False discovery rate (FDR) control methods are essential for voxel-wise multiple testing in neuroimaging data analysis, where hundreds of thousands or even millions of tests are conducted to detect brain regions associated with disease-related changes. Classical FDR control methods (e.g., BH, q-value, and LocalFDR) assume independence among tests and often lead to high false non-discovery rates (FNR). Although various spatial FDR control methods have been developed to improve power, they still fall short of jointly addressing three major challenges in neuroimaging applications: capturing complex spatial dependencies, maintaining low variability in both false discovery proportion (FDP) and false non-discovery proportion (FNP) across replications, and achieving computational scalability for high-resolution data. To address these challenges, we propose fcHMRF-LIS, a powerful, stable, and scalable spatial FDR control method for voxel-wise multiple testing. It integrates the local index of significance (LIS)-based testing procedure with a novel fully connected hidden Markov random field (fcHMRF) designed to model complex spatial structures using a parsimonious parameterization. We develop an efficient expectation-maximization algorithm incorporating mean-field approximation, the Conditional Random Fields as Recurrent Neural Networks (CRF-RNN) technique, and permutohedral lattice filtering, reducing the time complexity from quadratic to linear in the number of tests. Extensive simulations demonstrate that fcHMRF-LIS achieves accurate FDR control, lower FNR, reduced variability in FDP and FNP, and a higher number of true positives compared to existing methods. Applied to an FDG-PET dataset from the Alzheimer's Disease Neuroimaging Initiative, fcHMRF-LIS identifies neurobiologically relevant brain regions and offers notable advantages in computational efficiency.
We study the problem of estimating the average treatment effect (ATE) in adaptive experiments where treatment can only be encouraged--rather than directly assigned--via a binary instrumental variable. Building on semiparametric efficiency theory, we derive the efficiency bound for ATE estimation under arbitrary, history-dependent instrument-assignment policies, and show it is minimized by a variance-aware allocation rule that balances outcome noise and compliance variability. Leveraging this insight, we introduce AMRIV--an \textbf{A}daptive, \textbf{M}ultiply-\textbf{R}obust estimator for \textbf{I}nstrumental-\textbf{V}ariable settings with variance-optimal assignment. AMRIV pairs (i) an online policy that adaptively approximates the optimal allocation with (ii) a sequential, influence-function-based estimator that attains the semiparametric efficiency bound while retaining multiply-robust consistency. We establish asymptotic normality, explicit convergence rates, and anytime-valid asymptotic confidence sequences that enable sequential inference. Finally, we demonstrate the practical effectiveness of our approach through empirical studies, showing that adaptive instrument assignment, when combined with the AMRIV estimator, yields improved efficiency and robustness compared to existing baselines.
An important task in machine learning (ML) research is comparing prior work, which is often performed via ML leaderboards: a tabular overview of experiments with comparable conditions (e.g., same task, dataset, and metric). However, the growing volume of literature creates challenges in creating and maintaining these leaderboards. To ease this burden, researchers have developed methods to extract leaderboard entries from research papers for automated leaderboard curation. Yet, prior work varies in problem framing, complicating comparisons and limiting real-world applicability. In this position paper, we present the first overview of Automatic Leaderboard Generation (ALG) research, identifying fundamental differences in assumptions, scope, and output formats. We propose an ALG unified conceptual framework to standardise how the ALG task is defined. We offer ALG benchmarking guidelines, including recommendations for datasets and metrics that promote fair, reproducible evaluation. Lastly, we outline challenges and new directions for ALG, such as, advocating for broader coverage by including all reported results and richer metadata.
Construction of confidence intervals and hypothesis tests for functionals based on asymptotically normal estimators is a classical topic in statistical inference. The simplest and in many cases optimal inference procedure is the Wald interval or the likelihood ratio test, both of which require an estimator and an estimate of the asymptotic variance of the estimator. Estimators obtained from online/sequential algorithms forces one to consider the computational aspects of the inference problem, i.e., one cannot access all of the data as many times as needed. Several works on this topic explored the online estimation of asymptotic variance. In this article, we propose computationally efficient, rate-optimal, and asymptotically valid confidence regions based on the output of online algorithms {\em without} estimating the asymptotic variance. As a special case, this implies inference from any algorithm that yields an asymptotically normal estimator. We focus our efforts on stochastic gradient descent with Polyak averaging to understand the practical performance of the proposed method.
