This paper provides robust, new evidence on the causal drivers of market troughs. We demonstrate that conclusions about these triggers are critically sensitive to model specification, moving beyond restrictive linear models with a flexible DML average partial effect causal machine learning framework. Our robust estimates identify the volatility of options-implied risk appetite and market liquidity as key causal drivers, relationships misrepresented or obscured by simpler models. These findings provide high-frequency empirical support for intermediary asset pricing theories. This causal analysis is enabled by a high-performance nowcasting model that accurately identifies capitulation events in real-time.

Motivated by privacy regulations and the need to mitigate the effects of harmful data, machine unlearning seeks to modify trained models so that they effectively ``forget'' designated data. A key challenge in verifying unlearning is forging -- adversarially crafting data that mimics the gradient of a target point, thereby creating the appearance of unlearning without actually removing information. To capture this phenomenon, we consider the collection of data points whose gradients approximate a target gradient within tolerance $ε$ -- which we call an $ε$-forging set -- and develop a framework for its analysis. For linear regression and one-layer neural networks, we show that the Lebesgue measure of this set is small. It scales on the order of $ε$, and when $ε$ is small enough, $ε^d$. More generally, under mild regularity assumptions, we prove that the forging set measure decays as $ε^{(d-r)/2}$, where $d$ is the data dimension and $r

A/B testing is a widely adopted methodology for estimating conditional average treatment effects (CATEs) in both clinical trials and online platforms. While most existing research has focused primarily on maximizing estimation accuracy, practical applications must also account for additional objectives-most notably welfare or revenue loss. In many settings, it is critical to administer treatments that improve patient outcomes or to implement plans that generate greater revenue from customers. Within a machine learning framework, such objectives are naturally captured through the notion of cumulative regret. In this paper, we investigate the fundamental trade-off between social welfare loss and statistical accuracy in (adaptive) experiments with heterogeneous treatment effects. We establish matching upper and lower bounds for the resulting multi-objective optimization problem and employ the concept of Pareto optimality to characterize the necessary and sufficient conditions for optimal experimental designs. Beyond estimating CATEs, practitioners often aim to deploy treatment policies that maximize welfare across the entire population. We demonstrate that our Pareto-optimal adaptive design achieves optimal post-experiment welfare, irrespective of the in-experiment trade-off between accuracy and welfare. Furthermore, since clinical and commercial data are often highly sensitive, it is essential to incorporate robust privacy guarantees into any treatment-allocation mechanism. To this end, we develop differentially private algorithms that continue to achieve our established lower bounds, showing that privacy can be attained at negligible cost.

Motivated by the need for rigorous and scalable evaluation of large language models, we study contextual preference inference for pairwise comparison functionals of context-dependent preference score functions across domains. Focusing on the contextual Bradley-Terry-Luce model, we develop a semiparametric efficient estimator that automates the debiased estimation through aggregating weighted residual balancing terms across the comparison graph. We show that the efficiency is achieved when the weights are derived from a novel strategy called Fisher random walk. We also propose a computationally feasible method to compute the weights by a potential representation of nuisance weight functions. We show our inference procedure is valid for general score function estimators accommodating the practitioners' need to implement flexible deep learning methods. We extend the procedure to multiple hypothesis testing using a Gaussian multiplier bootstrap that controls familywise error and to distributional shift via a cross-fitted importance-sampling adjustment for target-domain inference. Numerical studies, including language model evaluations under diverse contexts, corroborate the accuracy, efficiency, and practical utility of our method.

We develop a new classification framework based on the theory of coherent risk measures and systemic risk. The proposed approach is suitable for multi-class problems when the data is noisy, scarce (relative to the dimension of the problem), and the labeling might be unreliable. In the first part of our paper, we provide the foundation of the use of systemic risk models and show how to apply it in the context of linear and kernel-based multi-class problems. More advanced formulation via a system-theoretic approach with non-linear aggregation is proposed, which leads to a two-stage stochastic programming problem. A risk-averse regularized decomposition method is designed to solve the problem. We use a popular multi-class method as a benchmark in the performance analysis of the proposed classification methods. We illustrate our ideas by proposing several generalization of that method by the use of coherent measures of risk. The viability of the proposed risk-averse methods are supported theoretically and numerically. Additionally, we demonstrate that the application of systemic risk measures facilitates enforcing fairness in classification. Analysis and experiments regarding the fairness of the proposed models are carefully conducted. For all methods, our numerical experiments demonstrate that they are robust in the presence of unreliable training data and perform better on unknown data than the methods minimizing expected classification errors. Furthermore, the performance improves when the number of classes increases.

Recent advances in neural density estimation have enabled powerful simulation-based inference (SBI) methods that can flexibly approximate Bayesian inference for intractable stochastic models. Although these methods have demonstrated reliable posterior estimation when the simulator accurately represents the underlying data generative process (GDP), recent work has shown that they perform poorly in the presence of model misspecification. This poses a significant problem for their use on real-world problems, due to simulators always misrepresenting the true DGP to a certain degree. In this paper, we introduce robust variational neural posterior estimation (R VNP), a method which addresses the problem of misspecification in amortised SBI by bridging the simulation-to-reality gap using variational inference and error modelling. We test R VNP on multiple benchmark tasks, including using real data from astronomy, and show that it can recover robust posterior inference in a data-driven manner without adopting tunable hyperparameters or priors governing the misspecification.

