This paper investigates group distributionally robust optimization (GDRO), with the purpose to learn a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem, and demonstrate that stochastic mirror descent (SMD), using $m$ samples in each iteration, achieves an $O(m (\log m)/\epsilon^2)$ sample complexity for finding an $\epsilon$-optimal solution, which matches the $\Omega(m/\epsilon^2)$ lower bound up to a logarithmic factor. Then, we make use of techniques from online learning to reduce the number of samples required in each round from $m$ to $1$, keeping the same sample complexity. Specifically, we cast GDRO as a two-players game where one player simply performs SMD and the other executes an online algorithm for non-oblivious multi-armed bandits. Next, we consider a more practical scenario where the number of samples that can be drawn from each distribution is different, and propose a novel formulation of weighted GDRO, which allows us to derive distribution-dependent convergence rates. Denote by $n_i$ the sample budget for the $i$-th distribution, and assume $n_1 \geq n_2 \geq \cdots \geq n_m$. In the first approach, we incorporate non-uniform sampling into SMD such that the sample budget is satisfied in expectation, and prove that the excess risk of the $i$-th distribution decreases at an $O(\sqrt{n_1 \log m}/n_i)$ rate. In the second approach, we use mini-batches to meet the budget exactly and also reduce the variance in stochastic gradients, and then leverage stochastic mirror-prox algorithm, which can exploit small variances, to optimize a carefully designed weighted GDRO problem. Under appropriate conditions, it attains an $O((\log m)/\sqrt{n_i})$ convergence rate, which almost matches the optimal $O(\sqrt{1/n_i})$ rate of only learning from the $i$-th distribution with $n_i$ samples.

The distribution shifts between training and test data typically undermine the performance of models. In recent years, lots of work pays attention to domain generalization (DG) where distribution shifts exist, and target data are unseen. Despite the progress in algorithm design, two foundational factors have long been ignored: 1) the optimization for regularization-based objectives, and 2) the model selection for DG since no knowledge about the target domain can be utilized. In this paper, we propose Mixup guided optimization and selection techniques for DG. For optimization, we utilize an adapted Mixup to generate an out-of-distribution dataset that can guide the preference direction and optimize with Pareto optimization. For model selection, we generate a validation dataset with a closer distance to the target distribution, and thereby it can better represent the target data. We also present some theoretical insights behind our proposals. Comprehensive experiments demonstrate that our model optimization and selection techniques can largely improve the performance of existing domain generalization algorithms and even achieve new state-of-the-art results.

We present a new method that includes three key components of distributed optimization and federated learning: variance reduction of stochastic gradients, partial participation, and compressed communication. We prove that the new method has optimal oracle complexity and state-of-the-art communication complexity in the partial participation setting. Regardless of the communication compression feature, our method successfully combines variance reduction and partial participation: we get the optimal oracle complexity, never need the participation of all nodes, and do not require the bounded gradients (dissimilarity) assumption.

This document outlines some of the common mistakes that occur when using machine learning, and what can be done to avoid them. Whilst it should be accessible to anyone with a basic understanding of machine learning techniques, it was originally written for research students, and focuses on issues that are of particular concern within academic research, such as the need to do rigorous comparisons and reach valid conclusions. It covers five stages of the machine learning process: what to do before model building, how to reliably build models, how to robustly evaluate models, how to compare models fairly, and how to report results.

With growing concerns regarding bias and discrimination in predictive models, the AI community has increasingly focused on assessing AI system trustworthiness. Conventionally, trustworthy AI literature relies on the probabilistic framework and calibration as prerequisites for trustworthiness. In this work, we depart from this viewpoint by proposing a novel trust framework inspired by the philosophy literature on trust. We present a precise mathematical definition of trustworthiness, termed $\mathcal{U}$-trustworthiness, specifically tailored for a subset of tasks aimed at maximizing a utility function. We argue that a model's $\mathcal{U}$-trustworthiness is contingent upon its ability to maximize Bayes utility within this task subset. Our first set of results challenges the probabilistic framework by demonstrating its potential to favor less trustworthy models and introduce the risk of misleading trustworthiness assessments. Within the context of $\mathcal{U}$-trustworthiness, we prove that properly-ranked models are inherently $\mathcal{U}$-trustworthy. Furthermore, we advocate for the adoption of the AUC metric as the preferred measure of trustworthiness. By offering both theoretical guarantees and experimental validation, AUC enables robust evaluation of trustworthiness, thereby enhancing model selection and hyperparameter tuning to yield more trustworthy outcomes.

The current paradigm of training deep neural networks for classification tasks includes minimizing the empirical risk that pushes the training loss value towards zero, even after the training error has been vanished. In this terminal phase of training, it has been observed that the last-layer features collapse to their class-means and these class-means converge to the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is termed as Neural Collapse (NC). To theoretically understand this phenomenon, recent works employ a simplified unconstrained feature model to prove that NC emerges at the global solutions of the training problem. However, when the training dataset is class-imbalanced, some NC properties will no longer be true. For example, the class-means geometry will skew away from the simplex ETF when the loss converges. In this paper, we generalize NC to imbalanced regime for cross-entropy loss under the unconstrained ReLU feature model. We prove that, while the within-class features collapse property still holds in this setting, the class-means will converge to a structure consisting of orthogonal vectors with different lengths. Furthermore, we find that the classifier weights are aligned to the scaled and centered class-means with scaling factors depend on the number of training samples of each class, which generalizes NC in the class-balanced setting. We empirically prove our results through experiments on practical architectures and dataset.

Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the performance of Bayesian optimization is assessed by regret-based metrics such as instantaneous, simple, and cumulative regrets. These metrics only rely on function evaluations, so that they do not consider geometric relationships between query points and global solutions, or query points themselves. Notably, they cannot discriminate if multiple global solutions are successfully found. Moreover, they do not evaluate Bayesian optimization's abilities to exploit and explore a search space given. To tackle these issues, we propose four new geometric metrics, i.e., precision, recall, average degree, and average distance. These metrics allow us to compare Bayesian optimization algorithms considering the geometry of both query points and global optima, or query points. However, they are accompanied by an extra parameter, which needs to be carefully determined. We therefore devise the parameter-free forms of the respective metrics by integrating out the additional parameter. Finally, we empirically validate that our proposed metrics can provide more convincing interpretation and understanding of Bayesian optimization algorithms from distinct perspectives, compared to the conventional metrics.

Large scale analytics engines have become a core dependency for modern data-driven enterprises to derive business insights and drive actions. These engines support a large number of analytic jobs processing huge volumes of data on a daily basis, and workloads are often inundated with overlapping computations across multiple jobs. Reusing common computation is crucial for efficient cluster resource utilization and reducing job execution time. Detecting common computation is the first and key step for reducing this computational redundancy. However, detecting equivalence on large-scale analytics engines requires efficient and scalable solutions that are fully automated. In addition, to maximize computation reuse, equivalence needs to be detected at the semantic level instead of just the syntactic level (i.e., the ability to detect semantic equivalence of seemingly different-looking queries). Unfortunately, existing solutions fall short of satisfying these requirements. In this paper, we take a major step towards filling this gap by proposing GEqO, a portable and lightweight machine-learning-based framework for efficiently identifying semantically equivalent computations at scale. GEqO introduces two machine-learning-based filters that quickly prune out nonequivalent subexpressions and employs a semi-supervised learning feedback loop to iteratively improve its model with an intelligent sampling mechanism. Further, with its novel database-agnostic featurization method, GEqO can transfer the learning from one workload and database to another. Our extensive empirical evaluation shows that, on TPC-DS-like queries, GEqO yields significant performance gains-up to 200x faster than automated verifiers-and finds up to 2x more equivalences than optimizer and signature-based equivalence detection approaches.

This work, in a pioneering approach, attempts to build a biometric system that works purely based on the fluid mechanics governing exhaled breath. We test the hypothesis that the structure of turbulence in exhaled human breath can be exploited to build biometric algorithms. This work relies on the idea that the extrathoracic airway is unique for every individual, making the exhaled breath a biomarker. Methods including classical multi-dimensional hypothesis testing approach and machine learning models are employed in building user authentication algorithms, namely user confirmation and user identification. A user confirmation algorithm tries to verify whether a user is the person they claim to be. A user identification algorithm tries to identify a user's identity with no prior information available. A dataset of exhaled breath time series samples from 94 human subjects was used to evaluate the performance of these algorithms. The user confirmation algorithms performed exceedingly well for the given dataset with over $97\%$ true confirmation rate. The machine learning based algorithm achieved a good true confirmation rate, reiterating our understanding of why machine learning based algorithms typically outperform classical hypothesis test based algorithms. The user identification algorithm performs reasonably well with the provided dataset with over $50\%$ of the users identified as being within two possible suspects. We show surprisingly unique turbulent signatures in the exhaled breath that have not been discovered before. In addition to discussions on a novel biometric system, we make arguments to utilise this idea as a tool to gain insights into the morphometric variation of extrathoracic airway across individuals. Such tools are expected to have future potential in the area of personalised medicines.

Causal inference is a crucial goal of science, enabling researchers to arrive at meaningful conclusions regarding the predictions of hypothetical interventions using observational data. Path models, Structural Equation Models (SEMs), and, more generally, Directed Acyclic Graphs (DAGs), provide a means to unambiguously specify assumptions regarding the causal structure underlying a phenomenon. Unlike DAGs, which make very few assumptions about the functional and parametric form, SEM assumes linearity. This can result in functional misspecification which prevents researchers from undertaking reliable effect size estimation. In contrast, we propose Super Learner Equation Modeling, a path modeling technique integrating machine learning Super Learner ensembles. We empirically demonstrate its ability to provide consistent and unbiased estimates of causal effects, its competitive performance for linear models when compared with SEM, and highlight its superiority over SEM when dealing with non-linear relationships. We provide open-source code, and a tutorial notebook with example usage, accentuating the easy-to-use nature of the method.