Many modern learning tasks require models that can take inputs of varying sizes. Consequently, dimension-independent architectures have been proposed for domains where the inputs are graphs, sets, and point clouds. Recent work on graph neural networks has explored whether a model trained on low-dimensional data can transfer its performance to higher-dimensional inputs. We extend this body of work by introducing a general framework for transferability across dimensions. We show that transferability corresponds precisely to continuity in a limit space formed by identifying small problem instances with equivalent large ones. This identification is driven by the data and the learning task. We instantiate our framework on existing architectures, and implement the necessary changes to ensure their transferability. Finally, we provide design principles for designing new transferable models. Numerical experiments support our findings.
We introduce a fast and flexible Machine Learning (ML) framework for pricing derivative products whose valuation depends on volatility surfaces. By parameterizing volatility surfaces with the 5-parameter stochastic volatility inspired (SVI) model augmented by a one-factor term structure adjustment, we first generate numerous volatility surfaces over realistic ranges for these parameters. From these synthetic market scenarios, we then compute high-accuracy valuations using conventional methodologies for two representative products: the fair strike of a variance swap and the price and Greeks of an American put. We then train the Gaussian Process Regressor (GPR) to learn the nonlinear mapping from the input risk factors, which are the volatility surface parameters, strike and interest rate, to the valuation outputs. Once trained, We use the GPR to perform out-of-sample valuations and compare the results against valuations using conventional methodologies. Our ML model achieves very accurate results of $0.5\%$ relative error for the fair strike of variance swap and $1.7\% \sim 3.5\%$ relative error for American put prices and first-order Greeks. More importantly, after training, the model computes valuations almost instantly, yielding a three to four orders of magnitude speedup over Crank-Nicolson finite-difference method for American puts, enabling real-time risk analytics, dynamic hedging and large-scale scenario analysis. Our approach is general and can be extended to other path-dependent derivative products with early-exercise features, paving the way for hybrid quantitative engines for modern financial systems.
Existing PLMs generate protein sequences based on a single-condition constraint from a specific modality, struggling to simultaneously satisfy multiple constraints across different modalities. In this work, we introduce CFP-Gen, a novel diffusion language model for Combinatorial Functional Protein GENeration. CFP-Gen facilitates the de novo protein design by integrating multimodal conditions with functional, sequence, and structural constraints. Specifically, an Annotation-Guided Feature Modulation (AGFM) module is introduced to dynamically adjust the protein feature distribution based on composable functional annotations, e.g., GO terms, IPR domains and EC numbers. Meanwhile, the Residue-Controlled Functional Encoding (RCFE) module captures residue-wise interaction to ensure more precise control. Additionally, off-the-shelf 3D structure encoders can be seamlessly integrated to impose geometric constraints. We demonstrate that CFP-Gen enables high-throughput generation of novel proteins with functionality comparable to natural proteins, while achieving a high success rate in designing multifunctional proteins. Code and data available at https://github.com/yinjunbo/cfpgen.
Understanding how protein mutations affect protein-nucleic acid binding is critical for unraveling disease mechanisms and advancing therapies. Current experimental approaches are laborious, and computational methods remain limited in accuracy. To address this challenge, we propose a novel topological machine learning model (TopoML) combining persistent Laplacian (from topological data analysis) with multi-perspective features: physicochemical properties, topological structures, and protein Transformer-derived sequence embeddings. This integrative framework captures robust representations of protein-nucleic acid binding interactions. To validate the proposed method, we employ two datasets, a protein-DNA dataset with 596 single-point amino acid mutations, and a protein-RNA dataset with 710 single-point amino acid mutations. We show that the proposed TopoML model outperforms state-of-the-art methods in predicting mutation-induced binding affinity changes for protein-DNA and protein-RNA complexes.
