Most existing literature on supervised machine learning assumes that the training dataset is drawn from an i.i.d. sample. However, many real-world problems exhibit temporal dependence and strong correlations between the marginal distributions of the data-generating process, suggesting that the i.i.d. assumption is often unrealistic. In such cases, models naturally include time-series processes with mixing properties, as well as irreducible and aperiodic ergodic Markov chains. Moreover, the learning rates typically obtained in these settings are independent of the data distribution, which can lead to restrictive choices of hypothesis classes and suboptimal sample complexities for the learning algorithm. In this article, we consider the case where the training dataset is generated by an iterated random function (i.e., an iteratively defined time-homogeneous Markov chain) that is not necessarily irreducible or aperiodic. Under the assumption that the governing function is contractive with respect to its first argument and subject to certain regularity conditions on the hypothesis class, we first establish a uniform convergence result for the corresponding sample error. We then demonstrate the learnability of the approximate empirical risk minimization algorithm and derive its learning rate bound. Both rates are data-distribution dependent, expressed in terms of the Rademacher complexities of the underlying hypothesis class, allowing them to more accurately reflect the properties of the data-generating distribution.

Cross-validation (CV) is a common method to tune machine learning methods and can be used for model selection in regression as well. Because of the structured nature of small, traditional experimental designs, the literature has warned against using CV in their analysis. The striking increase in the use of machine learning, and thus CV, in the analysis of experimental designs, has led us to empirically study the effectiveness of CV compared to other methods of selecting models in designed experiments, including the little bootstrap. We consider both response surface settings where prediction is of primary interest, as well as screening where factor selection is most important. Overall, we provide evidence that the use of leave-one-out cross-validation (LOOCV) in the analysis of small, structured is often useful. More general $k$-fold CV may also be competitive but its performance is uneven.

Gallstone disease is a complex, multifactorial condition with significant global health burdens. Identifying underlying risk factors and their interactions is crucial for early diagnosis, targeted prevention, and effective clinical management. Although logistic regression remains a standard tool for assessing associations between predictors and gallstone status, it often underperforms in high-dimensional settings and may fail to capture intricate relationships among variables. To address these limitations, we propose a hybrid machine learning framework that integrates robust variable selection with advanced interaction detection. Specifically, Adaptive LASSO is employed to identify a sparse and interpretable subset of influential features, followed by Bayesian Additive Regression Trees (BART) to model nonlinear effects and uncover key interactions. Selected interactions are further characterized by physiological knowledge through differential equation-informed interaction terms, grounding the model in biologically plausible mechanisms. The insights gained from these steps are then integrated into a final logistic regression model within a Bayesian framework, providing a balance between predictive accuracy and clinical interpretability. This proposed framework not only enhances prediction but also yields actionable insights, offering a valuable support tool for medical research and decision-making.

There is growing interest in extending average treatment effect (ATE) estimation to incorporate non-tabular data, such as images and text, which may act as sources of confounding. Neglecting these effects risks biased results and flawed scientific conclusions. However, incorporating non-tabular data necessitates sophisticated feature extractors, often in combination with ideas of transfer learning. In this work, we investigate how latent features from pre-trained neural networks can be leveraged to adjust for sources of confounding. We formalize conditions under which these latent features enable valid adjustment and statistical inference in ATE estimation, demonstrating results along the example of double machine learning. We discuss critical challenges inherent to latent feature learning and downstream parameter estimation arising from the high dimensionality and non-identifiability of representations. Common structural assumptions for obtaining fast convergence rates with additive or sparse linear models are shown to be unrealistic for latent features. We argue, however, that neural networks are largely insensitive to these issues. In particular, we show that neural networks can achieve fast convergence rates by adapting to intrinsic notions of sparsity and dimension of the learning problem.

In this paper, we develop a wide class Mirror Descent (MD) algorithms, which play a key role in machine learning. For this purpose we formulated the constrained optimization problem, in which we exploits the Bregman divergence with the Tempesta multi-parametric deformation logarithm as a link function. This link function called also mirror function defines the mapping between the primal and dual spaces and is associated with a very-wide (in fact, theoretically infinite) class of generalized trace-form entropies. In order to derive novel MD updates, we estimate generalized exponential function, which closely approximates the inverse of the multi-parametric Tempesta generalized logarithm. The shape and properties of the Tempesta logarithm and its inverse-deformed exponential functions can be tuned by several hyperparameters. By learning these hyperparameters, we can adapt to distribution or geometry of training data, and we can adjust them to achieve desired properties of MD algorithms. The concept of applying multi-parametric logarithms allow us to generate a new wide and flexible family of MD and mirror-less MD updates.

