We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including the following. We give an algorithm which, given positive definite $\mathbf{K} \in \mathbb{R}^{d \times d}$ with $\mathrm{nnz}(\mathbf{K})$ nonzero entries, computes an $\epsilon$-optimal diagonal preconditioner in time $\widetilde{O}(\mathrm{nnz}(\mathbf{K}) \cdot \mathrm{poly}(\kappa^\star,\epsilon^{-1}))$, where $\kappa^\star$ is the optimal condition number of the rescaled matrix. We give an algorithm which, given $\mathbf{M} \in \mathbb{R}^{d \times d}$ that is either the pseudoinverse of a graph Laplacian matrix or a constant spectral approximation of one, solves linear systems in $\mathbf{M}$ in $\widetilde{O}(d^2)$ time. Our diagonal preconditioning results improve state-of-the-art runtimes of $\Omega(d^{3.5})$ attained by general-purpose semidefinite programming, and our solvers improve state-of-the-art runtimes of $\Omega(d^{\omega})$ where $\omega > 2.3$ is the current matrix multiplication constant. We attain our results via new algorithms for a class of semidefinite programs (SDPs) we call matrix-dictionary approximation SDPs, which we leverage to solve an associated problem we call matrix-dictionary recovery.

Constrained submodular maximization is a fundamental problem at the heart of discrete optimization. The reason for this is as simple as it is clear: submodular functions capture the notion of diminishing returns present in a wide variety of real-world settings. Consequently to its striking importance and coinciding NP-hardness [20], extensive research has been conducted on submodular maximization since the seventies (e.g., [15, 42]), with focus lately shifting towards handling the massive datasets emerging in modern applications. With a wide variety of possible constraints, often regarding cardinality, independence in a matroid, or knapsacktype restrictions, the number of applications is vast. To name just a few, there are recent works on feature selection in machine learning [13, 14, 32], influence maximization in viral marketing [2, 31], and data summarization [43, 38, 45]. Many of these applications have non-monotone submodular objectives, meaning that adding an element to an existing set might actually decrease its value. Two such examples are discussed in detail in Section 5. This work was supported by the ERC Advanced Grant 788893 AMDROMA "Algorithmic and Mechanism Design Research in Online Markets" and the MIUR PRIN project ALGADIMAR "Algorithms, Games, and Digital Markets."

High-precision pose estimation based on visual markers has been a thriving research topic in the field of computer vision. However, the suitability of traditional flat markers on curved objects is limited due to the diverse shapes of curved surfaces, which hinders the development of high-precision pose estimation for curved objects. Therefore, this paper proposes a novel visual marker called CylinderTag, which is designed for developable curved surfaces such as cylindrical surfaces. CylinderTag is a cyclic marker that can be firmly attached to objects with a cylindrical shape. Leveraging the manifold assumption, the cross-ratio in projective invariance is utilized for encoding in the direction of zero curvature on the surface. Additionally, to facilitate the usage of CylinderTag, we propose a heuristic search-based marker generator and a high-performance recognizer as well. Moreover, an all-encompassing evaluation of CylinderTag properties is conducted by means of extensive experimentation, covering detection rate, detection speed, dictionary size, localization jitter, and pose estimation accuracy. CylinderTag showcases superior detection performance from varying view angles in comparison to traditional visual markers, accompanied by higher localization accuracy. Furthermore, CylinderTag boasts real-time detection capability and an extensive marker dictionary, offering enhanced versatility and practicality in a wide range of applications. Experimental results demonstrate that the CylinderTag is a highly promising visual marker for use on cylindrical-like surfaces, thus offering important guidance for future research on high-precision visual localization of cylinder-shaped objects. The code is available at: https://github.com/wsakobe/CylinderTag.

Software has eaten the world with many of the necessities and quality of life services people use requiring software. Therefore, tools that improve the software development experience can have a significant impact on the world such as generating code and test cases, detecting bugs, question and answering, etc. The success of Deep Learning (DL) over the past decade has shown huge advancements in automation across many domains, including Software Development processes. One of the main reasons behind this success is the availability of large datasets such as open-source code available through GitHub or image datasets of mobile Graphical User Interfaces (GUIs) with RICO [112] and ReDRAW [267] to be trained on. Therefore, the central research question my dissertation explores is: In what ways can the software development process be improved through leveraging DL techniques on the vast amounts of unstructured software engineering artifacts? We coin the approaches that leverage DL to automate or augment various software development task as Intelligent Software Tools.

It seems the usefulness of ChatGPT knows no bounds as even brewers are using the tool to make new beer. German brand Beck's is one of a number of companies to have turned to the clever AI chatbot to make a futuristic beverage, called Beck's Autonomous. ChatGPT not only came up with the beer's recipe but also its packaging, name, advertising campaign and even a design for the beer's website. Beck's is the first commercial brewery to work with ChatGPT, although other independent brew houses in North America have already done the same. MailOnline gave Beck's Autonomous a try to see how it compares with the brand's flagship lager.