Attractor dynamics are a hallmark of many complex systems, including the brain. Understanding how such self-organizing dynamics emerge from first principles is crucial for advancing our understanding of neuronal computations and the design of artificial intelligence systems. Here we formalize how attractor networks emerge from the free energy principle applied to a universal partitioning of random dynamical systems. Our approach obviates the need for explicitly imposed learning and inference rules and identifies emergent, but efficient and biologically plausible inference and learning dynamics for such self-organizing systems. These result in a collective, multi-level Bayesian active inference process. Attractors on the free energy landscape encode prior beliefs; inference integrates sensory data into posterior beliefs; and learning fine-tunes couplings to minimize long-term surprise. Analytically and via simulations, we establish that the proposed networks favor approximately orthogonalized attractor representations, a consequence of simultaneously optimizing predictive accuracy and model complexity. These attractors efficiently span the input subspace, enhancing generalization and the mutual information between hidden causes and observable effects. Furthermore, while random data presentation leads to symmetric and sparse couplings, sequential data fosters asymmetric couplings and non-equilibrium steady-state dynamics, offering a natural extension to conventional Boltzmann Machines. Our findings offer a unifying theory of self-organizing attractor networks, providing novel insights for AI and neuroscience.
Predicting protein complex structures is essential for protein function analysis, protein design, and drug discovery. While AI methods like AlphaFold can predict accurate structural models for many protein complexes, reliably estimating the quality of these predicted models (estimation of model accuracy, or EMA) for model ranking and selection remains a major challenge. A key barrier to developing effective machine learning-based EMA methods is the lack of large, diverse, and well-annotated datasets for training and evaluation. To address this gap, we introduce PSBench, a benchmark suite comprising four large-scale, labeled datasets generated during the 15th and 16th community-wide Critical Assessment of Protein Structure Prediction (CASP15 and CASP16). PSBench includes over one million structural models covering a wide range of protein sequence lengths, complex stoichiometries, functional classes, and modeling difficulties. Each model is annotated with multiple complementary quality scores at the global, local, and interface levels. PSBench also provides multiple evaluation metrics and baseline EMA methods to facilitate rigorous comparisons. To demonstrate PSBench's utility, we trained and evaluated GATE, a graph transformer-based EMA method, on the CASP15 data. GATE was blindly tested in CASP16 (2024), where it ranked among the top-performing EMA methods. These results highlight PSBench as a valuable resource for advancing EMA research in protein complex modeling. PSBench is publicly available at: https://github.com/BioinfoMachineLearning/PSBench.
Bounded continuous responses -- such as proportions -- arise frequently in diverse scientific fields including climatology, biostatistics, and finance. Beta regression is a widely adopted framework for modeling such data, due to the flexibility of the Beta distribution over the unit interval. While Bayesian extensions of Beta regression have shown promise, existing methods are limited to low-dimensional settings and lack theoretical guarantees. In this work, we propose a novel Bayesian approach for high-dimensional sparse Beta regression framework that employs a tempered posterior. Our method incorporates the Horseshoe prior for effective shrinkage and variable selection. Most notable, we propose a novel Gibbs sampling algorithm using P\'olya-Gamma augmentation for efficient inference in Beta regression model. We also provide the first theoretical results establishing posterior consistency and convergence rates for Bayesian Beta regression. Through extensive simulation studies in both low- and high-dimensional scenarios, we demonstrate that our approach outperforms existing alternatives, offering improved estimation accuracy and model interpretability. Our method is implemented in the R package ``betaregbayes" available on Github.
