We initiate the study of differentially private learning in the proportional dimensionality regime, in which the number of data samples $n$ and problem dimension $d$ approach infinity at rates proportional to one another, meaning that $d / n \to \delta$ as $n \to \infty$ for an arbitrary, given constant $\delta \in (0, \infty)$. This setting is significantly more challenging than that of all prior theoretical work in high-dimensional differentially private learning, which, despite the name, has assumed that $\delta = 0$ or is sufficiently small for problems of sample complexity $O(d)$, a regime typically considered "low-dimensional" or "classical" by modern standards in high-dimensional statistics. We provide sharp theoretical estimates of the error of several well-studied differentially private algorithms for robust linear regression and logistic regression, including output perturbation, objective perturbation, and noisy stochastic gradient descent, in the proportional dimensionality regime. The $1 + o(1)$ factor precision of our error estimates enables a far more nuanced understanding of the price of privacy of these algorithms than that afforded by existing, coarser analyses, which are essentially vacuous in the regime we consider. We incorporate several probabilistic tools that have not previously been used to analyze differentially private learning algorithms, such as a modern Gaussian comparison inequality and recent universality laws with origins in statistical physics.

In the measurement-constrained problems, despite the availability of large datasets, we may be only affordable to observe the labels on a small portion of the large dataset. This poses a critical question that which data points are most beneficial to label given a budget constraint. In this paper, we focus on the estimation of the optimal individualized threshold in a measurement-constrained M-estimation framework. Our goal is to estimate a high-dimensional parameter $\theta$ in a linear threshold $\theta^T Z$ for a continuous variable $X$ such that the discrepancy between whether $X$ exceeds the threshold $\theta^T Z$ and a binary outcome $Y$ is minimized. We propose a novel $K$-step active subsampling algorithm to estimate $\theta$, which iteratively samples the most informative observations and solves a regularized M-estimator. The theoretical properties of our estimator demonstrate a phase transition phenomenon with respect to $\beta\geq 1$, the smoothness of the conditional density of $X$ given $Y$ and $Z$. For $\beta>(1+\sqrt{3})/2$, we show that the two-step algorithm yields an estimator with the parametric convergence rate $O_p((s \log d /N)^{1/2})$ in $l_2$ norm. The rate of our estimator is strictly faster than the minimax optimal rate with $N$ i.i.d. samples drawn from the population. For the other two scenarios $1<\beta\leq (1+\sqrt{3})/2$ and $\beta=1$, the estimator from the two-step algorithm is sub-optimal. The former requires to run $K>2$ steps to attain the same parametric rate, whereas in the latter case only a near parametric rate can be obtained. Furthermore, we formulate a minimax framework for the measurement-constrained M-estimation problem and prove that our estimator is minimax rate optimal up to a logarithmic factor. Finally, we demonstrate the performance of our method in simulation studies and apply the method to analyze a large diabetes dataset.

Predicting Sea Surface Temperature (SST) in the Great Barrier Reef (GBR) region is crucial for the effective management of its fragile ecosystems. This study provides a rigorous comparative analysis of several machine learning techniques to identify the most effective method for SST prediction in this area. We evaluate the performance of ridge regression, Least Absolute Shrinkage and Selection Operator (LASSO), Random Forest, and Extreme Gradient Boosting (XGBoost) algorithms. Our results reveal that while LASSO and ridge regression perform well, Random Forest and XGBoost significantly outperform them in terms of predictive accuracy, as evidenced by lower Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Prediction Error (RMSPE). Additionally, XGBoost demonstrated superior performance in minimizing Kullback- Leibler Divergence (KLD), indicating a closer alignment of predicted probability distributions with actual observations. These findings highlight the efficacy of using ensemble methods, particularly XGBoost, for predicting sea surface temperatures, making them valuable tools for climatological and environmental modeling.

Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still struggle to generalise well beyond datasets that exhibit strong homophily, where nodes of the same class tend to connect. This limitation has led to the development of complex neural architectures that pose challenges in terms of efficiency and scalability. In response to these limitations, we focus on simpler and more scalable approaches and introduce Graph-aware Logistic Regression (GLR), a non-neural model designed for node classification tasks. Unlike traditional graph algorithms that use only a fraction of the information accessible to GNNs, our proposed model simultaneously leverages both node features and the relationships between entities. However instead of relying on message passing, our approach encodes each node's relationships as an additional feature vector, which is then combined with the node's self attributes. Extensive experimental results, conducted within a rigorous evaluation framework, show that our proposed GLR approach outperforms both foundational and sophisticated state-of-the-art GNN models in node classification tasks. Going beyond the traditional limited benchmarks, our experiments indicate that GLR increases generalisation ability while reaching performance gains in computation time up to two orders of magnitude compared to it best neural competitor.

