The management of modern IT systems poses unique challenges, necessitating scalability, reliability, and efficiency in handling extensive data streams. Traditional methods, reliant on manual tasks and rule-based approaches, prove inefficient for the substantial data volumes and alerts generated by IT systems. Artificial Intelligence for Operating Systems (AIOps) has emerged as a solution, leveraging advanced analytics like machine learning and big data to enhance incident management. AIOps detects and predicts incidents, identifies root causes, and automates healing actions, improving quality and reducing operational costs. However, despite its potential, the AIOps domain is still in its early stages, decentralized across multiple sectors, and lacking standardized conventions. Research and industrial contributions are distributed without consistent frameworks for data management, target problems, implementation details, requirements, and capabilities. This study proposes an AIOps terminology and taxonomy, establishing a structured incident management procedure and providing guidelines for constructing an AIOps framework. The research also categorizes contributions based on criteria such as incident management tasks, application areas, data sources, and technical approaches. The goal is to provide a comprehensive review of technical and research aspects in AIOps for incident management, aiming to structure knowledge, identify gaps, and establish a foundation for future developments in the field.

Stochastic gradient descent (SGD), which dates back to the work by Robbins and Monro Robbins and Monro [1951a] is widely observed in training modern Deep Neural Networks (DNNs), which are widely used to achieve state-of-the-art results in multiple problem domains like image classification problems Krizhevsky et al. [2017, 2009], object detection Redmon and Farhadi [2017], and classification automatic machine translation Zhang et al. [2015]. The value of the step size (or learning rate) is crucial for the convergence rate of SGD. Selecting an appropriate step size value in each iteration ensures that SGD iterations converge to an optimal solution. If the step size value is too large, it may prevent SGD iterations from reaching the optimal point. Conversely, excessively small step size values can lead to slow convergence or mistakenly identify a local minimum as the optimal solution Mishra and Sarawadekar [2019]. To address these challenges, various schemes have been proposed. One popular approach is the Armijo line search method, initially introduced for SGD by Vaswani et al. Vaswani et al. [2019], which provides theoretical results for strong-convex, convex, and non-convex objective functions.

We study the problem of distributed and rate-adaptive feature compression for linear regression. A set of distributed sensors collect disjoint features of regressor data. A fusion center is assumed to contain a pretrained linear regression model, trained on a dataset of the entire uncompressed data. At inference time, the sensors compress their observations and send them to the fusion center through communication-constrained channels, whose rates can change with time. Our goal is to design a feature compression {scheme} that can adapt to the varying communication constraints, while maximizing the inference performance at the fusion center. We first obtain the form of optimal quantizers assuming knowledge of underlying regressor data distribution. Under a practically reasonable approximation, we then propose a distributed compression scheme which works by quantizing a one-dimensional projection of the sensor data. We also propose a simple adaptive scheme for handling changes in communication constraints. We demonstrate the effectiveness of the distributed adaptive compression scheme through simulated experiments.

Machine learning methods often assume that the test data have the same distribution as the training data. However, this assumption may not hold due to multiple levels of heterogeneity in applications, raising issues in algorithmic fairness and domain generalization. In this work, we address the problem of fair and generalizable machine learning by invariant principles. We propose a training environment-based oracle, FAIRM, which has desirable fairness and domain generalization properties under a diversity-type condition. We then provide an empirical FAIRM with finite-sample theoretical guarantees under weak distributional assumptions. We then develop efficient algorithms to realize FAIRM in linear models and demonstrate the nonasymptotic performance with minimax optimality. We evaluate our method in numerical experiments with synthetic data and MNIST data and show that it outperforms its counterparts.

Multimodal representation learning techniques typically rely on paired samples to learn common representations, but paired samples are challenging to collect in fields such as biology where measurement devices often destroy the samples. This paper presents an approach to address the challenge of aligning unpaired samples across disparate modalities in multimodal representation learning. We draw an analogy between potential outcomes in causal inference and potential views in multimodal observations, which allows us to use Rubin's framework to estimate a common space in which to match samples. Our approach assumes we collect samples that are experimentally perturbed by treatments, and uses this to estimate a propensity score from each modality, which encapsulates all shared information between a latent state and treatment and can be used to define a distance between samples. We experiment with two alignment techniques that leverage this distance -- shared nearest neighbours (SNN) and optimal transport (OT) matching -- and find that OT matching results in significant improvements over state-of-the-art alignment approaches in both a synthetic multi-modal setting and in real-world data from NeurIPS Multimodal Single-Cell Integration Challenge.