The rapid development of sophisticated machine learning methods, together with the increased availability of financial data, has the potential to transform financial research, but also poses a challenge in terms of validation and interpretation. A good case study is the task of classifying financial investors based on their behavioral patterns. Not only do we have access to both classification and clustering tools for high-dimensional data, but also data identifying individual investors is finally available. The problem, however, is that we do not have access to ground truth when working with real-world data. This, together with often limited interpretability of modern machine learning methods, makes it difficult to fully utilize the available research potential. In order to deal with this challenge we propose to use a realistic agent-based model as a way to generate synthetic data. This way one has access to ground truth, large replicable data, and limitless research scenarios. Using this approach we show how, even when classifying trading agents in a supervised manner is relatively easy, a more realistic task of unsupervised clustering may give incorrect or even misleading results. We complete the results with investigating the details of how supervised techniques were able to successfully distinguish between different trading behaviors.
Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as of an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in high dimensions, kernelised Stein discrepancy (KSD) tests are a powerful tool. Here, we develop, test, and analyse a KSD-type goodness-of-fit test for IRG models that can be carried out with a single observation of the network. The test is applicable to a network of any size and does not depend on the asymptotic distribution of the test statistic. We also provide theoretical guarantees.
Hematotoxicity, drug-induced damage to the blood-forming system, is a frequent side effect of cytotoxic chemotherapy and poses a significant challenge in clinical practice due to its high inter-patient variability and limited predictability. Current mechanistic models often struggle to accurately forecast outcomes for patients with irregular or atypical trajectories. In this study, we develop and compare hybrid mechanistic and data-driven approaches for individualized time series modeling of platelet counts during chemotherapy. We consider hybrid models that combine mechanistic models with neural networks, known as universal differential equations. As a purely data-driven alternative, we utilize a nonlinear autoregressive exogenous model using gated recurrent units as the underlying architecture. These models are evaluated across a range of real patient scenarios, varying in data availability and sparsity, to assess predictive performance. Our findings demonstrate that data-driven methods, when provided with sufficient data, significantly improve prediction accuracy, particularly for high-risk patients with irregular platelet dynamics. This highlights the potential of data-driven approaches in enhancing clinical decision-making. In contrast, hybrid and mechanistic models are superior in scenarios with limited or sparse data. The proposed modeling and comparison framework is generalizable and could be extended to predict other treatment-related toxicities, offering broad applicability in personalized medicine.
In our original paper (Delavaux et al. 2024; https://www.nature.com/articles/s41586-024-07110-y), we find that the latitudinal diversity gradient (LDG) in plant species richness is reduced on oceanic islands worldwide. Moreover, we find that plants that associate with mutualists, including pollinators, AM fungi, and N-fixing bacteria, disproportionately contribute to this reduction. To make this assertion, we fit models of continental diversity to absolute latitude and compared mainland diversity estimated by these models to the observed diversity of individual islands. The critique of our work by Pitcher and Hartig (arXiv:2411.15105) questions our results through a reanalysis of the data. In their reanalysis, they add longitude as a predictor of richness on islands. However, we have several concerns about this reanalysis. In particular, we question (1) the biological/physical basis of predicting species richness with longitude as well as modelling non-linear relationships potentially leading to spurious relationships and (2) the justification for how this comment calculated island deficits from the data. Additionally, (3) described analyses and provided code (https://github.com/MaximilianPi/IslandLDG) are in many cases insufficient to understand or meaningfully engage with this work, precluding productive discussion about cited analytical concerns. Given these major issues with the reanalysis, we reject the conclusions from this critique that our prior results are due to statistical artifacts. We therefore do not have reason to question our original conclusion that the latitudinal diversity gradient is weakened by mutualisms among oceanic islands worldwide.
