SGLD can automatically shrink stepsizes in regions of high curvature and expand them in flatter regions, improving both stability and mixing without introducing bias. We show that our method can achieve more accurate posterior sampling than SGLD on high-curvature 2D toy examples and in image classification with BNNs using sharp priors.

We investigate how government-orchestrated assaults on the judiciary, disguised as modernization efforts, undermine judicial independence. Our study focuses on Venezuela's constitutional overhaul in the early 2000s, initiated by Hugo Chávez and implemented through a judicial emergency committee. We employ a hybrid synthetic control and difference-in-differences approach to estimate the impact of populist attacks on judicial independence trajectories. By comparing Venezuela to a stable pool of countries without radical constitutional changes, our identification strategy isolates the effect of populist assaults from unobservable confounders and common time trends. Our findings reveal that authoritarian interventions lead to an immediate and lasting breakdown of judicial independence. The deterioration in judicial independence vis-á-vis the estimated counterfactual is robust to variations in the donor pool composition. It does not appear to be driven by pre-existing judicial changes and withstands numerous temporal and spatial placebo checks across over nine million randomly sequenced donor samples.

Real-time energy forecasting on edge devices represents a major challenge for smart grid optimization and intelligent buildings. We present LAD-BNet (Lag-Aware Dual-Branch Network), an innovative neural architecture optimized for edge inference with Google Coral TPU. Our hybrid approach combines a branch dedicated to explicit exploitation of temporal lags with a Temporal Convolutional Network (TCN) featuring dilated convolutions, enabling simultaneous capture of short and long-term dependencies. Tested on real energy consumption data with 10-minute temporal resolution, LAD-BNet achieves 14.49% MAPE at 1-hour horizon with only 18ms inference time on Edge TPU, representing an 8-12 x acceleration compared to CPU. The multi-scale architecture enables predictions up to 12 hours with controlled performance degradation. Our model demonstrates a 2.39% improvement over LSTM baselines and 3.04% over pure TCN architectures, while maintaining a 180MB memory footprint suitable for embedded device constraints. These results pave the way for industrial applications in real-time energy optimization, demand management, and operational planning.

Many machine learning tasks in the natural sciences are precisely equivariant to particular symmetries. Nonetheless, equivariant methods are often not employed, perhaps because training is perceived to be challenging, or the symmetry is expected to be learned, or equivariant implementations are seen as hard to build. Group averaging is an available technique for these situations. It happens at test time; it can make any trained model precisely equivariant at a (often small) cost proportional to the size of the group; it places no requirements on model structure or training. It is known that, under mild conditions, the group-averaged model will have a provably better prediction accuracy than the original model. Here we show that an inexpensive group averaging can improve accuracy in practice. We take well-established benchmark machine learning models of differential equations in which certain symmetries ought to be obeyed. At evaluation time, we average the models over a small group of symmetries. Our experiments show that this procedure always decreases the average evaluation loss, with improvements of up to 37% in terms of the VRMSE. The averaging produces visually better predictions for continuous dynamics. This short paper shows that, under certain common circumstances, there are no disadvantages to imposing exact symmetries; the ML4PS community should consider group averaging as a cheap and simple way to improve model accuracy.

This study investigates the impact of adding noise to the training set classes in classification tasks using the BCOPS algorithm (Balanced and Conformal Optimized Prediction Sets), proposed by Guan & Tibshirani (2022). The BCOPS algorithm is an application of conformal prediction combined with a machine learning method to construct prediction sets such that the probability of the true class being included in the prediction set for a test observation meets a specified coverage guarantee. An observation is considered an outlier if its true class is not present in the training set. The study employs both synthetic and real datasets and conducts experiments to evaluate the prediction abstention rate for outlier observations and the model's robustness in this previously untested scenario. The results indicate that the addition of noise, even in small amounts, can have a significant effect on model performance.

For many taxonomic groups, online biodiversity portals used by naturalists and citizen scientists constitute the primary source of distributional information. Over the last decade, site-occupancy models have been advanced as a promising framework to analyse such loosely structured, opportunistically collected datasets. Current approaches often ignore important aspects of the detection process and do not fully capitalise on the information present in these datasets, leaving opportunities for fine-grained spatiotemporal backcasting untouched. We propose a flexible Bayesian spatiotemporal site-occupancy model that aims to mimic the data-generating process that underlies common citizen science datasets sourced from public biodiversity portals, and yields rich biological output. We illustrate the use of the model to a dataset containing over 3M butterfly records in Belgium, collected through the citizen science data portal Observations.be. We show that the proposed approach enables retrospective predictions on the occupancy of species through time and space at high resolution, as well as inference on inter-annual distributional trends, range dynamics, habitat preferences, phenological patterns, detection patterns and observer heterogeneity. The proposed model can be used to increase the value of opportunistically collected data by naturalists and citizen scientists, and can aid the understanding of spatiotemporal dynamics of species for which rigorously collected data are absent or too costly to collect.

This survey paper gives an overview of various known results on learning classes of Boolean functions in Valiant's Probably Approximately Correct (PAC) learning model and its commonly studied variants.

The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a Bregman divergence, which is relevant to maximum likelihood estimation with exponential families. While the result is already known, there was not previously a clear, standalone derivation, so we provide one for pedagogical purposes. A version of this note previously appeared on the author's personal website without context. Here we provide additional discussion and references to the relevant prior literature.