High-dimensional compositional data, such as those from human microbiome studies, pose unique statistical challenges due to the simplex constraint and excess zeros. While dimension reduction is indispensable for analyzing such data, conventional approaches often rely on log-ratio transformations that compromise interpretability and distort the data through ad hoc zero replacements. We introduce a novel framework for interpretable dimension reduction of compositional data that avoids extra transformations and zero imputations. Our approach generalizes the concept of amalgamation by softening its operation, mapping high-dimensional compositions directly to a lower-dimensional simplex, which can be visualized in ternary plots. The framework further provides joint visualization of the reduction matrix, enabling intuitive, at-a-glance interpretation. To achieve optimal reduction within our framework, we incorporate sufficient dimension reduction, which defines a new identifiable objective: the central compositional subspace. For estimation, we propose a compositional kernel dimension reduction (CKDR) method. The estimator is provably consistent, exhibits sparsity that reveals underlying amalgamation structures, and comes with an intrinsic predictive model for downstream analyses. Applications to real microbiome datasets demonstrate that our approach provides a powerful graphical exploration tool for uncovering meaningful biological patterns, opening a new pathway for analyzing high-dimensional compositional data.

Cryo-electron microscopy (Cryo-EM) enables high-resolution imaging of biomolecules, but structural heterogeneity remains a major challenge in 3D reconstruction. Traditional methods assume a discrete set of conformations, limiting their ability to recover continuous structural variability. In this work, we formulate cryo-EM reconstruction as a stochastic inverse problem (SIP) over probability measures, where the observed images are modeled as the push-forward of an unknown distribution over molecular structures via a random forward operator. We pose the reconstruction problem as the minimization of a variational discrepancy between observed and simulated image distributions, using statistical distances such as the KL divergence and the Maximum Mean Discrepancy. The resulting optimization is performed over the space of probability measures via a Wasserstein gradient flow, which we numerically solve using particles to represent and evolve conformational ensembles. We validate our approach using synthetic examples, including a realistic protein model, which demonstrates its ability to recover continuous distributions over structural states. We analyze the connection between our formulation and Maximum A Posteriori (MAP) approaches, which can be interpreted as instances of the discretize-then-optimize (DTO) framework. We further provide a consistency analysis, establishing conditions under which DTO methods, such as MAP estimation, converge to the solution of the underlying infinite-dimensional continuous problem. Beyond cryo-EM, the framework provides a general methodology for solving SIPs involving random forward operators.

--Nonnegative matrix factorization (NMF) is a known unsupervised data-reduction method. The principle of the common cause (PCC) is a basic methodological approach in probabilistic causality, which seeks an independent mixture model for the joint probability of two dependent random variables. It turns out that these two concepts are closely related. This relationship is explored reciprocally for several datasets of gray-scale images, which are conveniently mapped into probability models. On one hand, PCC provides a predictability tool that leads to a robust estimation of the effective rank of NMF . Unlike other estimates (e.g., those based on the Bayesian Information Criteria), our estimate of the rank is stable against weak noise. We show that NMF implemented around this rank produces features (basis images) that are also stable against noise and against seeds of local optimization, thereby effectively resolving the NMF nonidentifiability problem. On the other hand, NMF provides an interesting possibility of implementing PCC in an approximate way, where larger and positively correlated joint probabilities tend to be explained better via the independent mixture model. We work out a clustering method, where data points with the same common cause are grouped into the same cluster . We also show how NMF can be employed for data denoising. Nonnegative matrix factorization (NMF) was proposed and developed in data science [1]-[3].

Transformers have been successfully applied in the field of video-based 3D human pose estimation. However, the high computational costs of these video pose transformers (VPTs) make them impractical on resource-constrained devices. In this paper, we present a hierarchical plug-and-play pruning-and-recovering framework, called Hierarchical Hourglass Tokenizer (H$_{2}$OT), for efficient transformer-based 3D human pose estimation from videos. H$_{2}$OT begins with progressively pruning pose tokens of redundant frames and ends with recovering full-length sequences, resulting in a few pose tokens in the intermediate transformer blocks and thus improving the model efficiency. It works with two key modules, namely, a Token Pruning Module (TPM) and a Token Recovering Module (TRM). TPM dynamically selects a few representative tokens to eliminate the redundancy of video frames, while TRM restores the detailed spatio-temporal information based on the selected tokens, thereby expanding the network output to the original full-length temporal resolution for fast inference. Our method is general-purpose: it can be easily incorporated into common VPT models on both seq2seq and seq2frame pipelines while effectively accommodating different token pruning and recovery strategies. In addition, our H$_{2}$OT reveals that maintaining the full pose sequence is unnecessary, and a few pose tokens of representative frames can achieve both high efficiency and estimation accuracy. Extensive experiments on multiple benchmark datasets demonstrate both the effectiveness and efficiency of the proposed method. Code and models are available at https://github.com/NationalGAILab/HoT.