We consider estimation of a linear functional of the treatment effect using adaptively collected data. This task finds a variety of applications including the off-policy evaluation (\textsf{OPE}) in contextual bandits, and estimation of the average treatment effect (\textsf{ATE}) in causal inference. While a certain class of augmented inverse propensity weighting (\textsf{AIPW}) estimators enjoys desirable asymptotic properties including the semi-parametric efficiency, much less is known about their non-asymptotic theory with adaptively collected data. To fill in the gap, we first establish generic upper bounds on the mean-squared error of the class of AIPW estimators that crucially depends on a sequentially weighted error between the treatment effect and its estimates. Motivated by this, we also propose a general reduction scheme that allows one to produce a sequence of estimates for the treatment effect via online learning to minimize the sequentially weighted estimation error. To illustrate this, we provide three concrete instantiations in (\romannumeral 1) the tabular case; (\romannumeral 2) the case of linear function approximation; and (\romannumeral 3) the case of general function approximation for the outcome model. We then provide a local minimax lower bound to show the instance-dependent optimality of the \textsf{AIPW} estimator using no-regret online learning algorithms.

Continually evaluating large generative models provides a unique challenge. Often, human annotations are necessary to evaluate high-level properties of these models (e.g. in text or images). However, collecting human annotations of samples can be resource intensive, and using other machine learning systems to provide the annotations, or automatic evaluation, can introduce systematic errors into the evaluation. The Prediction Powered Inference (PPI) framework provides a way of leveraging both the statistical power of automatic evaluation and a small pool of labelled data to produce a low-variance, unbiased estimate of the quantity being evaluated for. However, most work on PPI considers a relatively sizable set of labelled samples, which is not always practical to obtain. To this end, we present two new PPI-based techniques that leverage robust regressors to produce even lower variance estimators in the few-label regime.

The paper describes a system designed by Advacheck team to recognise machine-generated and human-written texts in the monolingual subtask of GenAI Detection Task 1 competition. Our developed system is a multi-task architecture with shared Transformer Encoder between several classification heads. One head is responsible for binary classification between human-written and machine-generated texts, while the other heads are auxiliary multiclass classifiers for texts of different domains from particular datasets. As multiclass heads were trained to distinguish the domains presented in the data, they provide a better understanding of the samples. This approach led us to achieve the first place in the official ranking with 83.07% macro F1-score on the test set and bypass the baseline by 10%. We further study obtained system through ablation, error and representation analyses, finding that multi-task learning outperforms single-task mode and simultaneous tasks form a cluster structure in embeddings space.

Linear regression is often deemed inherently interpretable; however, challenges arise for high-dimensional data. We focus on further understanding how linear regression approximates nonlinear responses from high-dimensional functional data, motivated by predicting cycle life for lithium-ion batteries. We develop a linearization method to derive feature coefficients, which we compare with the closest regression coefficients of the path of regression solutions. We showcase the methods on battery data case studies where a single nonlinear compressing feature, $g\colon \mathbb{R}^p \to \mathbb{R}$, is used to construct a synthetic response, $\mathbf{y} \in \mathbb{R}$. This unifying view of linear regression and compressing features for high-dimensional functional data helps to understand (1) how regression coefficients are shaped in the highly regularized domain and how they relate to linearized feature coefficients and (2) how the shape of regression coefficients changes as a function of regularization to approximate nonlinear responses by exploiting local structures.

This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty quantification guarantees for machine learning systems. Much of the current interest in conformal prediction is due to its ability to integrate into complex machine learning workflows, solving the problem of forming prediction sets without any assumptions on the form of the data generating distribution. Since contemporary machine learning algorithms have generally proven difficult to analyze directly, conformal prediction's main appeal is its ability to provide formal, finite-sample guarantees when paired with such methods. The goal of this book is to teach the reader about the fundamental technical arguments that arise when researching conformal prediction and related questions in distribution-free inference. Many of these proof strategies, especially the more recent ones, are scattered among research papers, making it difficult for researchers to understand where to look, which results are important, and how exactly the proofs work. We hope to bridge this gap by curating what we believe to be some of the most important results in the literature and presenting their proofs in a unified language, with illustrations, and with an eye towards pedagogy.

Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works [Bhattacharyya et al.: SICOMP 2023, Daskalakis et al.: STOC 2021, Choo et al.: ALT 2024] focus on discrete distributions, the current work addresses the tree structure learning problem for Gaussian distributions, providing efficient algorithms with solid theoretical guarantees. This is crucial as real-world distributions are often continuous and differ from the discrete scenarios studied in prior works. In this work, we design a conditional mutual information tester for Gaussian random variables that can test whether two Gaussian random variables are independent, or their conditional mutual information is at least $\varepsilon$, for some parameter $\varepsilon \in (0,1)$ using $\mathcal{O}(\varepsilon^{-1})$ samples which we show to be near-optimal. In contrast, an additive estimation would require $\Omega(\varepsilon^{-2})$ samples. Our upper bound technique uses linear regression on a pair of suitably transformed random variables. Importantly, we show that the chain rule of conditional mutual information continues to hold for the estimated (conditional) mutual information. As an application of such a mutual information tester, we give an efficient $\varepsilon$-approximate structure-learning algorithm for an $n$-variate Gaussian tree model that takes $\widetilde{\Theta}(n\varepsilon^{-1})$ samples which we again show to be near-optimal. In contrast, when the underlying Gaussian model is not known to be tree-structured, we show that $\widetilde{{{\Theta}}}(n^2\varepsilon^{-2})$ samples are necessary and sufficient to output an $\varepsilon$-approximate tree structure. We perform extensive experiments that corroborate our theoretical convergence bounds.