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine the sign of the optimal regularization level under covariate and regression shifts. These conditions capture the alignment between the covariance and signal structures in the train and test data and reveal stark differences compared to the in-distribution setting. For example, a negative regularization level can be optimal under covariate shift or regression shift, even when the training features are isotropic or the design is underparameterized. Furthermore, we prove that the optimally-tuned risk is monotonic in the data aspect ratio, even in the out-of-distribution setting and when optimizing over negative regularization levels. In general, our results do not make any modeling assumptions for the train or the test distributions, except for moment bounds, and allow for arbitrary shifts and the widest possible range of (negative) regularization levels.

It is often important to detect nodes of novel categories under such distribution shifts for safety or insight discovery purposes. We introduce a new approach, Recall-Constrained Optimization with Selective Link Prediction (RECO-SLIP), to detect nodes belonging to novel categories in attributed graphs under subpopulation shifts. By integrating a recall-constrained learning framework with a sample-efficient link prediction mechanism, RECO-SLIP addresses the dual challenges of resilience against subpopulation shifts and the effective exploitation of graph structure. Our extensive empirical evaluation across multiple graph datasets demonstrates the superior performance of RECO-SLIP over existing methods.

The main challenge that sets transfer learning apart from traditional supervised learning is the distribution shift, reflected as the shift between the source and target models and that between the marginal covariate distributions. In this work, we tackle model shifts in the presence of covariate shifts in the high-dimensional regression setting. Specifically, we propose a two-step method with a novel fused-regularizer that effectively leverages samples from source tasks to improve the learning performance on a target task with limited samples. Nonasymptotic bound is provided for the estimation error of the target model, showing the robustness of the proposed method to covariate shifts. We further establish conditions under which the estimator is minimax-optimal. Additionally, we extend the method to a distributed setting, allowing for a pretraining-finetuning strategy, requiring just one round of communication while retaining the estimation rate of the centralized version. Numerical tests validate our theory, highlighting the method's robustness to covariate shifts.

Linear models are ubiquitous in data science, but are particularly prone to overfitting and data memorization in high dimensions. To guarantee the privacy of training data, differential privacy can be used. Many papers have proposed optimization techniques for high-dimensional differentially private linear models, but a systematic comparison between these methods does not exist. We close this gap by providing a comprehensive review of optimization methods for private high-dimensional linear models. Empirical tests on all methods demonstrate robust and coordinate-optimized algorithms perform best, which can inform future research. Code for implementing all methods is released online.

We study non-parametric frequency-domain system identification from a finite-sample perspective. We assume an open loop scenario where the excitation input is periodic and consider the Empirical Transfer Function Estimate (ETFE), where the goal is to estimate the frequency response at certain desired (evenly-spaced) frequencies, given input-output samples. We show that under sub-Gaussian colored noise (in time-domain) and stability assumptions, the ETFE estimates are concentrated around the true values. The error rate is of the order of $\mathcal{O}((d_{\mathrm{u}}+\sqrt{d_{\mathrm{u}}d_{\mathrm{y}}})\sqrt{M/N_{\mathrm{tot}}})$, where $N_{\mathrm{tot}}$ is the total number of samples, $M$ is the number of desired frequencies, and $d_{\mathrm{u}},\,d_{\mathrm{y}}$ are the dimensions of the input and output signals respectively. This rate remains valid for general irrational transfer functions and does not require a finite order state-space representation. By tuning $M$, we obtain a $N_{\mathrm{tot}}^{-1/3}$ finite-sample rate for learning the frequency response over all frequencies in the $ \mathcal{H}_{\infty}$ norm. Our result draws upon an extension of the Hanson-Wright inequality to semi-infinite matrices. We study the finite-sample behavior of ETFE in simulations.