Decision trees are powerful machine learning algorithms, widely used in fields such as economics and medicine for their simplicity and interpretability. However, decision trees such as CART are prone to overfitting, especially when grown deep or the sample size is small. Conventional methods to reduce overfitting include pre-pruning and post-pruning, which constrain the growth of uninformative branches. In this paper, we propose a complementary approach by introducing a covariance-driven splitting criterion for regression trees (CovRT). This method is more robust to overfitting than the empirical risk minimization criterion used in CART, as it produces more balanced and stable splits and more effectively identifies covariates with true signals. We establish an oracle inequality of CovRT and prove that its predictive accuracy is comparable to that of CART in high-dimensional settings. We find that CovRT achieves superior prediction accuracy compared to CART in both simulations and real-world tasks.

Bayesian Optimization with multi-objective acquisition functions such as q-Expected Hypervolume Improvement (qEHVI) requires efficient candidate optimization to maximize acquisition function values. Traditional approaches rely on continuous optimization methods like Sequential Least Squares Programming (SLSQP) for candidate selection. However, these gradient-based methods can become trapped in local optima, particularly in complex or high-dimensional objective landscapes. This paper presents a simulated annealing-based approach for candidate optimization in batch acquisition functions as an alternative to conventional continuous optimization methods. We evaluate our simulated annealing approach against SLSQP across four benchmark multi-objective optimization problems: ZDT1 (30D, 2 objectives), DTLZ2 (7D, 3 objectives), Kursawe (3D, 2 objectives), and Latent-Aware (4D, 2 objectives). Our results demonstrate that simulated annealing consistently achieves superior hypervolume performance compared to SLSQP in most test functions. The improvement is particularly pronounced for DTLZ2 and Latent-Aware problems, where simulated annealing reaches significantly higher hypervolume values and maintains better convergence characteristics. The histogram analysis of objective space coverage further reveals that simulated annealing explores more diverse and optimal regions of the Pareto front. These findings suggest that metaheuristic optimization approaches like simulated annealing can provide more robust and effective candidate optimization for multi-objective Bayesian optimization, offering a promising alternative to traditional gradient-based methods for batch acquisition function optimization.

Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose \texttt{FairSinkhorn}, a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, we then develop two relaxation strategies. The first one involves solving a penalised OT problem, for which we derive novel finite-sample complexity guarantees. This result is of independent interest as it can be generalized to arbitrary convex penalties. Our second strategy leverages bilevel optimization to learn a ground cost that induces a fair OT solution, and we establish a bound guaranteeing that the learned cost yields fair matchings on unseen data. Finally, we present empirical results that illustrate the trade-offs between fairness and performance.

Parameter estimation under quantization is a fundamental problem at the intersection of statistics [12], signal processing [14], and machine learning [4]. Quantization is of fundamental importance in these fields, mainly due to its role in reducing memory and storage costs. In distributed learning, quantization plays a key role to reduce the cost of communication between data servers, where the central server has to estimate a parameter from the quantized data sent by the data servers. As pointed out in [17], quantization also contributes to the recent paradigm of data privacy, since the quantized sample preserves sensitive information: the estimator only have access to bits, which reduces the chance to leak sensitive information. In this work, we consider what is arguably the most fundamental parameter estimation task: the estimation of the mean of a random vector X from n i.i.d.

Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows arbitrary non-Gaussian, and potentially multi-modal distributions. This study reviews recent approaches to state estimation via nonlinear filtering based on conditional normalizing flows, where the conditional embedding is generated by standard MLP architectures, transformers or selective state-space models (like Mamba-SSM). In addition, we test the effectiveness of an optimal-transport-inspired kinetic loss term in mitigating overparameterization in flows consisting of a large collection of transformations. We investigate the performance of these approaches on applications relevant to autonomous driving and patient population dynamics, paying special attention to how they handle time inversion and chained predictions. Finally, we assess the performance of various conditioning strategies for an application to real-world COVID-19 joint SIR system forecasting and parameter estimation.

Matching markets face increasing needs to learn the matching qualities between demand and supply for effective design of matching policies. In practice, the matching rewards are high-dimensional due to the growing diversity of participants. We leverage a natural low-rank matrix structure of the matching rewards in these two-sided markets, and propose to utilize matrix completion to accelerate reward learning with limited offline data. A unique property for matrix completion in this setting is that the entries of the reward matrix are observed with matching interference -- i.e., the entries are not observed independently but dependently due to matching or budget constraints. Such matching dependence renders unique technical challenges, such as sub-optimality or inapplicability of the existing analytical tools in the matrix completion literature, since they typically rely on sample independence. In this paper, we first show that standard nuclear norm regularization remains theoretically effective under matching interference. We provide a near-optimal Frobenius norm guarantee in this setting, coupled with a new analytical technique. Next, to guide certain matching decisions, we develop a novel ``double-enhanced'' estimator, based off the nuclear norm estimator, with a near-optimal entry-wise guarantee. Our double-enhancement procedure can apply to broader sampling schemes even with dependence, which may be of independent interest. Additionally, we extend our approach to online learning settings with matching constraints such as optimal matching and stable matching, and present improved regret bounds in matrix dimensions. Finally, we demonstrate the practical value of our methods using both synthetic data and real data of labor markets.

Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn disentangled and interpretable representations is critical for uncovering latent generative mechanisms. Traditional approaches to unsupervised representation learning, including variational autoencoders (VAEs), often struggle to capture the temporal and spectral diversity inherent in such data. Here we introduce variational decomposition autoencoding (VDA), a framework that extends VAEs by incorporating a strong structural bias toward signal decomposition. VDA is instantiated through variational decomposition autoencoders (DecVAEs), i.e., encoder-only neural networks that combine a signal decomposition model, a contrastive self-supervised task, and variational prior approximation to learn multiple latent subspaces aligned with time-frequency characteristics. We demonstrate the effectiveness of DecVAEs on simulated data and three publicly available scientific datasets, spanning speech recognition, dysarthria severity evaluation, and emotional speech classification. Our results demonstrate that DecVAEs surpass state-of-the-art VAE-based methods in terms of disentanglement quality, generalization across tasks, and the interpretability of latent encodings. These findings suggest that decomposition-aware architectures can serve as robust tools for extracting structured representations from dynamic signals, with potential applications in clinical diagnostics, human-computer interaction, and adaptive neurotechnologies.

Individualized treatment regimes (ITRs) aim to improve clinical outcomes by assigning treatment based on patient-specific characteristics. However, existing methods often struggle with high-dimensional covariates, limiting accuracy, interpretability, and real-world applicability. We propose a novel sufficient dimension reduction approach that directly targets the contrast between potential outcomes and identifies a low-dimensional subspace of the covariates capturing treatment effect heterogeneity. This reduced representation enables more accurate estimation of optimal ITRs through outcome-weighted learning. To accommodate observational data, our method incorporates kernel-based covariate balancing, allowing treatment assignment to depend on the full covariate set and avoiding the restrictive assumption that the subspace sufficient for modeling heterogeneous treatment effects is also sufficient for confounding adjustment. We show that the proposed method achieves universal consistency, i.e., its risk converges to the Bayes risk, under mild regularity conditions. We demonstrate its finite sample performance through simulations and an analysis of intensive care unit sepsis patient data to determine who should receive transthoracic echocardiography.

A central problem in machine learning theory is to characterize how learning dynamics select particular solutions among the many compatible with the training objective, a phenomenon, called implicit bias, which remains only partially characterized. In the present work, we identify a general mechanism, in terms of an explicit geometric correction of the learning dynamics, for the emergence of implicit biases, arising from the interaction between continuous symmetries in the model's parametrization and stochasticity in the optimization process. Our viewpoint is constructive in two complementary directions: given model symmetries, one can derive the implicit bias they induce; conversely, one can inverse-design a wide class of different implicit biases by computing specific redundant parameterizations. More precisely, we show that, when the dynamics is expressed in the quotient space obtained by factoring out the symmetry group of the parameterization, the resulting stochastic differential equation gains a closed form geometric correction in the stationary distribution of the optimizer dynamics favoring orbits with small local volume. We compute the resulting symmetry induced bias for a range of architectures, showing how several well known results fit into a single unified framework. The approach also provides a practical methodology for deriving implicit biases in new settings, and it yields concrete, testable predictions that we confirm by numerical simulations on toy models trained on synthetic data, leaving more complex scenarios for future work. Finally, we test the implicit bias inverse-design procedure in notable cases, including biases toward sparsity in linear features or in spectral properties of the model parameters.

Large language models (LLMs) such as GPT, Claude, Gemini, and Grok have been deeply integrated into our daily life. They now support a wide range of tasks -- from dialogue and email drafting to assisting with teaching and coding, serving as search engines, and much more. However, their ability to produce highly human-like text raises serious concerns, including the spread of fake news, the generation of misleading governmental reports, and academic misconduct. To address this practical problem, we train a classifier to determine whether a piece of text is authored by an LLM or a human. Our detector is deployed on an online CPU-based platform https://huggingface.co/spaces/stats-powered-ai/StatDetectLLM, and contains three novelties over existing detectors: (i) it does not rely on auxiliary information, such as watermarks or knowledge of the specific LLM used to generate the text; (ii) it more effectively distinguishes between human- and LLM-authored text; and (iii) it enables statistical inference, which is largely absent in the current literature. Empirically, our classifier achieves higher classification accuracy compared to existing detectors, while maintaining type-I error control, high statistical power, and computational efficiency.