We address the regression problem under the constraint of demographic parity, a commonly used fairness definition. Recent studies have revealed fair minimax optimal regression algorithms, the most accurate algorithms that adhere to the fairness constraint. However, these analyses are tightly coupled with specific data generation models. In this paper, we provide meta-theorems that can be applied to various situations to validate the fair minimax optimality of the corresponding regression algorithms. Furthermore, we demonstrate that fair minimax optimal regression can be achieved through post-processing methods, allowing researchers and practitioners to focus on improving conventional regression techniques, which can then be efficiently adapted for fair regression.

Anomaly detection (AD) is a critical task across domains such as cybersecurity and healthcare. In the unsupervised setting, an effective and theoretically-grounded principle is to train classifiers to distinguish normal data from (synthetic) anomalies. We extend this principle to semi-supervised AD, where training data also include a limited labeled subset of anomalies possibly present in test time. We propose a theoretically-grounded and empirically effective framework for semi-supervised AD that combines known and synthetic anomalies during training. To analyze semi-supervised AD, we introduce the first mathematical formulation of semi-supervised AD, which generalizes unsupervised AD. Here, we show that synthetic anomalies enable (i) better anomaly modeling in low-density regions and (ii) optimal convergence guarantees for neural network classifiers -- the first theoretical result for semi-supervised AD. We empirically validate our framework on five diverse benchmarks, observing consistent performance gains. These improvements also extend beyond our theoretical framework to other classification-based AD methods, validating the generalizability of the synthetic anomaly principle in AD.

Causal effect estimation seeks to determine the impact of an intervention from observational data. However, the existing causal inference literature primarily addresses treatment effects on frequently occurring events. But what if we are interested in estimating the effects of a policy intervention whose benefits, while potentially important, can only be observed and measured in rare yet impactful events, such as extreme climate events? The standard causal inference methodology is not designed for this type of inference since the events of interest may be scarce in the observed data and some degree of extrapolation is necessary. Extreme Value Theory (EVT) provides methodologies for analyzing statistical phenomena in such extreme regimes. We introduce a novel framework for assessing treatment effects in extreme data to capture the causal effect at the occurrence of rare events of interest. In particular, we employ the theory of multivariate regular variation to model extremities. We develop a consistent estimator for extreme treatment effects and present a rigorous non-asymptotic analysis of its performance. We illustrate the performance of our estimator using both synthetic and semi-synthetic data.

Adaptation is the holy grail of intelligence, but even the best AI models (like GPT) lack the adaptivity of toddlers. So the question remains: how can machines adapt quickly? Despite a lot of progress on model adaptation to facilitate continual and federated learning, as well as model merging, editing, unlearning, etc., little is known about the mechanisms by which machines can naturally learn to adapt in a similar way as humans and animals. Here, we show that all such adaptation methods can be seen as different ways of `correcting' the approximate posteriors. More accurate posteriors lead to smaller corrections, which in turn imply quicker adaptation. The result is obtained by using a dual-perspective of the Bayesian Learning Rule of Khan and Rue (2023) where interference created during adaptation is characterized by the natural-gradient mismatch over the past data. We present many examples to demonstrate the use of posterior-correction as a natural mechanism for the machines to learn to adapt quickly.

--In this paper, we propose a novel neural speaker diarization system using memory-aware multi-speaker embedding with sequence-to-sequence architecture (NSD-MS2S), which integrates a memory-aware multi-speaker embedding module with a sequence-to-sequence architecture. The system leverages a memory module to enhance speaker embeddings and employs a Seq2Seq framework to efficiently map acoustic features to speaker labels. Additionally, we explore the application of mixture of experts in spkeaker diarization, and introduce a Shared and Soft Mixture of Experts (SS-MoE) module, to further mitigate model bias and enhance performance. Incorporating SS-MoE leads to the extended model NSD-MS2S-SSMoE. Experiments on multiple complex acoustic datasets, including CHiME-6, DiPCo, Mixer 6 and DIHARD-III evaluation sets, demonstrate meaningful improvements in robustness and generalization. The proposed methods achieve state-of-the-art results, showcasing their effectiveness in challenging real-world scenarios. PEAKER diarization, which aims to determine the temporal boundaries of individual speakers within an audio stream and assign appropriate speaker identities, addresses the fundamental question of "who spoke when" [1]. It serves as a foundational component in numerous downstream speech-related tasks, including automatic meeting summarization, conversational analysis, and dialogue transcription [2].