This paper explores the application of emerging machine learning methods from image super-resolution (SR) to the task of statistical downscaling. We specifically focus on convolutional neural network-based Generative Adversarial Networks (GANs). Our GANs are conditioned on low-resolution (LR) inputs to generate high-resolution (HR) surface winds emulating Weather Research and Forecasting (WRF) model simulations over North America. Unlike traditional SR models, where LR inputs are idealized coarsened versions of the HR images, WRF emulation involves using non-idealized LR and HR pairs resulting in shared-scale mismatches due to internal variability. Our study builds upon current SR-based statistical downscaling by experimenting with a novel frequency-separation (FS) approach from the computer vision field. To assess the skill of SR models, we carefully select evaluation metrics, and focus on performance measures based on spatial power spectra. Our analyses reveal how GAN configurations influence spatial structures in the generated fields, particularly biases in spatial variability spectra. Using power spectra to evaluate the FS experiments reveals that successful applications of FS in computer vision do not translate to climate fields. However, the FS experiments demonstrate the sensitivity of power spectra to a commonly used GAN-based SR objective function, which helps interpret and understand its role in determining spatial structures. This result motivates the development of a novel partial frequency-separation scheme as a promising configuration option. We also quantify the influence on GAN performance of non-idealized LR fields resulting from internal variability. Furthermore, we conduct a spectra-based feature-importance experiment allowing us to explore the dependence of the spatial structure of generated fields on different physically relevant LR covariates.

In recent years, by utilizing optimization techniques to formulate the propagation of deep model, a variety of so-called Optimization-Derived Learning (ODL) approaches have been proposed to address diverse learning and vision tasks. Although having achieved relatively satisfying practical performance, there still exist fundamental issues in existing ODL methods. In particular, current ODL methods tend to consider model construction and learning as two separate phases, and thus fail to formulate their underlying coupling and depending relationship. In this work, we first establish a new framework, named Hierarchical ODL (HODL), to simultaneously investigate the intrinsic behaviors of optimization-derived model construction and its corresponding learning process. Then we rigorously prove the joint convergence of these two sub-tasks, from the perspectives of both approximation quality and stationary analysis. To our best knowledge, this is the first theoretical guarantee for these two coupled ODL components: optimization and learning. We further demonstrate the flexibility of our framework by applying HODL to challenging learning tasks, which have not been properly addressed by existing ODL methods. Finally, we conduct extensive experiments on both synthetic data and real applications in vision and other learning tasks to verify the theoretical properties and practical performance of HODL in various application scenarios.

Music Structure Analysis (MSA) is the task aiming at identifying musical segments that compose a music track and possibly label them based on their similarity. In this paper we propose a supervised approach for the task of music boundary detection. In our approach we simultaneously learn features and convolution kernels. For this we jointly optimize -- a loss based on the Self-Similarity-Matrix (SSM) obtained with the learned features, denoted by SSM-loss, and -- a loss based on the novelty score obtained applying the learned kernels to the estimated SSM, denoted by novelty-loss. We also demonstrate that relative feature learning, through self-attention, is beneficial for the task of MSA. Finally, we compare the performances of our approach to previously proposed approaches on the standard RWC-Pop, and various subsets of SALAMI.

We study the differential privacy (DP) of a core ML problem, linear ordinary least squares (OLS), a.k.a. $\ell_2$-regression. Our key result is that the approximate LS algorithm (ALS) (Sarlos, 2006), a randomized solution to the OLS problem primarily used to improve performance on large datasets, also preserves privacy. ALS achieves a better privacy/utility tradeoff, without modifications or further noising, when compared to alternative private OLS algorithms which modify and/or noise OLS. We give the first {\em tight} DP-analysis for the ALS algorithm and the standard Gaussian mechanism (Dwork et al., 2014) applied to OLS. Our methodology directly improves the privacy analysis of (Blocki et al., 2012) and (Sheffet, 2019)) and introduces new tools which may be of independent interest: (1) the exact spectrum of $(\epsilon, \delta)$-DP parameters (``DP spectrum") for mechanisms whose output is a $d$-dimensional Gaussian, and (2) an improved DP spectrum for random projection (compared to (Blocki et al., 2012) and (Sheffet, 2019)). All methods for private OLS (including ours) assume, often implicitly, restrictions on the input database, such as bounds on leverage and residuals. We prove that such restrictions are necessary. Hence, computing the privacy of mechanisms such as ALS must estimate these database parameters, which can be infeasible in big datasets. For more complex ML models, DP bounds may not even be tractable. There is a need for blackbox DP-estimators (Lu et al., 2022) which empirically estimate a data-dependent privacy. We demonstrate the effectiveness of such a DP-estimator by empirically recovering a DP-spectrum that matches our theory for OLS. This validates the DP-estimator in a nontrivial ML application, opening the door to its use in more complex nonlinear ML settings where theory is unavailable.

Real-world software applications must constantly evolve to remain relevant. This evolution occurs when developing new applications or adapting existing ones to meet new requirements, make corrections, or incorporate future functionality. Traditional methods of software quality control involve software quality models and continuous code inspection tools. These measures focus on directly assessing the quality of the software. However, there is a strong correlation and causation between the quality of the development process and the resulting software product. Therefore, improving the development process indirectly improves the software product, too. To achieve this, effective learning from past processes is necessary, often embraced through post mortem organizational learning. While qualitative evaluation of large artifacts is common, smaller quantitative changes captured by application lifecycle management are often overlooked. In addition to software metrics, these smaller changes can reveal complex phenomena related to project culture and management. Leveraging these changes can help detect and address such complex issues. Software evolution was previously measured by the size of changes, but the lack of consensus on a reliable and versatile quantification method prevents its use as a dependable metric. Different size classifications fail to reliably describe the nature of evolution. While application lifecycle management data is rich, identifying which artifacts can model detrimental managerial practices remains uncertain. Approaches such as simulation modeling, discrete events simulation, or Bayesian networks have only limited ability to exploit continuous-time process models of such phenomena. Even worse, the accessibility and mechanistic insight into such gray- or black-box models are typically very low. To address these challenges, we suggest leveraging objectively [...]