The diverse nature of protein prediction tasks has traditionally necessitated specialized models, hindering the development of broadly applicable and computationally efficient Protein Language Models (PLMs). In this work, we introduce Prot2Token, a unified framework that overcomes these challenges by converting a wide spectrum of protein-related predictions, from sequence-level properties and residue-specific attributes to complex inter-protein interactions, into a standardized next-token prediction format. At its core, Prot2Token employs an autoregressive decoder, conditioned on embeddings from pre-trained protein encoders and guided by learnable task tokens, to perform diverse predictions. This architecture uniquely facilitates multi-task learning, enabling a single model to master numerous tasks with improved efficiency. We present extensive experimental validation across a variety of benchmarks, demonstrating Prot2Tokens strong predictive power in different types of protein-prediction tasks. Key results include significant speedups (e.g., near 1000x over AlphaFold2 with MSA) and performance often matching or exceeding specialized approaches. Beyond that, we introduce an auxiliary self-supervised decoder pre-training approach to improve spatially sensitive task performance. Prot2Token thus offers a significant step towards a versatile, high-throughput paradigm for protein modeling, promising to accelerate biological discovery and the development of novel therapeutics. The code is available at https://github.com/mahdip72/prot2token .
Designing regulatory DNA sequences that achieve precise cell-type-specific gene expression is crucial for advancements in synthetic biology, gene therapy and precision medicine. Although transformer-based language models (LMs) can effectively capture patterns in regulatory DNA, their generative approaches often struggle to produce novel sequences with reliable cell-specific activity. Here, we introduce Ctrl-DNA, a novel constrained reinforcement learning (RL) framework tailored for designing regulatory DNA sequences with controllable cell-type specificity. By formulating regulatory sequence design as a biologically informed constrained optimization problem, we apply RL to autoregressive genomic LMs, enabling the models to iteratively refine sequences that maximize regulatory activity in targeted cell types while constraining off-target effects. Our evaluation on human promoters and enhancers demonstrates that Ctrl-DNA consistently outperforms existing generative and RL-based approaches, generating high-fitness regulatory sequences and achieving state-of-the-art cell-type specificity. Moreover, Ctrl-DNA-generated sequences capture key cell-type-specific transcription factor binding sites (TFBS), short DNA motifs recognized by regulatory proteins that control gene expression, demonstrating the biological plausibility of the generated sequences.
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings to represent distributions as mean functions in RKHS. However, it remains unclear if the mean function is the only meaningful RKHS representation. Inspired by generalised quantiles, we introduce the notion of kernel quantile embeddings (KQEs). We then use KQEs to construct a family of distances that: (i) are probability metrics under weaker kernel conditions than MMD; (ii) recover a kernelised form of the sliced Wasserstein distance; and (iii) can be efficiently estimated with near-linear cost. Through hypothesis testing, we show that these distances offer a competitive alternative to MMD and its fast approximations.
A pivotal area of research in antibody engineering is to find effective modifications that enhance antibody-antigen binding affinity. Traditional wet-lab experiments assess mutants in a costly and time-consuming manner. Emerging deep learning solutions offer an alternative by modeling antibody structures to predict binding affinity changes. However, they heavily depend on high-quality complex structures, which are frequently unavailable in practice. Therefore, we propose ProtAttBA, a deep learning model that predicts binding affinity changes based solely on the sequence information of antibody-antigen complexes. ProtAttBA employs a pre-training phase to learn protein sequence patterns, following a supervised training phase using labeled antibody-antigen complex data to train a cross-attention-based regressor for predicting binding affinity changes. We evaluated ProtAttBA on three open benchmarks under different conditions. Compared to both sequence- and structure-based prediction methods, our approach achieves competitive performance, demonstrating notable robustness, especially with uncertain complex structures. Notably, our method possesses interpretability from the attention mechanism. We show that the learned attention scores can identify critical residues with impacts on binding affinity. This work introduces a rapid and cost-effective computational tool for antibody engineering, with the potential to accelerate the development of novel therapeutic antibodies.
We present a variation of the well-known binomial model of asset prices. This variation incorporates a bound to short-selling, inspired by a model from Gunduz Caginalp[2]. We formalize this model and prove a formula for all the moments of the logarithmic returns. We also derive a formula for the case with infinitely many investors. As an application of the model, we show how to compute parameters in order to approximate given moments, enabling the modeling of skewness and excess kurtosis. Finally, we generalize the model and give the corresponding formula for the moments of the logarithmic returns, and the algorithm for fitting given moments.